Question 11 Mark
Identify constant, linear, quadratic, cubic and quadrtic polynomials from the following: $1 - y - y^3$
Answer$1 - y - y^3$ is a polynomial with degree $3.$ So, it is a cubic polynomial.
View full question & answer→Question 21 Mark
Which of the following expressions are polynomials? In case of a polynomial, write its degree.
1
AnswerClearly, 1 is a constant polynomial of degree 0.
View full question & answer→Question 31 Mark
Which of the following expressions are polynomials? In case of a polynomial, write its degree.
$\frac{1}{2\text{x}^2}$
Answer$\frac{1}{2\text{x}^2}=\frac{1}{2}\text{x}^{-2}$ is an expression having negative power of x. So, it is not a polynomial.
View full question & answer→Question 41 Mark
Determine the degree of the following polynomials.
$-\frac{1}{2}\text{x}+3$
Answer$-\frac{1}{2}\text{x}+3$
Here, the highest power of x is 1. So, the degree of the polynomial is 1.
View full question & answer→Question 51 Mark
Find the zero of the polynomial:q(x) = 4x
Answerq(x) = 0
⇒ 4x = 0
⇒ x = 0
Hence, 0 is the zero of the polynomial q(x).
View full question & answer→Question 61 Mark
Determine the degree of the following polynomials. $x^{-2}(x^4 + x^2)$
Answer$x^{-2}(x^4 + x^2) = x^2 + x^0 = x^2 + 1$
Here, the highest power of $x$ is $2$. So, the degree of the polynomial is $2.$
View full question & answer→Question 71 Mark
Determine the degree of the following polynomials. $y^2(y - y^3)$
Answer$y^2(y - y^3) = y^y - y^5$
Here, the highest power of $y$ is $5$. So, the degree of the polynomial is $5.$
View full question & answer→Question 81 Mark
Identify constant, linear, quadratic, cubic and quadrtic polynomials from the following:
-p
Answer-p is a polynomial with degree 1. So, it is a linear polynomial.
View full question & answer→Question 91 Mark
Which of the following expressions are polynomials? In case of a polynomial, write its degree.
$2\text{x}^3+3\text{x}^2+\sqrt{\text{x}}-1$
Answer $2\text{x}^3+3\text{x}^2+\sqrt{\text{x}}-1$ $=2\text{x}^3+3\text{x}^2+\text{x}^\frac{1}{2}-1$In this expression, one of the powers of x is $\frac{1}{2}$ which is a fraction. Since it is an expression having fractional power of x, so, it is not a polynomial.
View full question & answer→Question 101 Mark
Find the zero of the polynomial:
$\text{p}(\text{x})=\text{ax},\ \text{a}\neq0$
Answer $\text{p}(\text{x})=0$$\Rightarrow\text{ax}+\text{b}=0$
$\Rightarrow\text{x}=-\frac{\text{b}}{\text{a}}$
Hence, $-\frac{\text{b}}{\text{a}}$ is the zero of the polynomial p(x).
View full question & answer→Question 111 Mark
Which of the following expressions are polynomials? In case of a polynomial, write its degree.
$\text{x}^5-2\text{x}^3+\text{x}+\sqrt3$
Answer$\text{x}^5-2\text{x}^3+\text{x}+\sqrt3$ is an expression having only non-negative integral powers of x. So, it is a polynomial. Also, the highest power of x is 5, so, it is polynimial of degree 5.
View full question & answer→Question 121 Mark
Write:
The cofficient of x in $\sqrt3-2\sqrt2\text{x}+6\text{x}^2.$
AnswerThe cofficient of x in $\sqrt3-2\sqrt2\text{x}+6\text{x}^2$ is $-2\sqrt2.$
View full question & answer→Question 131 Mark
Which of the following expressions are polynomials? In case of a polynomial, write its degree.
$\text{x}^{100}-1$
Answer$\text{x}^{100}-1$ is an expression having only non-negative integral powers of x. So, it is a polynomial. Also, the highest power of x is 100, so, it is polynimial of degree 100.
View full question & answer→Question 141 Mark
Identify constant, linear, quadratic, cubic and quadrtic polynomials from the following:
-7 + x
Answer-7 + x is a polynomial with degree 1. So, it is a linear polynomial.
View full question & answer→Question 151 Mark
Rewrite the following polynomial in standard form.
$\frac{2}{3}+4\text{y}^2-3\text{y}+2\text{y}^3$
Answer$\frac{2}{3}-3\text{y}+4\text{y}^2+2\text{y}^3$ is a polynomial in standard form as the powers of y are in ascending order.
View full question & answer→Question 161 Mark
Which of the following expressions are polynomials? In case of a polynomial, write its degree.
$\frac{\text{x}^2}{2}-\frac{2}{\text{x}^2}$
Answer$\frac{\text{x}^2}{2}-\frac{2}{\text{x}^2}=\frac{\text{x}^2}{2}-2\text{x}^{-2}$
This is an expression having negative integral power of x i.e. -2. So, it is not a polynomial.
View full question & answer→Question 171 Mark
Determine the degree of the following polynomials. $(3x - 2)(2x^3 + 3x^2)$
Answer$(3x - 2)(2x^3 + 3x^2)$
$= 6x^4 + 9x^3 - 4x^3 - 6x^2$
$= 6x^4 + 5x^3 - 6x^2$
Here, the highest power of $x$ is $4.$ So, the degree of the polynomial is $4.$
View full question & answer→Question 181 Mark
Which of the following expressions are polynomials? In case of a polynomial, write its degree.
$\text{x}^{-2}+2\text{x}^{-1}+3$
Answer$\text{x}^{-2}+2\text{x}^{-1}+3$ is an expression having negative integral powers of x. So, it is not a polynomial.
View full question & answer→Question 191 Mark
Find the zero of the polynomial:
f(x) = 3x + 1
Answerf(x) = 0
⇒ 3x + 1 = 0
$\Rightarrow\text{x}=-\frac{1}{3}$
Hence, $-\frac{1}{3}$ is the zero of the polynomial f(x).
View full question & answer→Question 201 Mark
Verify that:
4 is a zero of the polynomial, p(x) = x - 4.
Answerp(x) = x - 4
⇒ p(4) = 4 - 4
= 0
Hence, 4 is the zero of the given polynomial.
View full question & answer→Question 211 Mark
Write: The cofficient of $x^2$ in $2x - 3 + x^3.$
Answer$2x - 3 + x^3 = -3 + 2x + 0x^2 + x^3.$
The cofficient of $x^2$ in $2x - 3 + x^3$ is $0.$
View full question & answer→Question 221 Mark
Verify that:
$\frac{-1}{2}$ is a zero of the polynomial, g(y) = 2y + 1.
Answer$\text{p}(\text{y}) = 2\text{y}+ 1$
$\Rightarrow\text{p}\Big(-\frac{1}{2}\Big)=2\times\Big(-\frac{1}{2}\Big)+1$
$=-1+1$
$=0$
Hence, $-\frac{1}{2}$ is the zero of the given polynomial.
View full question & answer→Question 231 Mark
Write:
The constant term in $\frac{\pi}{2}\text{x}^2+7\text{x}-\frac{2}{5}\pi.$
AnswerThe constant term in $\frac{\pi}{2}\text{x}^2+7\text{x}-\frac{2}{5}\pi$ is $-\frac{2}{5}\pi.$
View full question & answer→Question 241 Mark
Which of the following expressions are polynomials? In case of a polynomial, write its degree.
$\sqrt[3]{2}\text{x}^2-8$
Answer$\sqrt[3]{2}\text{x}^2-8$ is an expression having only non-negative power of x. So, it is a polynomial. Also, the highest power of x is 2, so, it is a polynomial of degree 2.
View full question & answer→Question 251 Mark
If $p(x) = x^3 - 5x^2 + 4x - 3$ and $g(x) = x - 2,$ show that $p(x)$ is not a multiple of $g(x).$
Answer$p(x)$ is a multiple of $g(x)$ or not
$\because g(x) = x - 2 [$given$]$
Then, zero of $g(x)$ is $2.$
Now,
$p(2) = (2)^3 - 5(2)^2 + 4(2) - 3 \big[\because p(x) = x^3 - 5x^2 + 4x - 3,$ given$\big]$
$= 8 - 20 + 8 - 3$
$=7\neq0$
Since, remainder $\neq0,$ so $p(x)$ is not a multiple of $g(x).$
View full question & answer→Question 261 Mark
Which of the following expressions are polynomials? In case of a polynomial, write its degree.
$\text{t}^2-\frac{2}{5}\text{t}+\sqrt{5}$
Answer$\text{t}^2-\frac{2}{5}\text{t}+\sqrt{5}$ is an expression having only non-negative integral powers of t. So, it is a polynomial. Also, the highest power of t is 2, so, it is polynimial of degree 2.
View full question & answer→Question 271 Mark
Verify that:
$\frac{2}{5}$ is a zero of the polynomial, f(x) = 2 - 5x.
Answer$\text{f}(\text{x}) = 2 - 5\text{x}$
$\Rightarrow\Big(\frac{2}{5}\Big)=2-5\times\Big(\frac{2}{5}\Big)$
$=2-2$
$=0$
Hence, $\frac{2}{5}$ is the zero of the given polynomial.
View full question & answer→Question 281 Mark
Find the zero of the polynomial:
g(x) = 5 - 4x
Answerg(x) = 0
⇒ 5 - 4x = 0
$\Rightarrow\text{x}=\frac{5}{4}$
Hence, $\frac{5}{4}$ is the zero of the polynomial g(x).
View full question & answer→Question 291 Mark
Which of the following expressions are polynomials? In case of a polynomial, write its degree.
$\frac{-3}{5}$
AnswerClearly, $\frac{-3}{5}$ is a constant polynomial of degree 0.
View full question & answer→Question 301 Mark
Which of the following expressions are polynomials? In case of a polynomial, write its degree.
$\text{x}^4-\text{x}^\frac{3}{2}+\text{x}-3$
Answer$\text{x}^4-\text{x}^\frac{3}{2}+\text{x}-3$
In this expression, one of the powers of x is $\frac{3}{2}$ which is a fraction. Since it is an expression having fractional power of x, so, it is not a polynomial.
View full question & answer→Question 311 Mark
Verify that:
-3 is a zero of the polynomial, q(x) = x + 3.
Answerq(x) = (-3) + 3
⇒ q(-3) = 0
Hence, 3 is the zero of the given polynomial.
View full question & answer→Question 321 Mark
Write:
The cofficient of x in $\frac{3}{8}\text{x}^2-\frac{2}{7}\text{x}+\frac{1}{6}.$
AnswerThe cofficient of x in $\frac{3}{8}\text{x}^2-\frac{2}{7}\text{x}+\frac{1}{6}$ is $\frac{2}{7}.$
View full question & answer→Question 331 Mark
If $p(x) = 2x^3 - 11x^2 - 4x + 5$ and $g(x) = 2x + 1,$ show that $p(x)$ is not a factor of $g(x).$
Answer$p(x) = 2x^3 - 11x^2 - 4x + 1$
If $p(x)$ is divided by $(2x + 1),$ then $\text{f}\Big(\frac{-1}{2}\Big)$ is the remainder.
$\text{p}\Big(\frac{-1}{2}\Big)=2\Big(\frac{-1}{2}\Big)^3-11\Big(\frac{-1}{2}\Big)^2-4\Big(\frac{-1}{2}\Big)+1$
$=2\Big(\frac{-1}{8}\Big)-11\Big(\frac{1}{4}\Big)-4\Big(\frac{-1}{2}\Big)+1$
$=\frac{-1}{4}-\frac{11}{4}+2+1$
$= 3 - \frac{12}{4}$
$= 3-3$
$= 0$
$(2x + 1)$ is a factor of $g(x)$ as remainder is zero.
View full question & answer→Question 341 Mark
Identify constant, linear, quadratic, cubic and quadrtic polynomials from the following: $x - x^3 + x^4$
Answer$x - x^3 + x^4$ is a polynomial with degree $4.$ So, it is a quadratic polynomial.
View full question & answer→Question 351 Mark
Determine the degree of the following polynomials.
$\frac{4\text{x}-5\text{x}^2+6\text{x}^3}{2\text{x}}$
Answer$\frac{4\text{x}-5\text{x}^2+6\text{x}^3}{2\text{x}}=\frac{4\text{x}}{2\text{x}}-\frac{5\text{x}^2}{2\text{x}}+\frac{6\text{x}^3}{2\text{x}}=2-\frac{5}{2}\text{x}+3\text{x}^2$
Here, the highest power of x is 2. So, the degree of the polynomial is 2.
View full question & answer→Question 361 Mark
Find the zero of the polynomial:
h(x) = 6x - 2
Answerh(x) = 0
⇒ 6x - 1 = 0
$\Rightarrow\text{x}=\frac{1}{6}$
Hence, $\frac{1}{6}$ is the zero of the polynomial h(x).
View full question & answer→Question 371 Mark
Find the zero of the polynomial:
r(x) = 2x + 5
Answerr(x) = 0
⇒ 2x + 5
⇒ 2x + 5 = 0
⇒ 2x = -5
$\Rightarrow\text{x}=-\frac{ 5}{2}$
View full question & answer→Question 381 Mark
Rewrite the following polynomial in standard form. $2 + t - 3t^3 + t^4 - t^2$
Answer$2 + t - t^2 - 3t^3 + t^4$ is a polynomial in standard form as the powers of $t$ are in ascending order.
View full question & answer→Question 391 Mark
Which of the following expressions are polynomials? In case of a polynomial, write its degree.
$\frac{1}{\sqrt5}\text{x}^\frac{1}{2}+1$
Answer$\frac{1}{\sqrt5}\text{x}^\frac{1}{2}+1$
In this expression, the power of x is $\frac{1}{2}$ which is a fraction. Since it is an expression having fractional power of x, so, it is not a polynomial.
View full question & answer→Question 401 Mark
Which of the following expressions are polynomials? In case of a polynomial, write its degree.
$\frac{1}{\sqrt2}\text{x}^2-\sqrt2\text{x}+2$
Answer$\frac{1}{\sqrt2}\text{x}^2-\sqrt2\text{x}+2$ is an expression having only non-negative integral powers of x. So, it is a polynomial. Also, the highest power of x is 2, so, it is polynimial of degree 2.
View full question & answer→Question 411 Mark
Identify constant, linear, quadratic, cubic and quadrtic polynomials from the following:
-13
Answer-13 is a polynomial with degree 0. So, it is a constant polynomial.
View full question & answer→Question 421 Mark
Which of the following expressions are polynomials? In case of a polynomial, write its degree.
$\text{y}^3+\sqrt{3}\text{y}$
Answer$\text{y}^3+\sqrt{3}\text{y}$ is an expression having only non-negative integral powers of y. So, it is a polynomial. Also, the highest power of y is 3, so, it is polynimial of degree 3.
View full question & answer→Question 431 Mark
Find the zero of the polynomial:
p(x) = x - 5
Answerp(x) = 0
⇒ x - 5 = 0
⇒ x = 5
Hence, 5 is the zero of the polynomial p(x).
View full question & answer→Question 441 Mark
Identify constant, linear, quadratic, cubic and quadrtic polynomials from the following: $-6x^2$
Answer$-6x^2$ is a polynomial with degree $2.$ So, it is a quadratic polynomial.
View full question & answer→Question 451 Mark
Which of the following expressions are polynomials? In case of a polynomial, write its degree.
$\frac{3}{5}\text{x}^2-\frac{7}{3}\text{x}+9$
Answer$\frac{3}{5}\text{x}^2-\frac{7}{3}\text{x}+9$ is an expression having only non-negative integral powers of x. So, it is a polynomial. Also, the highest power of x is 2, so, it is a polynomial of degree 2.
View full question & answer→Question 461 Mark
Find the zero of the polynomial:
q(x) = x + 4
Answerq(x) = 0
⇒ x + 4 = 0
⇒ x = -4
Hence, -4 is the zero of the polynomial q(x).
View full question & answer→Question 471 Mark
Write: The coefficient of $x^3$ in $x + 3x^2 - 5x^3 + x^4.$
AnswerThe cofficient of $x^3$ in $x + 3x^2 - 5x^2 + x^4$ is $-5.$
View full question & answer→Question 481 Mark
Identify constant, linear, quadratic, cubic and quadrtic polynomials from the following:
6y
Answer6y is a polynomial with degree 1. So, it is a linear polynomial.
View full question & answer→Question 491 Mark
Identify constant, linear, quadratic, cubic and quadrtic polynomials from the following: $-z^3$
Answer$6y$ is a polynomial with degree $1.$ So, it is a linear polynomial.
View full question & answer→Question 501 Mark
Determine the degree of the following polynomials.
-8
Answer-8
-8 is a constant polynomial. So, the degree of the polynomial.
View full question & answer→