Sample QuestionsFactorization Of Polynomials [NEW] questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Zero of the zero polynomial is
Answer: C.
View full solution →Zero of the polynomial $f(x)=3 x+7$ is
- A
$\frac{7}{3}$
- B
$\frac{-3}{7}$
- ✓
$-\frac{7}{3}$
- D
$-7$
Answer: C.
View full solution →$(x+1)$ is a factor of $x^n+1$ only if
Answer: A.
View full solution →$x+1$ is a factor of the polynomial
- A
$x^3+x^2-x+1$
- ✓
$x^3+x^2+x+1$
- C
$x^4+x^3+x^2+1$
- D
$x^4+3 x^3+3 x^2+x+1$
Answer: B.
View full solution →Which one of the following is a polynomial?
Statement-1 (A): If $x+7$ is a factor of $f(x)=x^2+11 x-2 a$, then $a=-14$
Statcment-2 $(R)$ : If $x+a$ is a factor of a polynomial, then $f(a)=0$.
- A
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-2
- B
Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is True, Statement-2 is False.
- D
Statement-1 is False, Statement-2 is True.
View full solution →Statement-1 (A): If $x+2 a$ is a factor of $f(x)=x^5-4 a^2 x^3+2 x+2 a+3$, then $2 a-3=0$
Statement-2 (R): If $f(x)$ is divisible by $(a x+b)$, then $f\left(-\frac{b}{a}\right)=0$.
- ✓
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-5
- C
Statement-1 is true, Statement-2 is false.
- D
Statement-1 is false, Statement-2 is true.
Answer: A.
View full solution →Statement-1 (A): If $x+2 a$ is a factor of $f(x)=x^5-4 a^2 x^3+2 x+2 a+3$, then $2 a-3=0$.
Statement-2 (R): If $f(x)$ is divisible by $(a x+b)$, then $f\left(-\frac{b}{a}\right)=0$.
- ✓
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement-2 is false.
- D
Statement-1 is false, Statement-2 is true.
Answer: A.
View full solution →Statement-1 (A): If $x+1$ is a factor of $f(x)=p x^2+5 x+r$, then $p+r+5=0$.
Statement-2 (R): If $x-2$ and $2 x-1$ are factors of $f(x)=p x^2+5 x+r$, then $p=r$.
- A
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-4
- C
Statement-1 is true, Statement-2 is false.
- ✓
Statement-1 is false, Statement-2 is true.
Answer: D.
View full solution →Statement-1 (A): If $x+1$ is a factor of $f(x)=p x^2+5 x+r$ then $p+r+5=0$.
Statement-2 (R): If $x-2$ and $2 x-1$ are factors of $f(x)=p x^2+5 x+r$, then $p=r$.
- A
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement-2 is false.
- ✓
Statement-1 is false, Statement-2 is true.
Answer: D.
View full solution →The remainder when $x^{15}$ is divided by $x+1$ is _______________ .
View full solution →The remainder when $f(x)=x^{45}$ is divided by $x^2-1$ is _______________ .
View full solution →The remainder when $f(x)=4 x^3-3 x^2+2 x-1$ is divided by $2 x+1$ is _______________ .
View full solution →The remainders obtained when $x^3+x^2-9 x-9$ is divided by $x, x+1$ and $x+2$ respectively are _______________ .
View full solution →The degree of a polynomial $f(x)$ is 7 and that of polynomial $f(x) g(x)$ is 56 , then degree of $g(x)$ is $\qquad$ . _______________ .
View full solution →Write the remainder when the polynomial $f(x)=x^3+x^2-3 x+2$ is divided by $x+1$.
View full solution →If $x=\frac{1}{2}$ is a zero of the polynomial $f(x)=8 x^3+a x^2-4 x+2$, find the value of $a$.
View full solution →If $x+1$ is a factor of $x^3+a$, then write the value of $a$.
View full solution →If $f(x)=x^4-2 x^3+3 x^2-a x-b$ when divided by $x-1$, the remainder is 6 , then find the value of $a+b$
View full solution →Find the remainder when $x^3+4 x^2+4 x-3$ is divided by $x$.
View full solution →What must be subtracted from x3 - 6x2 - 15x + 80 so that the result is exactly divisible by x2 + x - 12?
Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following case:
$\text{f(x)}=\text{l(x)}+\text{m},\text{x}=-\frac{\text{m}}{\text{l}}$
View full solution →Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following case:
$\text{f(x)}=3\text{x}+1,\text{x}=-\frac{1}{3}$
View full solution →Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following case:
f(x) = x2, x = 0
In the following, use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x) or, not:
f(x) = x3 - 6x2 - 19x + 84, g(x) = x - 7
What must be added to 3x3 + x2 - 22x + 9 so that the result is exactly divisible by 3x2 + 7x - 6?
Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following case:
$\text{g(x)}=3\text{x}^2-2,\text{x}=\frac{2}{\sqrt{3}},\frac{-2}{\sqrt{3}}$
View full solution →Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following case:
$\text{f(x)}=5\text{x}-\pi,\text{x}=\frac{4}{5}$
View full solution →Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following case:
$\text{f(x)}=2\text{(x)}+1,\text{x}=\frac{1}{2}$
View full solution →Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following case:
f(x) = x2 - 1, x = 1, -1
x4 - 2x3 - 7x2 + 8x + 12.
x4 + 10x3 + 35x2 + 50x + 24.
What must be added to x3 - 3x2 - 12x + 19 so that the result is exactly divisibly by x2 + x - 6?
Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following case:
p(x) = x3 - 6x2 + 11x - 6, x = 1, 2, 3
Using factor theorem, factorize the following polynomials:
y3 - 7y + 6
(x + y)
3 - (x - y)
3 can be factorized as:
- 2y(3x2 + y2)
- 2x(3x2 + y2)
- 2y(3y2 + x2)
- 2x(x2+ 3y2)
The value of $\frac{(2.3)^3-0.027}{(2.3)^2+0.69+0.09},$ is:
- 2
- 3
- 2.327
- 2.273
View full solution →The value of $\frac{(0.013)^3+(0.007)^3}{(0.013)^2-0.013\times0.007+(0.007)^2},$ is:
- 0.006
- 0.02
- 0.0091
- 0.00185
View full solution →The factors of x
3 - 1 + y
3 + 3xy are:
- (x - 1 + y)(x2 + 1 + y2 + x + y - xy)
- (x + y + 1)(x2 + y2 + 1 - xy - x - y)
- (x - 1 + y)(x2 - 1 - y2 + x + y + xy)
- 3(x + y - 1)(x2 + y2 - 1)
The factors of x
4 + x
2 + 25 are:
- (x2 + 3x + 5)(x2 - 3x + 5)
- (x2 + 3x + 5)(x2 + 3x − 5)
- (x2 + x +5)(x2 - x + 5)
- None of these.