Sample QuestionsFactorization Of Polynomials questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $x - 3$ is a factor of $x^2 - ax - 15, $ then $a =$
Answer: A.
View full solution →If $x - a$ is a factor of $x^3 - 3x^2a + 2a^2x + b,$ then the value of $b$ is:
Answer: A.
View full solution →The value of $k$ for which $x - 1$ is a factor of $4x^3 + 3x^2 - 4x + k,$ is:
Answer: D.
View full solution →If $x - 2$ is a factor of $x^2 + 3ax - 2a,$ then $a =$
Answer: D.
View full solution →If $x + 1$ is a factor of the polynomial $2x^2 + kx,$ then $k =$
Answer: D.
View full solution →Write the degrees of the following polynomials:
0
Write the coefficients of $x^2 $in the following: $17 - 2x + 7x^2$
View full solution →Write the coefficients of $x^2$ in the following: $9 - 12x + x^3$
View full solution →Write the remainder when the polynomial $f(x) = x^3 + x^2 - 3x + 2$ is divided by $x + 1.$
View full solution →Identify constant, linear, quadratic and cubic polynomial from the following polynomials: $p(x) = 2x^2 - x + 4$
View full solution →What must be subtracted from $x^3 - 6x^2 - 15x + 80$ so that the result is exactly divisible by $x^2 + x - 12$?
View full solution →Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following case: $f(x) = x^2, x = 0$
View full solution →Find the remainder when $x^3 + 3x^3 + 3x + 1$ is divided by: $x$
View full solution →In the following, use factor theorem to find whether polynomial $g(x)$ is a factor of polynomial $f(x)$ or, not:
$f(x) = 3x^4 + 17x^3 + 9x^2 - 7x - 10; g(x) = x + 5$
View full solution →If $x + 1$ is a factor of $x^3 + a,$ then write the value of $a$.
View full solution →Find the remainder when $x^3 + 3x^3 + 3x + 1$ is divided by:$5 + 2x$
View full solution →In the following, use factor theorem to find whether polynomial $g(x)$ is a factor of polynomial $f(x)$ or, not:
$f(x) = 2x^3 - 9x^2 + x + 12, g(x) = 3 - 2x$
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: $f(x) = x^2 - 1, x = 1, -1$
View full solution →Find the value of a such that $(x - 4)$ is a factors of $5x^3 - 7x^2 - ax - 28.$
View full solution →If $(x + y)^3 - (x - y)^3 - 6y(x^2 - y^2) = ky^2,$ then $k =$
Answer: D.
View full solution →The expression $(a - b)^3 + (b - c)^3 + (c - a)^3$ can be factorized as:
Answer: C.
View full solution →The factors of$ x^3 - 7x + 6$ are:
- A
$x(x - 6)(x - 1)$
- B
$(x^2 - 6)(x - 1)$
- C
$(x + 1)(x + 2)(x + 3)$
- ✓
$(x - 1)(x + 3)(x - 2)$
Answer: D.
View full solution →The expression $x^4 + 4$ can be factorized as:
- ✓
$(x^2 + 2x + 2)(x^2 - 2x + 2)$
- B
$(x^2 + 2x + 2)(x^2 + 2x - 2)$
- C
$(x^2 - 2x - 2)(x^2{ }- 2x + 2)$
- D
$(x^2 + 2)(x^2 - 2)$
Answer: A.
View full solution →The factors of $x^2 + 4y^2 + 4y - 4xy - 2x - 8,$ are:
- ✓
$(x - 2y - 4)(x - 2y + 2)$
- B
$(x - y + 2)(x - 4y - 4)$
- C
$(x + 2y - 4)(x + 2y + 2)$
- D
Answer: A.
View full solution →Using factor theorem, factorize the following polynomials: $x^3 + 6x^2 + 11x + 6$
View full solution →Find the value of $a,$ if $x + 2$ is a factor of $4x^4 + 2x^3 - 3x^2 + 8x + 5a.$
View full solution →If the polynomials $ax^3 + 3x^2 − 13$ and $2x^3 − 5x + a,$ when divided by $(x - 2)$ leave the same remainder, Find the value of $a.$
View full solution →Find the rational roots of the polynomial $f(x) = 2x^3 + x^2 - 7x - 6$
View full solution →In the following, using the remainder theorem, find the remainder when $f(x)$is divided by $g(x)$ and verify the by actual division:$ f(x) = 4x^4 - 3x^3 - 2x^2 + x - 7, g(x) = x - 1$
View full solution →