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 $x+1$ is a factor of the polynomial $2 x^2+k x$, then $k=$
Answer: D.
View full solution →If both $x-2$ and $x-\frac{1}{2}$ are factor of $p x^2+5 x+r$, then
- ✓
$p=r$
- B
$p+r=0$
- C
$2 p+r=0$
- D
$p+2 r=0$
Answer: A.
View full solution →If $x-3$ is a factor of $x^2-a x-15$, then $a=$
Answer: A.
View full solution →If $x^3+6 x^2+4 x+k$ is exactly divisible by $x+2$, then $k$
Answer: C.
View full solution →If $x-a$ is a factor of $x^3-3 x^2 a+2 a^2 x+b$, then the value of $b$ is:
Answer: A.
View full solution →Identify constant, linear, quadratic and cubic polynomial from the following polynomials:
$r(x)=3 x^3+4 x^2+5 x-7$
View full solution →Write the coefficients of $x^2$ in the following:
$9-12 x+x^3$
View full solution →Identify the polynomials in the following: $\text{p(x)}=\frac{2}{3}\text{x}^2-\frac{7}{4}\text{x}+9$
View full solution →Identify the polynomials in the following: $\text{f(x)}=2+\frac{3}{\text{x}}+4\text{x}$
View full solution →Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials: $3x - 2$
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 $x^3+3 x^3+3 x+1$ 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: $f(x)=3 x^4+17 x^3+9 x^2-$ $7 x-10 ; g(x)=x+5$
View full solution →If $x+1$ is a factor of $x^3+a$, then write the value of $a$.
View full solution →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 →Find the remainder when $x^3 + 3x^3 + 3x + 1$ is divided by: $\text{x}+\pi$
View full solution →Factorize the following polynomials: $4x^3 + 20x^2 + 33x + 18$ given that $2x + 3$ is a factor.
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: B.
View full solution →The value of $\frac{(2.3)^3-0.027}{(2.3)^2+0.69+0.09},$ is:
Answer: A.
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 →In the following, using the remainder theorem, find the remainder when $f(x)$ is divided by $g(x)$ and verify the by actual division: $f(x) = 9x^3 - 3x^2 + x - 5$, $\text{g(x)}=\text{x}-\frac{2}{3}$
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 → Using factor theorem, factorize the following polynomials: $2y^3 + y^2 - 2y - 1$
View full solution →If $\text{x}=-\frac{1}{2}$ is zero of the polynomial $p(x) = 8x^3 - ax^2 - x + 2$, Find the value of a.
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: $f(x) = x^3 + 4x^2 - 3x + 10, g(x) = x + 4$
View full solution →