(A) According to the Factor Theorem,$(x-1)$ is a factor of $p(x)$ if $p(1) = 0$.Substitute $x = 1$ into the polynomial:$p(1) = (1)^{3} - 7(1)^{2} + 14

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(A) According to the Factor Theorem,$(x-1)$ is a factor of $p(x)$ if $p(1) = 0$.Substitute $x = 1$ into the polynomial:$p(1) = (1)^{3} - 7(1)^{2} + 14(1) - 8$$p(1) = 1 - 7 + 14 - 8$$p(1) = 15 - 15 = 0$Since $p(1) = 0$,$(x-1)$ is a factor of the given polynomial.

Class 9 Mathematics Polynomials Mix Examples - Polynomials

Medium

Check whether $(x-1)$ is a factor of the polynomial $p(x) = x^{3}-7x^{2}+14x-8$.

A
Yes
B
No
C
Cannot be determined
D
None of these

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Check whether $(x-1)$ is a factor of the polynomial $p(x) = x^{3}-7x^{2}+14x-8$.

Similar Questions

Without actual division,prove that $2x^4 - 5x^3 + 2x^2 - x + 2$ is divisible by $x^2 - 3x + 2$.

Evaluate the following using suitable identities: $(105)^{3}$

Evaluate $(132)^{2}$ by using suitable identities.

State whether the following statement is true or false:The degree of the polynomial $5x^{2} - 7x + 2$ is $5$.

Expand the following:$\left(\frac{1}{x}+\frac{y}{3}\right)^{3}$

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State whether the following statement is true or false:
The degree of the polynomial $5x^{2} - 7x + 2$ is $5$.

Expand the following:
$\left(\frac{1}{x}+\frac{y}{3}\right)^{3}$