Question

The polynomial (4x-3) is a factor of the polynomial p(x)= 4x^3+ x^2- 11x+2r. What is the value of r?​

Answer 1

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Answer 2

Tip:

• A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Explanation:

• We have given the polynomial $(4x-3)$ is a factor of the polynomial $p(x)=4x^3+x^2-11x+2r$.

• We have to find the value of $r$

Step

Step 1 of 1:

If $(4x-3)$ is a factor of the polynomial $p(x)=4x^3+x^2-11x+2r$, then $p(x)=0$

∴     $4x-3=0\\4x=3\\x=\frac{3}{4}$

Putting thee value of $x$ in $p(x)$

$p(\frac{3}{4})=4\left(\frac{3}{4}\right)^3+\left(\frac{3}{4}\right)^2-11\left(\frac{3}{4}\right)+2r$

$\frac{27}{16}+\frac{9}{16}-\frac{33}{4}+2r=0\\\\\frac{27+9-132}{16}+2r=0\\\\-\frac{96}{16}+2r=0\\\\2r=\frac{96}{16}\\\\2r=6\\\\r=\frac{6}{2}\\\\r=3$