Question

If polynomial p(x) is divided by x + 4, the quotient is x^2-7x+34-144/x+4. Which of the following must be true?
A. P(-4) doesn’t exist
B. P(-4)=-144
C. P(0)=-2
D. P(0)=34

Answer 1

Answer:

B. P(-4)=-144

Step-by-step explanation:

From the question, we have that:

$\frac{p(x)}{x + 4} = {x}^{2} - 7x + 34 - \frac{144}{x + 4}$

This implies that:

$p(x)=(x + 4)( {x}^{2} - 7x + 34) - 144$

To find p(-4), we put x=-4

$p( - 4)=( - 4+ 4)( {( - 4)}^{2} - 7 \times - 4 + 34) - 144$

$p( - 4)=( 0)( {( - 4)}^{2} - 7 \times - 4 + 34) - 144 = - 144$

To find p(0), we put x=0 to get:

$p( 0)=( 0+ 4)( {( 0)}^{2} - 7 \times 0+ 34) - 144$

$p( 0)=(4)( 34) - 144 = - 8$

The correct answer is B