Question

The expression $4x^2-px+7$ leaves the reminder -2 when divided by x - 3. Find the value of p

• A. 15
• B. 12
• C. 10
• D. 18

Answer 1

Answer:

A. 15

when a polynomial p(x) is divided by (x - a) for some number a , the reminder r = p(a)

When p(a) = 0 then (x -a) is a factor of p(x)

$r(x)=4x^2-px+7$

$x-3=0\implies{x=3}$

$r(3)=4(3^2)-p\times3+7=-2$

$36-3p+7=-2$

$-3p+43=-2$

$-3p=-45$

$p=45/3=15$