Question

Find the value of and b it 2x² + x ² - 16 2²
+ ax + b is exactly divisible by
${x}^{2}$-9​

Answer 1

IF A AND B ARE EXACTLY DIVISIBLE By x² -9

THEN BY REMAINDER THEOREM THE REMAINDER IF ZERO

x² -9=0

(x)² -(3)² =0

(x+3)(x-3)=0

x=-3 or x=3

now let p(x)=2x² + x ² - 16 2²+ax+b

p(-3)=-55+ax+b

-55+ax+b=0------------------1

p(3)=2x² + x ² - 16 2²+ax+b

p(3)=-55+ax+b

-55+ax+b=0------------2