Question

Can anyone solve the problem on the picture?

Answer 1

Quotient:

$\dfrac{9x^2 +68x +35}{x+7}\\\\\\=\dfrac{9x^2 +63x +5x +35}{x+7}\\\\\\=\dfrac{9x(x+7) +5(x+7)}{x+7}\\\\\\=\dfrac{(9x+5)(x+7)}{x+7}\\\\\\=9x+5$

Remainder:

$f(x) = 9x^2+68x+35$

By the remainder theorem,

$f(-7) = 9(-7)^2 +68(-7) +35 = 441 - 476+35 = 476 - 476 =0$

Which is the remainder when f(x) is divided by (x+7)