Question

What should be added to $8x^4+14x^3-2x^2+7x-8$ so that the resulting polynomial is exactly divisible by $4x^2+3x-2$?

• A. $10-14x$
• B. $4x-10$
• C. $3x-5$
• D. $5-3x$

Answer 1

The correct option is A $10-14x$

$4x^2+3x-2)\overline{8x^4+14x^3-2x^2+7x-8}$ ( $2x^2+2x-1$
$\underset{–}{\underset{-}{8}{x}^4\underset{-}{+}6x^3\underset{+}{-}4x^2}$
$8x^3+2x^2+7x-8$
$\underset{–}{\underset{-}{8}{x}^3\underset{-}{+}6x^2\underset{+}{-}4x}$
$-4x^2+11x-8$
$\underset{–}{\underset{+}{-}4x^2\underset{+}{-}3x\underset{-}{+}2}$
$14x-10$
We have to add $10-14x$ so that $8x^4+14x^3-2x^2+7x-8$ is completely divisible by $4x^2+3x-2$.