Question

What must be subtracted from
$8x {}^{4} + 14x {}^{3} + x {}^{2} + 7x + 8$
so that polynomial is exactly divisible by
$4x {}^{2} - 3x + 2$

Answer 1

Answer:

6x + 2

Step-by-step explanation:

Let p(x) = 8x⁴ + 14x³ + x² + 7x + 8 and q(x) = 4x² - 3x + 2.

Long Division method:

4x² - 3x + 2) 8x⁴ + 14x³ + x² + 7x + 8 (2x² + 5x + 3

                    8x⁴ - 6x³ + 4x²

                    --------------------------------

                           20x³ - 3x² + 7x

                           20x³ - 15x² + 10x

                     -------------------------------

                                       12x² - 3x + 8

                                       12x² - 9x + 6

                       --------------------------------

                                                     6x + 2

∴ Remainder = 6x + 2

Hence, (6x + 2) must be subtracted from p(x) so that it is divisible by q(x)

Hope it helps!