Question

The polynomial 2x³ + 3x² - a and ax² - 5x + 2 have the same remainder when each is divided by x - 2

Answer 1

$Reminder\of\ 2x^3+3x^2-a = 2*2^3+3*2^2-a = 16+12-a =28-a \\ \\ Reminder\ of\ ax^2-5x+2= a*2^2-5*2+2 = 4a-10+2 = 4a- 8\\ \\ 28 - a = 4a - 8 \\ \\ 28+8 = 4a+a \\ \\ 5a = 36 \\ \\ a = 36/5$

Answer 2

Remainder when $2x^3 + 3x^2 - a$ is divided by (x - 2) is

$2(2)^3 +3(2)^2 - a \Rightarrow 28 - a$

Remainder when $ax^2 - 5x + 2$ is divided by (x - 2) is

$a(2)^2 - 5(2) + 2 \Rightarrow 4a-8$

Give the remainders equal.

$28 - a = 4a - 8$

⇒ 5a = 36

⇒ a = 7.2