Question

Without actual division, find the remainder when 8x squared - 2x - 15 is divided by 2x + 3

Answer 1

Let P(x) is polynomial and D(x) is the divisor

K(x) is Dividend and R is remainder than

P(x) = K(x) * D(x) + R(x)

Let the value of x for which D(x) = 0 is a

Than at x = a ,D(a) =0 And P(a) = K(a)D(a) + R = R

So by putting value of x = a in polynomial we can find value of remainder

Now in our question

P(x) = 8x² - 2x - 15

D(x) = 2x+3

D(x) = 0 when x = -3/2

So a = -3/2

We will get P(a) = Remainder

P(-3/2) = 8*(3/2)² - 2*3/2 -15 = 0

Remainder equal to 0