Question

Find the polynomial g(x), if q(x) =2x – 3 is the quotient and r(x) = - 3x +2 is the remainder

When f(x) =6 x3

- 17 x2 +13x -4 is divided by g(x)​

Answer 1

Answer:

Given,

f(x) = 6x³ - 17x² + 13x - 4

q(x) = 2x - 3

r(x) = -3x + 2

We want to find g(x).

We know that,

f(x) = g(x) • q(x) + r(x)

f(x) - r(x) /q(x) = g(x)

g(x) = 6x³ - 17x² + 13x - 4 - (-3x + 2) / 2x - 3

= 6x³ - 17x² + 13x - 4 + 3x - 2 / 2x - 3

= 6x³ - 17x² + 16x - 6 / 2x - 3

= 3x² - 4x + 2

So, g(x) = 3x² - 4x + 2