Question

x^3+8x^2-7x-2 determine it has the polynomials has x-1 a factor​

Answer 1

Solution!!

The concept of factor and remainder theorem has to be used here.

Remainder Theorem → If f(x), a polynomial in x, is divided by (x - a), the remainder = f(a).

Factor Theorem → When a polynomial f(x) is divided by x - a, the remainder = f(a). And, if remainder f(a) = 0; x - a is a factor of the polynomial f(x).

We have to find out if x - 1 is a factor of x³ + 8x² - 7x - 2.

x - 1 = 0

x = 1

f(x) = x³ + 8x² - 7x - 2

f(1) = (1)³ + 8(1)² - 7(1) - 2

= 1 + 8 - 7 - 2

= 9 - 9

= 0

The value at the end is 0. Hence, x - 1 is a factor of the polynomial x³ + 8x² - 7x - 2.