Using the factor theorem, factorize each of the following polynomials: x³ - 6x² + 3x + 10.

Question

asked May 7, 2024 172k views

1 Answer

Jcjr · Answer 1 · 2024-05-12T05:27:45+0000

Explanation:

$p(x) = x {}^(3) - 6 {x}^(2) + 3x + 10$

When trying to factor polynomials, try plugging in 1 and -1 to see if that works

$p(1) = 1 {}^(3) - 6(1) {}^(2) + 3(1) + 10 = 8$

p( - 1) = - 1 - 6 - 3 + 10 = 0

So p(-1) is a factor

Since p(-1) is a factor, that means (x+1) is a factor of the above polynomial.

Use synthetic division to find the other factor.

We get

${x}^(2) - 7x + 10$

Using basic algebra, that factor will give us

(x - 2)(x - 5)

So our factors are

(x - 2)(x - 5)(x + 1)