Which shows one way to determine the factors of x³ + 5x² - 6x - 30 by grouping?
x(x² - 5) + 6(x² - 5)
x(x² + 5) - 6(x² + 5)
x²(x - 5) + 6(x - 5)
x²(x + 5) - 6(x + 5)

Solution:

Factoring quadratics is a method of expressing the polynomial as a product of its linear factors.

It is a process that allows us to simplify quadratic expressions, find their roots and solve equations.

A quadratic polynomial is of the form ax² + bx + c, where a, b, c are real numbers.

Factoring quadratics is a method that helps us to find the zeros of the quadratic equation ax² + bx + c = 0.

Given:

Polynomial is x³ + 5x² - 6x - 30

By grouping,

x³ + 5x² - 6x - 30

x²(x + 5) - 6(x + 5)

On simplification, we get

(x² - 6)(x + 5)

Therefore, the factors obtained by grouping are (x² - 6)(x + 5).

Which shows one way to determine the factors of x³ + 5x² - 6x - 30 by grouping?

Summary:

The factors of x³ + 5x² - 6x - 30 by grouping are (x² - 6)(x + 5).