Which shows one way to determine the factors of x³ + 11x² - 3x - 33 by grouping?
x²(x + 11) + 3(x - 11)
x²(x - 11) - 3(x - 11)
x²(x + 11) + 3(x + 11)
x²(x + 11) - 3(x + 11) 

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 + 11x² - 3x - 33

By grouping,

⇒ x³ + 11x² - 3x - 33

Taking out the common terms

⇒ x²(x + 11) - 3(x + 11)

On simplification,

⇒ (x² - 3)(x + 11)

Therefore, the factors obtained by grouping are (x² - 3)(x + 11).

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Which shows one way to determine the factors of x³ + 11x² - 3x - 33 by grouping?

Summary:

The factors of x³ + 11x² - 3x - 33 by grouping are (x² - 3)(x + 11).