Factor by Grouping

Front

What is Factor by Grouping?

Back

Factor by Grouping is a method used to factor polynomials by grouping terms with common factors together.

Front

What is the first step in Factor by Grouping?

Back

The first step is to rearrange the polynomial into two groups that can be factored separately.

Front

How do you factor the expression 30x^3 + 15x^2 - 18x - 9?

Back

Group the terms: (30x^3 + 15x^2) + (-18x - 9) = 15x^2(2x + 1) - 9(2x + 1) = (2x + 1)(15x^2 - 9) = 3(5x^2 - 3)(2x + 1).

Front

What is the result of factoring 20x^3 - 25x^2 + 4x - 5?

Back

Group the terms: (20x^3 - 25x^2) + (4x - 5) = 5x^2(4x - 5) + 1(4x - 5) = (4x - 5)(5x^2 + 1).

Front

What does it mean to solve for x in an equation?

Back

To solve for x means to find the value(s) of x that make the equation true.

Front

How do you solve the equation x^3 + 7x^2 - 2x - 14 = 0?

Back

Use synthetic division or factor by grouping to find the roots: x = -7, x = ±√2.

Tags

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Front

What is the significance of the roots of a polynomial?

Back

The roots of a polynomial are the values of x where the polynomial equals zero; they represent the x-intercepts of the graph.

Front

How do you factor the expression x^3 - 5x^2 + 5x - 25?

Back

Group the terms: (x^3 - 5x^2) + (5x - 25) = x^2(x - 5) + 5(x - 5) = (x - 5)(x^2 + 5).

Front

What is the formula for factoring a cubic polynomial?

Back

A cubic polynomial can often be factored using the Rational Root Theorem or synthetic division to find at least one root.

Front

What is the result of factoring 7r^3 - 8r^2 + 42r - 48?

Back

Group the terms: (7r^3 - 8r^2) + (42r - 48) = r^2(7r - 8) + 6(7r - 8) = (7r - 8)(r^2 + 6).