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?

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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?

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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?

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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?

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

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

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

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What is the significance of the roots of a polynomial?

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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?

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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?

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