Factoring by Grouping Review

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What is factoring by grouping?

Back

Factoring by grouping is a method used to factor polynomials by grouping terms with common factors and then factoring out the common binomial.

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What is the first step in factoring by grouping?

Back

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

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How do you factor the expression 4p³ + 8p² + 3p + 6?

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Group the terms: (4p³ + 8p²) + (3p + 6) = 4p²(p + 2) + 3(p + 2) = (4p² + 3)(p + 2).

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What is the factored form of 4x² + 8x + 10?

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The factored form is 2(2x² + 4x + 5).

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What is the factored form of 6d⁴ + 9d³ - 12d²?

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The factored form is 3d²(2d² + 3d - 4).

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How do you simplify the product (x + 2)(x - 5)?

Back

Use the distributive property: x² - 5x + 2x - 10 = x² - 3x - 10.

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What is the result of simplifying (3x³ + 9x² - 2x) - (7x³ - 6x² + 1)?

Back

Combine like terms: -4x³ + 15x² - 2x - 1.

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What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents.

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What does it mean to factor a polynomial?

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Factoring a polynomial means expressing it as a product of its factors, which can be simpler polynomials.

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What is a common factor?

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A common factor is a number or expression that divides two or more numbers or expressions without leaving a remainder.