factoring by grouping

Front

What is factoring by grouping?

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Factoring by grouping is a method used to factor polynomials by grouping terms with common factors together, allowing for easier factorization.

Front

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.

Front

How do you factor the polynomial 12x^3 + 4x^2 + 3x + 1?

Back

(4x^2 + 1)(3x + 1)

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What is the result of factoring 5x^3 - 10x^2 + 3x - 6?

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(5x^2 + 3)(x - 2)

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What is the factored form of 3x^3 - 4x^2 + 9x - 12?

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(x^2 + 3)(3x - 4)

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How do you factor the polynomial 12x^3 - 21x^2 + 28x - 49?

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(3x^2 + 7)(4x - 7)

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What is the factored form of 63x^3 + 54x^2 - 105x - 90?

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3(3x^2 - 5)(7x + 6)

Front

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.

Front

What does it mean to factor a polynomial?

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Factoring a polynomial means to express it as a product of its factors, which are polynomials of lower degrees.

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What is the significance of the distributive property in factoring?

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The distributive property allows us to factor out common terms from a polynomial, making it easier to simplify and solve.