Question

factoring by grouping

complete the steps to factor (56x^2 - 8x - 7x + 1) by grouping.

1. group pairs of terms with common factors.

((56x^2 - 8x) + (-7x + 1))

1. factor the gcf from each group.

(8x(7x - 1) - 1(7x - 1))

1. use the distributive property.

what is the factorization of the polynomial?

(8x - 1)(7x - 1)
(8x + 1)(7x - 1)
(8x + 7x)(1 - 1)

Explanation:

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<reasoning>

Identify the expression and current step

Using the Factoring Polynomials knowledge point
\[
8x(7x-1) - 1(7x-1)
\]

Apply the distributive property

Using the Distributive Property knowledge point
\[
(8x-1)(7x-1)
\]
</reasoning>

<answer>
<mcq-correct>(A) \((8x-1)(7x-1)\)</mcq-correct>
<mcq-option>(B) \((8x+1)(7x-1)\)</mcq-option>
<mcq-option>(C) \((8x+7x)(1-1)\)</mcq-option>
</answer>

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"question_type": "Multiple Choice",
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"Mathematics",
"Algebra",
"Factoring by Grouping"
]
}
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Answer:

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<reasoning>

Identify the expression and current step

Using the Factoring Polynomials knowledge point
\[
8x(7x-1) - 1(7x-1)
\]

Apply the distributive property

Using the Distributive Property knowledge point
\[
(8x-1)(7x-1)
\]
</reasoning>

<answer>
<mcq-correct>(A) \((8x-1)(7x-1)\)</mcq-correct>
<mcq-option>(B) \((8x+1)(7x-1)\)</mcq-option>
<mcq-option>(C) \((8x+7x)(1-1)\)</mcq-option>
</answer>

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