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Complete the steps to factor 56x2 – 8x – 7x + 1 by grouping. group pairs of terms with common factors. (56x2 – 8x) + (–7x + 1) factor the gcf from each group. 8x(7x – 1) –1(7x – 1) use the distributive property. what is the factorization of the polynomial? (8x – 1)(7x – 1) (8x + 1)(7x – 1) (8x + 7x)(1 – 1)

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W0lf93
(8x-1)(7x-1) The question leaves you with the partially factored equation: 8x(7x-1) - 1(7x-1) Now if you look at the partially factored equation, you'll see that both terms have (7x-1) as one of their factors. So let's take that (7x-1) as a factor and divide both terms by (7x-1), giving us (8x(7x-1) - 1(7x-1)) / (7x-1) The (7x-1) factors cancel out, leaving us with (8x - 1) So our 2 factors are (7x-1) and (8x-1). Looking at the available options, the only correct one is (8x-1)(7x-1)

Based on the distributive property of multiplication over addition. The factorized form of the given polynomial is (8x-1)(7x-1)

What is distributive property?

The distributive property states that an expression of the form A(B + C) can be solved by a multiplication over addition operation that is

A(B + C) = AB + AC

This property is known by distributive law and applies to subtraction also.

The given polynomial is [tex]56x^2 - 8x - 7x + 1[/tex]

It can be grouped and factored as

[tex]56x^2 - 8x - 7x + 1[/tex]

= [tex]8x\times 7x - 8x \times 1-7x+1[/tex]

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

= (8x – 1)(7x – 1)

Thus, the factorized form of the given polynomial is (8x-1)(7x-1).

Learn more about factors of a polynomial here:

brainly.com/question/16078564

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