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dlinn [17]
3 years ago
7

Lucas and Erick are factoring the polynomial 12x3 – 6x2 + 8x – 4. Lucas groups the polynomial (12x3 + 8x) + (–6x2 – 4) to factor

. Erick groups the polynomial (12x3 – 6x2) + (8x – 4) to factor. Who correctly grouped the terms to factor? Explain.
Mathematics
1 answer:
daser333 [38]3 years ago
6 0

Answer:

Lucas groups the polynomial (12x^3 + 8x) + (–6x^2 – 4) to factor → 2 (2 x - 1) (3 x^2 + 2)

Step-by-step explanation:

Factor the following:

12 x^3 - 6 x^2 + 8 x - 4

Hint: | Factor out the greatest common divisor of the coefficients of 12 x^3 - 6 x^2 + 8 x - 4.

Factor 2 out of 12 x^3 - 6 x^2 + 8 x - 4:

2 (6 x^3 - 3 x^2 + 4 x - 2)

Hint: | Factor pairs of terms in 6 x^3 - 3 x^2 + 4 x - 2 by grouping.

Factor terms by grouping. 6 x^3 - 3 x^2 + 4 x - 2 = (6 x^3 - 3 x^2) + (4 x - 2) = 3 x^2 (2 x - 1) + 2 (2 x - 1):

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

Hint: | Factor common terms from 3 x^2 (2 x - 1) + 2 (2 x - 1).

Factor 2 x - 1 from 3 x^2 (2 x - 1) + 2 (2 x - 1):

Answer: 2 (2 x - 1) (3 x^2 + 2)

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Let's solve step by step

So all we need to do is simplify the equation 

<span><span>(<span>5x − 8</span>)</span><span>(<span>2x + 4</span>)

</span></span><span>= <span><span>(<span>5x + −8</span>)</span><span>(<span>2x + 4</span>)

</span></span></span><span>= <span><span><span><span><span>(5x)</span><span>(2x) </span></span>+ <span><span>(5x)</span>(4) </span></span>+ <span><span>(−8)</span><span>(2x) </span></span></span>+ <span><span>(−8)</span><span>(4)

</span></span></span></span><span>= <span><span><span><span>10x^2 </span>+ 20x </span>− 16x </span>− 32

</span></span><span>= <span><span><span>10x^2 </span>+ 4x </span>− <span>32

Therefore the simplified form of this is </span></span></span>10x^2 + 4x − 32
Hope this helps! - Alyssa

(Please mark as Brianliest Answer, Thanks)
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