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Factor the quadratic expression completely.
15x^2-4x-4=

User Sprague
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2 Answers

2 votes

Answer:


\sf \longmapsto \: 15 {x}^(2) - 4x - 4


\sf \longmapsto \:(15 {x}^(2) + 6x) + ( - 10x - 4)


\sf \longmapsto \:3x(5x + 2) - 2(5x + 2)


\sf \longmapsto \:(3x - 2)(5x + 2)

User Aabilio
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4.8k points
6 votes

Answer:

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

Explanation:

To factor a quadratic ax²+bx+c, you look for factors of ac that total b. Here, that means you're looking for factors of (15)(-4) = -60 that total -4. We can look at factor pairs of -60 to see what the choices might be:

-60 = -60·1 = -30·2 = -20·3 = -15·4 = -12·5 = -10·6

The sums of these pairs are -59, -28, -17, -11, -7, and -4. So, the numbers we're looking for are -10 and 6. We can rewrite the expression using these numbers to divide -4x into parts that have the sum of -4x:

= 15x² -10x +6x -4

Grouping terms in pairs and factoring the pairs gives ...

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

Using the distributive property again, we get ...

= (5x +2)(3x -2) . . . . . . . . factorization of the given quadratic

User Nouse
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