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

  (3x -2)(5x +2)

Step-by-step 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

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

hope it