Question

Factor the quadratic expression completely. 15xˆ2-4x-4

Answer 1

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

consider the factors of the product 15 × - 4 = - 60

which sum to give the coefficient of the middle term ( - 4 )

the factors required are - 10 and + 6

split the x- term using these factors

15x² - 10x + 6x - 4 ( factor by grouping )

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

Take out the common factor (3x - 2)

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

Answer 2

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

Explanation:

we have to multiply 15 and 4.

then find the factors of this product.

we get,

15 x 4=60

Now, factors of 60 which make 4 are 6 and 10

because 6-10=-4

So,

`15 x^(2)-4x-4\\ =15x^(2) -10x+6x-4\\`

Now, we have to take common factor pairwise.

Taking 5x as common factor from first pair and 2 from second pair,

we get

`15x^(2) -10x+6x-4\\=5x(3x-2)+2(3x-2)\\=(3x-2)(5x+2)`