Factoring Quadratic Expressions (a>1) please help

Question

Factor 3x^2−16x+20. Rewrite the Trinomial with the x-term expanded, using the two factors.

3x^2_____ +20

Answer 1

Factor 3x²−16x+20.

Rewrite the Trinomial with the x-term expanded, using the two factors.

To rewrite this with the x term expanded you would think about a few things.

1) What are the factors of the x² term (3 x 1)

2) What are the possible factors of the constant term (20)

Since the middle term is negative (-16x) and the constant term is positive (+20) The factors are both negative

(-20) x (-1) (-10) x (-2) (-5) x (-4)

3) Now think about combinations that would work

(3x -20) (x -1) ; This would give you 3x² - 3x - 20x + 20.. The x term adds to -23x so this is not the solution

(3x -1) (x-20) ; = 3x² - 60x - x +20. The x term adds to -61x so this does not work

(3x-10) (x-2) ; = 3x² - 6x - 10x +20 The x term adds to -16x. This is the one we want.

So the expanded x term solutions is as follows

3x² - 6x - 10x +20

Factors: (3x-10)(x-2)

Hope this helps :)

Answer 2

3x² + 16x + 20 = 3x² + 6x + 10x + 20 = 3x(x + 2) + 10(x + 2) = (x + 2)(3x + 10)