more factoring? :-\?

Question

Ok, so im stuck on these factoring problems..

One of which I thought I did correctly, but im not sure. can anyone help? if so, that would be great. thankyou.

1) 2x^2+12x+16
For this, I got the answer: 2(x+6)(x+8) is this correct or incorrect?

2) 5x^4+40x^3+75x^2

3) 2x^3+42x^2+40x

Answer 1

1) 2(x+4)(x+2)
2) 5x^2(x+5)(x+3)
3) 2(x+20)(x+1)

Answer 2

1. Not correct. Taking out the 2, we have 2(x*2 + 6x + 8), and the paren expression is by inspection (x + 2)(x + 4). So the final result is 2(x + 2)(x + 4).

2. Take out 5x^2, to get 5x^2(x^2 + 8x + 15). The paren expression is by inspection (x + 3)(x + 5). I will let you do the final step.

3. Take out 2x to get 2x(x^2 + 21x +20). The paren expression is in this case (x + 1)(x + 20). You take it from here.

Notice that in all of these, the trick in factoring the quadratic is to look for two numbers whose sum (or difference, depending on the signs) matches the linear term and whose product matches the constant term. If it is not obvious what such numbers are, you can always determine them by using the quadratic formula: if the roots are r1 and r2, the factors are (x - r1)(x - r2). If the roots are complex, it is common to say that the quadratic expression is prime.

Answer 3

[1]
2x^2 + 12x + 16
(2x + 4)(x + 4)
2(x + 2)(x + 4)

[2]
5x^4 + 40x^3 + 75x^2
5x^2(x^2 + 8x + 15)
5x^2(x + 5)(x + 3)

[3]
2x^3 + 42x^2 + 40x
2x(x^2 + 21x + 20)
2x(x + 20)(x + 1)