Expression?

Question

Can't remember how to do this kind of factoring...help please??
4x^2+20x+25

There's also this one...
10x^2-21x-10

But I think it's the same idea as the other one.

Answer 1

4x^2 + 20x + 25
25 is perfect square so 5 is going to be in there
25 is also positive so signs of both 5's is positive
(x +5) (x + 5)
x's have to multiply to form 4x^2
factor of 4 is 2
so
(2x + 5) (2x + 5)
or
(2x + 5)^2

10x^2 - 21x -10
factors of ten 1, 2, 5, 10
(5x + 2) (2x - 5)
is only way that works
5x * 2x = 10x^2
2*2x -5*5x = -21x
and 2 * -5 = -10
so
(5x + 2) (2x - 5)

Answer 2

In the first, recognize that the first and last terms are perfect squares. so the first thing to try is (2x + 5)^2 and check the middle term. Here you are lucky, since the middle term is 10x + 10x = 20x.

The second you must do by trial and error, finding numbers whole product are 10 and sums/difference are 21. You should get (5x+2)*(2x-5) = 10x - 21x - 10

Answer 3

use the FOIL method backwards.
(a+b)(c+d)
a * c should equal the x^2 term, b*c + a*d should equation the x term and b*d should equal the numeric term.

for example: (2x+5)(2x+5) or (2x+5)^2

Answer 4

(4 + 5x) ( 1 + 5x) is the first one.