How do you factor?

Question

Im in math A30 and i dont remeber how, so like can someone explain these few questions to me, that would be really awesome...

20+6x-2x^2 (i know that you change it to -2x^2+6x+20 but then what)

and the other one is.... x^2+16x+64

Can anyone help?

but what if there its like this...
20a^3+54a^2-56a
2a(10a^2+27a-28) then what happends with the 10?

Answer 1

-2x^2 + 6x + 20
= -2(x^2 - 3x - 10)
= -2 (x - 5)(x + 2) --> you have to find two numbers that multiply to 10 and add to 3

x^2 + 16x + 64
= (x + 8) (x + 8) --> you have to find two numbers that multiply to 64 and add to 16
= (x + 8)^2

In general if you have ax^2 + bx + c, then you want to put the equation in the form:
a(x^2 + (b/a)x + (c/a))
= a(x + ?)(x + ?)

To figure out the question marks, you need to find two numbers that multiply to give you (c/a) and add to give you (b/a). You can do this by trial and error. Note that sometimes the numbers may be the same, and sometimes they might not be the same.

Good luck!

=)

Answer 2

20 + 6x - 2x^2
-2x^2 + 6x + 20
-2(x^2 - 3x - 10)
-2(x - 5)(x + 2)

and the other one is.... x^2+16x+64

x^2 + 16x + 64
(x + 8)^2 or (x + 8)(x + 8)

20a^3 + 54a^2 - 56a
(2a)(10a^2 + 27a - 28)
(2a)(2a + 7)(5a - 4)

Answer 3

Well lets look at the last one since it is the easier of the two. You first have to setup your brackets, since your x^2 value has no coefficent you can safely assume that the x value in each of the brackets is just an x, (x _ _)(x _ _) and since the middle and end value are both positive you can assume that both the factors will be a +. (x+_)(x+_). Now you must find two factors of 64 that when are added together will give you 16. Or you can use the Quradratic formula. A is the coefficent infront of x^2, b is infront of x, and c is the last number. -b+or- the sq. root of (b^2-4ac) then divide all of that by 2a.

Answer 4

20+6x-2x^2 = -2 (x - 5) (x + 2) (by founding the roots)
x^2+16x+64 = (x + 8)^2 (notable case)

Answer 5

in the first one its gonna be like this: -2x^2+6x+20 you have to multibly it by -1 then divided it by 2 to simblify it so its gonna be like this: x^2-3-10 then (x-5)(x+2) so the answe is x=5 or x=-2, the second one will be (x+8)(x+8) & the answer is x=-8

Answer 6

calculator