Question

Which is the factored form of a^2 - 10a + 25?

(a + 5)^2
(a - 5)^2
(a + 5)(a - 5)
(a -10)(a - 2)

Answer 1

@phi

Answer 2

you could test each choice (multiply them out)
or
you could factor a^2 - 10a + 25

Answer 3

how do you factor

Answer 4

Factoring: Finding what to multiply together to get an expression.

Answer 5

It is like "splitting" an expression into a multiplication of simpler expressions.

Answer 6

yeah but still dont understand??

Answer 7

I do factor like this for quadratics like yours
1) look at the last number +25
the + sign means the factors will HAVE THE SAME SIGN
- would mean the factors will have different signs.

list all pairs of numbers that when you multiply them you get 25:
1,25
5,5
(easy for this problem. For a test try listing the pairs for 60)

2) look at the "middle" number: -10 (ignore the a)
the - sign means the bigger factor is negative

From step 1, make the bigger number minus, and because the factors have the SAME SIGN, make the smaller number minus also. Then add up each pair:

-1 - 25 = -26
-5 - 5 = -10

3) if any of the sums add up to the middle number, you found the factors.

in this case, -5 and -5
write down the answer
(a-5)(a-5)

4) to check, multiply it out using FOIL