c^2 - 4c - 32
I got
(c - 4) (c - 8)
but i think its wrong because the do not match to make it squared, what am I doing wrong?
Nothing gets squared. When you "FOIL" multiply your factors, you do not get the right polynomial. That must be what you mean.
The correct factors are (c+4)(c-8). One of the constants has to be odd and the other has to be even to get -32 as the last term.
Factor Completely: 2x2 - 32
7-3b/b^2-12b+20
To factor the expression c^2 - 4c - 32 correctly, you need to identify two numbers that multiply to -32 (the last term) and add up to -4 (the coefficient of the middle term).
In this case, the correct factorization is (c - 8)(c + 4).
To understand why, let's break it down step by step:
1. We know that the first term of the factorization will be (c - __) (c + __), where the blanks will be filled with the factors of c^2. So, we need two numbers that multiply to give c^2.
2. The coefficient of c^2 is 1, which means c^2 = c × c. Therefore, the first term will be (c - __) (c + __).
3. Since the middle term is -4c, we need to find two numbers that add up to -4 and also multiply to -32 (the product of the first and last terms). The factors of -32 are: -1 × 32, 1 × -32, -2 × 16, 2 × -16, -4 × 8, and 4 × -8.
Among these, -4 × 8 = -32 and -4 + 8 = 4 is the pair that satisfies both conditions.
4. Therefore, we can replace the blanks in the first term with -8 and -4. The factorization becomes (c - 8)(c - 4).
So, your original factorization (c - 4)(c - 8) is almost correct—you just need to switch the order of the factors for it to be accurate.