Rewrite the middle term as the sum of two terms and then factor by grouping.
x2 – 2x – 63
Factor. 9x(x – 7y) – 6(x – 7y)
Factor completely. x^2+8x+15
Rewrite the middle term as the sum of two terms and then factor completely.
To rewrite the middle term as the sum of two terms and then factor by grouping, we need to identify two numbers that multiply to give us the product of the first and last terms (the coefficients of x^2 and the constant term) and also add up to give us the coefficient of the middle term.
For the expression x^2 - 2x - 63, the product of the first and last terms is (-63)(1) = -63, and the coefficient of the middle term is -2. We need to find two numbers that multiply to give -63 and add up to -2.
The two numbers that satisfy this condition are -9 and 7.
So, we can rewrite the middle term -2x as -9x + 7x.
Now, let's factor by grouping:
x^2 - 2x - 63
= x^2 - 9x + 7x - 63
= (x^2 - 9x) + (7x - 63)
= x(x - 9) + 7(x - 9)
= (x + 7)(x - 9)
Therefore, the expression x^2 - 2x - 63 can be factored as (x + 7)(x - 9).