Answer:
x 2 + 7 x − 8 = ( x − 1 ) ( x + 8 )
Step-by-step explanation:
Given
x 2 + 7 x − 8
Note that the sum of the coefficients is 0
That is 1 + 7 − 8 = 0
So x = 1 is a zero and ( x − 1 )
a factor: x 2 + 7 x − 8 = ( x − 1 ) ( x + 8 )
The linear factor ( x + 8 ) can be constructed by looking at the coefficients of
x 2 and the constant term − 8
that we want in the product:
Since the coefficient of x 2 is 1 in the product, we require a coefficient
1 for x
Since the constant term is − 8 in the product, we require a constant + 8
in the factor which will become − 8 when multiplied by − 1
