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
