Answer:
C. x-2
Step-by-step explanation:
x² + 7x - 18 = 0
the factor must be p and q from the form.of
(x+p)(x+q) = 0
then find the value of p and q by this rules
p + q = 7
p x q = -18
p = 9
q = -2
(x + 9)(x + (-2)) = 0
(x+9)(x-2) = 0
Answer:
c.) [tex](x-2)[/tex]
Step-by-step explanation:
The given expression is written in the form [tex]ac^2+bx+c[/tex]. To factor, find two numbers whose sum is b and whose product is c:
_×_=-18
_+_=7
Use -2 and 7:
-2×9=-18
-2+9=7
Substitute the two numbers for b:
[tex]x^2-2x+9x-18[/tex]
[tex](x^2-2x)+(9x-18)[/tex]
Factor out common terms. The common term in the first parentheses is x and the common term in the second is 9:
[tex]x(\frac{x^2-2x}{x} )+9(\frac{9x-18}{9})\\\\x(x-2)+9(x-2)[/tex]
Cancel out one of the parentheses since they have the same terms and plug the factored numbers in:
[tex](x-2)(x+9)[/tex]
:Done
Check Your Work:
To see if the given factored form is true, simplify it using FOIL:
First, Outside, Inside, Last
[tex](x-2)(x+9)[/tex]
Multiply the first terms:
[tex]x*x=x^2[/tex]
Multiply the terms on the outside:
[tex]x*9=9x\\\\x^2+9x[/tex]
Multiply the inside terms:
[tex]-2*x=-2x\\\\x^2+9x-2x[/tex]
Multiply the last terms:
[tex]-2*9=-18\\\\x^2+9x-2x-18[/tex]
Combine like terms:
[tex]x^2+(9x-2x)-18\\\\x^2+7x-18[/tex]
Therefore, the factored form is true.
