Which is a factor of x2 + 8x – 48?
Mathematics · High School · Sun Jan 24 2021
Answered on
Given the quadratic equation:
x^2 + 8x - 48
Determine the factors of the equation.
Solution:
In order to solve for the factors of an equation, we simply must look at the 2nd and 3rd value. First we must think of two numbers that when added, the answer is 8, and when multiplied, the answer is -48. Hence, if we are unable to find the number, we will use the quadratic formula.
The numbers that satisfy the equation are, -12 and 4. It can be written as,
( x + 12) ( x - 4 )
In order to prove the factors are true, we will use the FOIL Method. Multiply the first term of the first equation, to the first and last term of the second equation. Then, multiply the last term of the first equation, to the first and last term of the second equation.
To clearly see how it works, here's a step by step solution.
= (x)(x)
=x^2
First term of the first equation multiplied to the first term of the second equation.
=(x)(-4)
= -4x
First term of the first equation multiplied to the last term of the second equation.
=(12)(x)
= 12x
Last term of the first equation multiplied to the first term of the second equation.
=(12)(-4)
= -48
Last term of the first equation multiplied to the fast term of the second equation.
= x^2 - 4x + 12x - 48
= x^2 + 8x - 48
Final answer:
x = -12
x = 4