Which polynomial has factors of 4x – 7 and x + 4? A) 3x^2 + x – 3 B) 4x^2 + 9x – 28 C) 3x^2 – 7x – 3 D) 4x^2 – 23x – 28
Mathematics · Middle School · Wed Jan 13 2021
Answered on
Given the equation:
4x - 7
x + 4
Determine the polynomial equivalent of the factors.
Solution:
In order to determine the polynomial equivalent of the factors, we simply needed to 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.
= (4x)(x)
=4x^2
First term of the first equation multiplied to the first term of the second equation.
=(4x)(4)
= 16x
First term of the first equation multiplied to the last term of the second equation.
=(-7)(x)
=-7x
Last term of the first equation multiplied to the first term of the second equation.
=(-7)(4)
= -28
Last term of the first equation multiplied to the fast term of the second equation.
= 4x^2 + 16x - 7x - 28
= 4x^2 + 9x - 28
Final answer:
= 4x^2 + 9x - 28