In the equation x^2 + 10x + 24 = (x + a)(x + b), b is an integer. Find algebraically all possible values of b.
Mathematics · High School · Thu Feb 04 2021
Answered on
Given:
x^2 + 10x + 24 = (x + a) (x + b)
Find the possible values of b.
Solution:
n order to solve for the factorsof 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 10, and when multiplied, the answer is 24 Hence, if we are unable to find the number, we will use the quadratic formula.
In our case, the two factors that satisfy the equation are, (x + 4)(x + 6). To check if the factors is true, we simply apply 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.
= ( x + 4 ) ( x + 6 )
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)(6)
= 6x
First term of the first equation multiplied to the last term of the second equation.
=(4)(x)
=4x
Last term of the first equation multiplied to the first term of the second equation.
=(4)(6)
= 24
Last term of the first equation multiplied to the fast term of the second equation.
= x^2 + 6x + 4x + 24
= x^2 + 10x + 24
Final answer:
b = 4 or 6