Factor the trinomial x2+6x-27
Mathematics · Middle School · Sun Jan 24 2021
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Given the quadratic equation:
x^2 + 6x - 27
Factor the trinomial.
Solution:
In order to solve for the roots of an equation or factor the equation completely, we simply must look at the 2nd and 3rd value. First we must think of two numbers that when added, the answer is 6, and when multiplied, the answer is -27. Hence, if we are unable to find the number, we will use the quadratic formula.
The numbers that satisfy this equation are -9 and 3. It can be represented as,
(x + 9) ( x - 3)
To determine if the factors are true, we solve for its product by doing 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)(-3)
= -3x
First term of the first equation multiplied to the last term of the second equation.
=(9)(x)
=9x
Last term of the first equation multiplied to the first term of the second equation.
=(9)(-3)
= -27
Last term of the first equation multiplied to the fast term of the second equation.
= x^2 - 3x + 9x - 27
= x^2 + 6x - 27
Final answer:
= x^2 + 6x - 27