How To Factorize X²+3X-88: A Step-By-Step Guide

x²+3x-88

(x+11)(x-8)

To factorize x²+3x-88, we need to find two numbers that add up to 3 and multiply to -88. One way to do this is to list all pairs of factors of -88 and find the pair that adds up to 3:

-1, 88 -> -1 + 88 ≠ 3
-2, 44 -> -2 + 44 ≠ 3
-4, 22 -> -4 + 22 ≠ 3
-8, 11 -> -8 + 11 = 3

So, we can write x²+3x-88 as (x-8)(x+11). This is the factored form of the expression.

Alternatively, we can use the quadratic formula to find the roots of the equation and then factorize it using the roots. The quadratic formula gives us:

x = (-b ± √(b²-4ac)) / 2a

where a=1, b=3, and c=-88. Substituting these values, we get:

x = (-3 ± √(3²-4(1)(-88))) / 2(1)
x = (-3 ± √(9+352)) / 2
x = (-3 ± √361) / 2
x = (-3 ± 19) / 2

So the roots are x = -11 and x = 8. Thus, we can write:

x²+3x-88 = (x+11)(x-8)

which is the factored form of the expression.

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