STEP - STEP EXPLANATION:
Trying to factor by splitting the middle term
Factoring 4x2-19x-5
The first term is, 4x2 its coefficient is 4 .
The middle term is, -19x its coefficient is -19 .
The last term, "the constant", is -5
Step-1 : Multiply the coefficient of the first term by the constant 4 • -5 = -20
Step-2 : Find two factors of -20 whose sum equals the coefficient of the middle term, which is -19 .
-20 + 1 = -19 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -20 and 1
4x2 - 20x + 1x - 5
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (x-5)
Add up the last 2 terms, pulling out common factors :
1 • (x-5)
Step-5 : Add up the four terms of step 4 :
(4x+1) • (x-5)
Which is the desired factorization
Equation at the end of step
2
:
(x - 5) • (4x + 1) = 0
STEP
3
:
Theory - Roots of a product
3.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
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