Factorize :
3x2 − x − 4
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Answers
Step-by-step explanation:
Step 1 :
Equation at the end of step 1 :
(3x2 - x) - 4 = 0
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 3x2-x-4
The first term is, 3x2 its coefficient is 3 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -4
Step-1 : Multiply the coefficient of the first term by the constant 3 • -4 = -12
Step-2 : Find two factors of -12 whose sum equals the coefficient of the middle term, which is -1 .
-12 + 1 = -11
-6 + 2 = -4
-4 + 3 = -1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 3
3x2 - 4x + 3x - 4
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (3x-4)
Add up the last 2 terms, pulling out common factors :
1 • (3x-4)
Step-5 : Add up the four terms of step 4 :
(x+1) • (3x-4)
Which is the desired factorization
Equation at the end of step 2 :
(3x - 4) • (x + 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.
Solving a Single Variable Equation :
3.2 Solve : 3x-4 = 0