x(x – 4) –21 splitting the middle term
Answers
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
x • (x - 4) - 21 = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring x2-4x-21
The first term is, x2 its coefficient is 1 .
The middle term is, -4x its coefficient is -4 .
The last term, "the constant", is -21
Step-1 : Multiply the coefficient of the first term by the constant 1 • -21 = -21
Step-2 : Find two factors of -21 whose sum equals the coefficient of the middle term, which is -4 .
-21 + 1 = -20
-7 + 3 = -4 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and 3
x2 - 7x + 3x - 21
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-7)
Add up the last 2 terms, pulling out common factors :
3 • (x-7)
Step-5 : Add up the four terms of step 4 :
(x+3) • (x-7)
Which is the desired factorization
Equation at the end of step
2
:
(x + 3) • (x - 7) = 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.
Step-by-step explanation:
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