Divide: (35x2y2 – 42xy2) ÷ 7y2
Answers
Step-by-step explanation:
STEP1:Equation at the end of step 1
(7y2 - 35y) + 42 = 0
STEP2:
STEP3:Pulling out like terms
3.1 Pull out like factors :
7y2 - 35y + 42 = 7 • (y2 - 5y + 6)
Trying to factor by splitting the middle term
3.2 Factoring y2 - 5y + 6
The first term is, y2 its coefficient is 1 .
The middle term is, -5y its coefficient is -5 .
The last term, "the constant", is +6
Step-1 : Multiply the coefficient of the first term by the constant 1 • 6 = 6
Step-2 : Find two factors of 6 whose sum equals the coefficient of the middle term, which is -5 .
-6 + -1 = -7 -3 + -2 = -5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and -2
y2 - 3y - 2y - 6
Step-4 : Add up the first 2 terms, pulling out like factors :
y • (y-3)
Add up the last 2 terms, pulling out common factors :
2 • (y-3)
Step-5 : Add up the four terms of step 4 :
(y-2) • (y-3)
Which is the desired factorization
Equation at the end of step3:
7 • (y - 2) • (y - 3) = 0
STEP4:Theory - Roots of a product
4.1 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.