4x²+2y² -5xy from 15 -3y² + 120
Answers
Answer:
my dear friend your answer is
Step-by-step explanation:
Step by step solution :
STEP
1
:
Equation at the end of step 1
((0 - 2y2) + 11y) - 15 = 0
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
-2y2 + 11y - 15 = -1 • (2y2 - 11y + 15)
Trying to factor by splitting the middle term
3.2 Factoring 2y2 - 11y + 15
The first term is, 2y2 its coefficient is 2 .
The middle term is, -11y its coefficient is -11 .
The last term, "the constant", is +15
Step-1 : Multiply the coefficient of the first term by the constant 2 • 15 = 30
Step-2 : Find two factors of 30 whose sum equals the coefficient of the middle term, which is -11 .
-30 + -1 = -31
-15 + -2 = -17
-10 + -3 = -13
-6 + -5 = -11 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and -5
2y2 - 6y - 5y - 15
Step-4 : Add up the first 2 terms, pulling out like factors :
2y • (y-3)
Add up the last 2 terms, pulling out common factors :
5 • (y-3)
Step-5 : Add up the four terms of step 4 :
(2y-5) • (y-3)
Which is the desired factorization
Equation at the end of step
3
:
(3 - y) • (2y - 5) = 0
STEP
4
:
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.