Respuesta :
Answer: y = − 12 + 2 √ 43 , − 12 - 2√ 43
Step-by-step explanation:
Answer: 2⋅(y+3)⋅(y−6)
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Exsplanation
2
1
See steps
Step by Step Solution:
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STEP
1
:
10y
Simplify ————————————
y2 - 3y - 18
Trying to factor by splitting the middle term
1.1 Factoring y2 - 3y - 18
The first term is, y2 its coefficient is 1 .
The middle term is, -3y its coefficient is -3 .
The last term, "the constant", is -18
Step-1 : Multiply the coefficient of the first term by the constant 1 • -18 = -18
Step-2 : Find two factors of -18 whose sum equals the coefficient of the middle term, which is -3 .
-18 + 1 = -17
-9 + 2 = -7
-6 + 3 = -3 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 3
y2 - 6y + 3y - 18
Step-4 : Add up the first 2 terms, pulling out like factors :
y • (y-6)
Add up the last 2 terms, pulling out common factors :
3 • (y-6)
Step-5 : Add up the four terms of step 4 :
(y+3) • (y-6)
Which is the desired factorization
Equation at the end of step
1
:
10y
————————————————— ÷ 5y ÷ (4y - 24)
(y + 3) • (y - 6)
STEP
2
:
10y
Divide ——————————— by 5y
(y+3)•(y-6)
Canceling Out :
2.1 Canceling out y as it appears on both sides of the fraction line
Equation at the end of step
2
:
2
————————————————— ÷ (4y - 24)
(y + 3) • (y - 6)
STEP
3
:
2
Divide ——————————— by 4y-24
(y+3)•(y-6)
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
4y - 24 = 4 • (y - 6)
Multiplying Exponential Expressions:
4.2 Multiply (y - 6) by (y - 6)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (y-6) and the exponents are :
1 , as (y-6) is the same number as (y-6)1
and 1 , as (y-6) is the same number as (y-6)1
The product is therefore, (y-6)(1+1) = (y-6)2
Final result :
1
——————————————————————
2 • (y + 3) • (y - 6)2
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