divide by method of factorisation= 66(y^4-5y^3-24y^2)➗6y(y-8)
Answers
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
(((y4)-(5•(y3)))-(23•3y2))
((66•——————————————————————————)•y)•(y-8)
6
STEP
2
:
Equation at the end of step
2
:
(((y4)-5y3)-(23•3y2))
((66•—————————————————————)•y)•(y-8)
6
STEP
3
:
y4 - 5y3 - 24y2
Simplify ———————————————
6
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
y4 - 5y3 - 24y2 = y2 • (y2 - 5y - 24)
Trying to factor by splitting the middle term
4.2 Factoring y2 - 5y - 24
The first term is, y2 its coefficient is 1 .
The middle term is, -5y its coefficient is -5 .
The last term, "the constant", is -24
Step-1 : Multiply the coefficient of the first term by the constant 1 • -24 = -24
Step-2 : Find two factors of -24 whose sum equals the coefficient of the middle term, which is -5 .
-24 + 1 = -23
-12 + 2 = -10
-8 + 3 = -5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and 3
y2 - 8y + 3y - 24
Step-4 : Add up the first 2 terms, pulling out like factors :
y • (y-8)
Add up the last 2 terms, pulling out common factors :
3 • (y-8)
Step-5 : Add up the four terms of step 4 :
(y+3) • (y-8)
Which is the desired factorization
Equation at the end of step
4
:
y2•(y+3)•(y-8)
((66•——————————————)•y)•(y-8)
6
STEP
5
:
Equation at the end of step 5
(11y2 • (y + 3) • (y - 8) • y) • (y - 8)
STEP
6
:
Multiplying exponential expressions :
6.1 y2 multiplied by y1 = y(2 + 1) = y3
Equation at the end of step
6
:
11y3 • (y + 3) • (y - 8) • (y - 8)
STEP
7
:
Multiplying Exponential Expressions:
7.1 Multiply (y-8) by (y-8)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (y-8) and the exponents are :
1 , as (y-8) is the same number as (y-8)1
and 1 , as (y-8) is the same number as (y-8)1
The product is therefore, (y-8)(1+1) = (y-8)2
Final result :
11y3 • (y + 3) • (y - 8)2