factorise 6 - 5y - y²
Answers
Step-by-step explanation:
factorise 6 - 5y - y²
Step by Step Solution
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Reformatting the input :
Changes made to your input should not affect the solution:
(1): "y2" was replaced by "y^2".
STEP
1
:
STEP
2
:
Pulling out like terms
2.1 Pull out like factors :
-y2 - 5y + 6 = -1 • (y2 + 5y - 6)
Trying to factor by splitting the middle term
2.2 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 = -5
-3 + 2 = -1
-2 + 3 = 1
-1 + 6 = 5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -1 and 6
y2 - 1y + 6y - 6
Step-4 : Add up the first 2 terms, pulling out like factors :
y • (y-1)
Add up the last 2 terms, pulling out common factors :
6 • (y-1)
Step-5 : Add up the four terms of step 4 :
(y+6) • (y-1)
Which is the desired factorization
Final result :
(-y - 6) • (y - 1)
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Answer:
6-5y-y2
=6-6y+y-y2
=6(1-y)+y(1-y)
=(1-y)(6+y)