factorise (y²+2y-3)÷(y-1)
Answers
Answer:
y +3
Step-by-step explanation:
The first term is, y2 its coefficient is 1 .
The middle term is, +2y its coefficient is 2 .
The last term, "the constant", is -3
Step-1 : Multiply the coefficient of the first term by the constant 1 • -3 = -3
Step-2 : Find two factors of -3 whose sum equals the coefficient of the middle term, which is 2 .
-3 + 1 = -2
-1 + 3 = 2 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -1 and 3
y2 - 1y + 3y - 3
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 :
3 • (y-1)
Step-5 : Add up the four terms of step 4 :
(y+3) • (y-1)
Which is the desired factorization
Cancel out (y-1) which appears on both sides of the fraction line.
Final result :
y + 3
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