Question

Find the factors of the polynomials given below.
(i) 3y2-2y-1
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Answer 1

Answer:

Factoring 3y2-2y-1

The first term is, 3y2 its coefficient is 3 .

The middle term is, -2y its coefficient is -2 .

The last term, "the constant", is -1

Step-1 : Multiply the coefficient of the first term by the constant 3 • -1 = -3

Step-2 : Find two factors of -3 whose sum equals the coefficient of the middle term, which is -2 .

-3 + 1 = -2 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and 1

3y2 - 3y + 1y - 1

Step-4 : Add up the first 2 terms, pulling out like factors :

3y • (y-1)

Add up the last 2 terms, pulling out common factors :

1 • (y-1)

Step-5 : Add up the four terms of step 4 :

(3y+1) • (y-1)

Which is the desired factorization

Answer 2

Step-by-step explanation:

3y2 – 2y – 1

⟹ 3y2 – 3y + y – 1

⟹ 3y (y - 1) + 1 (y - 1)

⟹ (3y + 1) (y – 1)

Therefore, the factors of the given polynomial = (3y + 1) (y – 1)