Question

Factorise: 2a2 − 7a − 15

Answer 1

STEP

1

:

Equation at the end of step 1

(2a2 - 7a) - 15

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring 2a2-7a-15

The first term is, 2a2 its coefficient is 2 .

The middle term is, -7a its coefficient is -7 .

The last term, "the constant", is -15

Step-1 : Multiply the coefficient of the first term by the constant 2 • -15 = -30

Step-2 : Find two factors of -30 whose sum equals the coefficient of the middle term, which is -7 .

-30 + 1 = -29

-15 + 2 = -13

-10 + 3 = -7 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and 3

2a2 - 10a + 3a - 15

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

2a • (a-5)

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

3 • (a-5)

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

(2a+3) • (a-5)

Which is the desired factorization

Final result :

(a - 5) • (2a + 3)

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