Question

Factorise the following using splitting middle term:

a) a2

- 3a – 4​

Answer 1

Step-by-step explanation:

The first term is, a2 its coefficient is 1 .

The middle term is, -3a its coefficient is -3 .

The last term, "the constant", is -4

Step-1 : Multiply the coefficient of the first term by the constant 1 • -4 = -4

Step-2 : Find two factors of -4 whose sum equals the coefficient of the middle term, which is -3 .

-4 + 1 = -3 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 1

a2 - 4a + 1a - 4

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

a • (a-4)

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

1 • (a-4)

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

(a+1) • (a-4)

Which is the desired factorization

Answer 2

Step-by-step explanation:

a2 - 3a -4

= a2 -4a+a -4

=a(a-4) +1(a-4)

= (a-4)(a+1)

hence roots are a= -1,4