Question

Factorise: a² + 19a + 78 using middle term splitting method​

Answer 1

Step-by-step explanation:

Correct Question :-

Factorise a² + 19a + 78

Solution:-

Factoring a²-19a+78

The first term is, a² its coefficient is 1 .

The middle term is, -19a its coefficient is -19 .

The last term, "the constant", is +78

Step-1 : Multiply the coefficient of the first term by the constant 1 • 78 = 78

Step-2 : Find two factors of 78 whose sum equals the coefficient of the middle term, which is -19 .

-78 + -1 = -79

-39 + -2 = -41

-26 + -3 = -29

-13 + -6 = -19 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -13 and -6

a² - 13a - 6a - 78

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

a • (a-13)

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

6 • (a-13)

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

(a-6) • (a-13)

Which is the desired factorization

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