Question

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

Answer 1

Answer:

$a {}^{2} + 19a + 78 \\ + a {}^{2} - 59a \\ - 58a$

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Answer 2

Step-by-step explanation:

The first term is, x2 its coefficient is 1 .

The middle term is, -19x 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

x2 - 13x - 6x - 78

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

x • (x-13)

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

6 • (x-13)

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

(x-6) • (x-13)

Which is the desired factorization