Question

factorise the following expression 7a^2-19-6​

Answer 1

Answer:

7a - 2) • (a + 3)

Step-by-step explanation:

Step by Step Solution:

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Reformatting the input :

Changes made to your input should not affect the solution:

(1): "a2" was replaced by "a^2".

STEP

1

:

Equation at the end of step 1

(7a2 + 19a) - 6

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring 7a2+19a-6

The first term is, 7a2 its coefficient is 7 .

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

The last term, "the constant", is -6

Step-1 : Multiply the coefficient of the first term by the constant 7 • -6 = -42

Step-2 : Find two factors of -42 whose sum equals the coefficient of the middle term, which is 19 .

-42 + 1 = -41

-21 + 2 = -19

-14 + 3 = -11

-7 + 6 = -1

-6 + 7 = 1

-3 + 14 = 11

-2 + 21 = 19 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 21

7a2 - 2a + 21a - 6

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

a • (7a-2)

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

3 • (7a-2)

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

(a+3) • (7a-2)

Which is the desired factorization

Final result :

(7a - 2) • (a + 3)