Question

Factor completely the trinomial 10x^2 + 19x + 7

Answer 1

From the problem :

$10x^2+19x+7$

Factor completely :

We need to find the factors of 10 and 7

We have :

10 = 1 x 10

10 = 2 x 5

7 = 1 x 7

We will do trial and error, The sum of the product of the factors must be equal to the middle term which is 19

Let's say for 10 = 1 x 10 and 7 = 1 x 7

(1 x 7) + (1 x 10) = 17 not equal to 19

(7 x 10) + (1 x 1) = 71 not equal to 19

try the other factors of 10.

10 = 2 x 5 and 7 = 1 x 7

(2 x 7) + (5 x 1) = 19 Equal to 19

Now we have the factors, let's arrange in this way :

$(O+I)(I+O)$

O will be the outer and I will be the inner.

O is the paired factors of 10 and 7

For O, we have 2 and 7

For I, we have 5 and 1

This will be :

$(2x+5)(x+7)$

The answer is (2x + 5)(x + 7)