Question

what will be the factors of
6x² - 13x +5.?
​

Answer 1

Answer:

$6x ^{2} - 10x - 3x + 5 \\ 2x(3x - 5) - 1(3x - 5) \\ (2x - 1) \: (3x - 5) \\ x = \frac{1}{2} \: and \: x = \frac{5}{3}.$

Answer 2

Step-by-step explanation:

We have 6x² - 13x + 5

We can factor it by middle term splitting.

Step 1. Multiply the coefficient of x² with "c" term (here, coefficient is 6 and c=5).

Therefore, 6 x 5 = 30

Step 2. Check the sign in front of "c" term and then find sum or difference accordingly.

Here, it is (+) sign so we will find sum.

Find two numbers that when multiply equals the number obtained in step 1 (30) and when added equals the coefficient of x (here, 13).

Those numbers are 10 and 3.

As 10 x 3 = 30 and 10 + 3 = 13.

Step 3. Substitute the coefficient of x with your new numbers 10 and 3.

You can see that 10 + 3 = 13, so we can replace 13 with 10 + 3.

Step 4. We do that,

Therefore, 6x² - (10 + 3) x+ 5

= 6x² - 10x - 3x + 5

( You can factor out some terms)

> 2x (3x - 5) + 1 (3x + 5)

Taking (3x + 5) common

= (2x + 1) (3x + 5)

That is the answer.