Question

Factor the expression 6x^2 + 5x + 1

Answer 1

(2x + 1)(3x + 1)

Explanation:

Given

6x² + 5x + 1

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 6 × 1 = 6 and sum = + 5

The factors are + 3 and + 2

Use these factors to split the x0 term

6x² + 3x + 2x + 1 ( factor the first/second and third/fourth terms )

= 3x(2x + 1) + 1 (2x + 1) ← factor out (2x + 1) from each term

= (2x + 1)(3x + 1) ← in factored form

Answer 2

The factors are (3x+1)(2x+1)

Explanation:

The expression is:

6x^2 + 5x + 1

We have to break the middle term to find its factors. For this first we have to multiply the coefficient of 1st terms with the constant term:

6*1 = 6

Now we have to find any two numbers whose product is 6 and whose sum is the middle term:

3*2=6

3+2=5

Now break the middle term by these two numbers.

6x^2 + 5x + 1

6x^2+3x+2x+1

Group the first two terms and last two terms:

(6x^2+3x)+(2x+1)

Now take out common factor from each term:

3x(2x+1)+1(2x+1)

(3x+1)(2x+1)

Therefore the factors are (3x+1)(2x+1)....