Question

Factorise : 48x²-13x-1​

Answer 1

(3x-1)(16x+1)

Explanation:

`\tt 48x^2-13x-1`

we can factorize it by using middle factorization method

We need to find the two numbers that subtract up to 13 and multiply to 48.

and the two numbers are 16 and 3.

Th expression can be written as:

`\tt 48x^2-(16-3)x-1`

`\tt 48x^2-16x+3x-1`

taking common from each two terms

16x(3x-1)+1(3x-1)

again, taking common and keeping remaining on another bracket

(3x-1)(16x+1) is a factorized form.

Answer 2

`(16x+1)(3x-1)`

Explanation:

Given quadratic:

`48x^2-13x-1`

To factor a quadratic in the form ax² + bx + c, we first need to find two numbers that multiply to ac and sum to b.

The coefficients of the given quadratic are:

• a = 48
• b = -13
• c = -1

Therefore, the product of a and c is -48.

The factors pairs of -48 are:

• 1 × -48
• -1 × 48
• 2 × -24
• -2 × 24
• 3 × -16
• -3 × 16
• 4 × -12
• -4 × 12
• 6 × -8
• -6 × 8

Therefore, the two numbers that multiply to -48 and sum to -13 are 3 and -16.

Rewrite b as the sum of these two numbers:

`48x^2+3x-16x-1`

Factor the first two terms and the last two terms separately:

`3x(16x+1)-1(16x+1)`

Factor out the common term (16x + 1):

`(16x+1)(3x-1)`

Therefore, the given quadratic factored is:

`\large\boxed{\boxed{(16x+1)(3x-1)}}`