Learn Factorise The Equation 6x2 5x 6

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# Factorise the equation 6x^{2}-5x-6.

A quadratic expression is a polynomial of degree 2.** **We use the middle term factorization to solve this problem.

## Answer: The factors of 6x² - 5x- 6 are (2x-3) (3x+2)

Let us proceed by using middle term factorization.

**Explanation**:

Step 1: Multiply the first term by the constant term, i.e., (6x^{2} and -6) = -36x^{2}

Step 2: Find the two factors of -36x^{2} such that their sum is equal to the middle term, i.e., -5x.

Hence, two such factors are -9x and 4x

The product of -9x and 4x = -36x^{2}

The sum of -9x and 4x = -5x

Thus, by splitting the middle term we have,

6x² - 9x + 4x - 6=0.

⇒ 3x(2x-3) + 2(2x-3) = 0

⇒ (2x-3)(3x+2) = 0

### Thus, the factors of 6x² - 5x - 6 are (2x-3) (3x+2).

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