Factorise the equation 6x2-5x-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.
Step 1: Multiply the first term by the constant term, i.e., (6x2 and -6) = -36x2
Step 2: Find the two factors of -36x2 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 = -36x2
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).