Answer:
(2x + 3)(3x - 7)
Explanation:
Factorize 6x² - 5x - 21
Find two numbers which are factors of the product of the coefficient of x² and the constant, and sum to the coefficient of x.
coefficient of x² mulitplied by the constant = 6 x -21 = -126
So we need to find two numbers that multiply together to make -126 and sum to -5.
Factors of -126 that sum to -5: 9 and -14
As 9 x -14 = -126, and 9 - 14 = -5
Rewrite the center term of the quadratic as these numbers, so - 5x becomes 9x - 14x:
⇒ 6x² + 9x - 14x - 21
Factorize each pair of terms, checking that the bracket created is the same:
⇒ 3x(2x + 3) - 7(2x + 3)
The first bracket is the common factor of (2x + 3) and the second bracket is the factorized terms outside of each bracket (3x - 7). So the final factorization is:
(2x + 3)(3x - 7)