Q12.

Factor each polynomial.

$6 x^{2} - 5 x - 4$

Verified

Answer

The factors of given polynomial are $(3 x - 4) (2 x + 1)$ .

1Step 1. Find the GCF.

Find the GCF of $6 x^{2}, 5 x$ and 4.

$6 x^{2} = 1 \cdot 2 \cdot 3 \cdot x \cdot x 6 x^{2} = 1 \cdot 2 \cdot 3 \cdot x \cdot x 4 = 1 \cdot 2 \cdot 2$

Therefore, GCF is 1.

2Step 2. Apply factoring pattern of a x 2 + b x + c .

There are two numbers having product of 24 and sum of $- 5$ . The numbers are $3$ and $- 8$ .

$6 x^{2} + m x + n x - 4 = 6 x^{2} + 3 x - 8 x - 4$

3Step 3. Group terms with common factors and factor out GCF.

Group terms with common factors and factor out GCF from each grouping.

$\begin{matrix} (6 x^{2} + 3 x) + (- 8 x - 4) = 3 x (2 x + 1) - 4 (2 x + 1) \\ = (3 x - 4) (2 x + 1) \end{matrix}$

Therefore, the factors of $6 x^{2} - 5 x - 4$ are $(3 x - 4) (2 x + 1)$ .