Question

factor the polynomial: $5x^2 - 15x + 6$
options:
$(x + 2)(5x + 3)$
$(x + 3)(5x - 2)$
$(x - 2)(5x - 3)$
$(x - 3)(5x + 2)$

Explanation:

Step1: Identify coefficients

For $5x^2 -13x +6$, $a=5$, $b=-13$, $c=6$

Step2: Find product $a \times c$

$a \times c = 5 \times 6 = 30$

Step3: Find factor pair of 30

Find two numbers that multiply to 30 and add to $-13$: $-10$ and $-3$

Step4: Split middle term

$5x^2 -10x -3x +6$

Step5: Factor by grouping

$$\begin{align} &5x(x-2) -3(x-2) \\ &=(x-2)(5x-3) \end{align}$$

Answer:

$(x - 2)(5x - 3)$