Question

1. factor: $6x^2 - x - 15$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(6\times(-15)= -90\) and add up to \(-1\). The numbers are \(-10\) and \(9\) since \(-10\times9 = -90\) and \(-10 + 9=-1\).

Step2: Rewrite the middle term

Rewrite \(-x\) as \(-10x + 9x\) in the expression:
\(6x^{2}-10x + 9x-15\)

Step3: Group the terms

Group the first two and the last two terms:
\((6x^{2}-10x)+(9x - 15)\)

Step4: Factor out the GCF from each group

Factor out \(2x\) from the first group and \(3\) from the second group:
\(2x(3x - 5)+3(3x - 5)\)

Step5: Factor out the common binomial factor

Factor out \((3x - 5)\):
\((2x + 3)(3x - 5)\)

Answer:

\((2x + 3)(3x - 5)\)