Question

2b $2x^2 - 13x + 15$ common factor

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(2\times15 = 30\) and add up to \(-13\). The numbers are \(-10\) and \(-3\) since \((-10)\times(-3)=30\) and \(-10 + (-3)=-13\).

Step2: Rewrite the middle term

Rewrite \(-13x\) as \(-10x - 3x\) in the expression:
\(2x^{2}-10x - 3x + 15\)

Step3: Group the terms

Group the first two and the last two terms:
\((2x^{2}-10x)+(-3x + 15)\)

Step4: Factor out the common factors

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

Step5: Factor out the common binomial factor

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

Answer:

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