Question

1. $8x^2 - 10x + 3$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(8\times3 = 24\) and add up to \(- 10\). The numbers are \(-6\) and \(-4\) since \((-6)\times(-4)=24\) and \(-6 + (-4)=-10\).

Step2: Rewrite the middle term

Rewrite \(-10x\) as \(-6x-4x\) in the quadratic expression:
\(8x^{2}-6x - 4x+3\)

Step3: Group the terms

Group the first two terms and the last two terms:
\((8x^{2}-6x)+(-4x + 3)\)

Step4: Factor out the GCF from each group

Factor out \(2x\) from the first group and \(-1\) from the second group:
\(2x(4x - 3)-1(4x - 3)\)

Step5: Factor out the common binomial factor

Now, factor out \((4x - 3)\) from both terms:
\((2x - 1)(4x - 3)\)

Answer:

\((2x - 1)(4x - 3)\)