Question

5x² - 14x + 9

Explanation:

Step1: Find two numbers that multiply to \(5\times9 = 45\) and add up to \(-14\). The numbers are \(-5\) and \(-9\) since \((-5)\times(-9)=45\) and \(-5 + (-9)=-14\).

Rewrite the middle term using these numbers: \(5x^{2}-5x - 9x + 9\)

Step2: Group the first two terms and the last two terms: \((5x^{2}-5x)+(-9x + 9)\)

Step3: Factor out the greatest common factor (GCF) from each group. From the first group, GCF is \(5x\), so \(5x(x - 1)\). From the second group, GCF is \(-9\), so \(-9(x - 1)\)

Now we have: \(5x(x - 1)-9(x - 1)\)

Step4: Factor out the common binomial factor \((x - 1)\): \((x - 1)(5x - 9)\)

Answer:

\((x - 1)(5x - 9)\)