Question

factor completely. \\(2h^2 - 7h + 5\\)

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(2\times5 = 10\) and add up to \(- 7\). The numbers are \(-2\) and \(-5\) since \((-2)\times(-5)=10\) and \((-2)+(-5)=-7\).

Step2: Rewrite the middle term

Rewrite \(-7h\) as \(-2h-5h\) in the polynomial:
\(2h^{2}-2h - 5h + 5\)

Step3: Group the terms

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

Step4: Factor out the GCF from each group

Factor out \(2h\) from the first group and \(- 5\) from the second group:
\(2h(h - 1)-5(h - 1)\)

Step5: Factor out the common binomial factor

Factor out \((h - 1)\) from both terms:
\((2h - 5)(h - 1)\)

Answer:

\((2h - 5)(h - 1)\)