Question

factor by grouping.
10r² - 29r + 10

10r² - 29r + 10 = \square

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(10\times10 = 100\) and add up to \(- 29\). The numbers are \(-25\) and \(-4\) since \((-25)\times(-4)=100\) and \(-25 + (-4)=-29\).

Step2: Rewrite the middle term

\(10r^{2}-25r - 4r + 10\)

Step3: Group the terms

\((10r^{2}-25r)+(-4r + 10)\)

Step4: Factor out the GCF from each group

\(5r(2r - 5)-2(2r - 5)\)

Step5: Factor out the common binomial factor

\((2r - 5)(5r - 2)\)

Answer:

\((2r - 5)(5r - 2)\)