Question

exit ticket (cfa) name: factor the polynomial by grouping. show your work. \\((24x^3 + 8x^2)+(30x + 10)\\) \\(\underline{quadquad}(\quadquad) + \underline{quadquad}(\quadquad)\\) \\((\quadquad)(\quadquad)\\)

Explanation:

Step1: Factor first group

Find GCF of \(24x^3\) and \(8x^2\). GCF is \(8x^2\).
\(24x^3 + 8x^2 = 8x^2(3x + 1)\)

Step2: Factor second group

Find GCF of \(30x\) and \(10\). GCF is \(10\).
\(30x + 10 = 10(3x + 1)\)

Step3: Rewrite with factored groups

Now the expression is \(8x^2(3x + 1) + 10(3x + 1)\)

Step4: Factor out common binomial

Factor out \((3x + 1)\) from both terms.
\((3x + 1)(8x^2 + 10)\) (Optional: Factor GCF of \(8x^2 + 10\) as \(2(4x^2 + 5)\), so \((3x + 1) \cdot 2(4x^2 + 5) = 2(3x + 1)(4x^2 + 5)\), but based on grouping steps, first factoring gives \((3x + 1)(8x^2 + 10)\) or simplified \(2(3x + 1)(4x^2 + 5)\))

Answer:

First blanks: \(8x^2\), \(3x + 1\); Second blanks: \(10\), \(3x + 1\); Final factoring: \(\boldsymbol{(3x + 1)(8x^2 + 10)}\) (or \(\boldsymbol{2(3x + 1)(4x^2 + 5)}\))