Question

factor.
2q² + 23q + 21
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Explanation:

Step1: Identify the quadratic form

We have the quadratic expression \(2q^{2}+23q + 21\). For a quadratic \(ax^{2}+bx + c\), we need to find two numbers that multiply to \(a\times c\) and add to \(b\). Here, \(a = 2\), \(b=23\), \(c = 21\). So \(a\times c=2\times21 = 42\).

Step2: Find factors of 42

We need two numbers that multiply to 42 and add to 23. The numbers are 21 and 2 (since \(21\times2 = 42\) and \(21 + 2=23\)).

Step3: Split the middle term

Rewrite the middle term using these factors: \(2q^{2}+2q+21q + 21\).

Step4: Group and factor

Group the first two and last two terms: \((2q^{2}+2q)+(21q + 21)\). Factor out the GCF from each group: \(2q(q + 1)+21(q + 1)\). Now factor out \((q + 1)\): \((2q + 21)(q + 1)\).

Answer:

\((2q + 21)(q + 1)\)