Question
Factor the following polynomial completely. \[ a^{2}+10 c a+9 c^{2} \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( a^{2}+10 c a+9 c^{2}=\square \) B. The polynomial is pirne.
Ask by Mccarthy Black. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( a^{2}+10 c a+9 c^{2}=(a+c)(a+9c) \)
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The Deep Dive
To factor the polynomial \( a^{2}+10 c a+9 c^{2} \), we need to find two numbers that multiply to \( 9c^{2} \) and add to \( 10c \). These numbers are \( 9c \) and \( c \). Thus, we can write the polynomial in factored form: \[ a^{2}+10 c a+9 c^{2} = (a + 9c)(a + c). \] So the correct choice is: A. \( a^{2}+10 c a+9 c^{2}=(a + 9c)(a + c) \).