Question
Write the trinomial in descending powers of one variable and then factor. \[ y^{2}+80+21 y \] SUBMIT ANSWER
Ask by Malone Romero. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The trinomial \( y^2 + 21y + 80 \) can be factored as \( (y + 5)(y + 16) \).
Solution
1. Write the trinomial in descending powers:
\[
y^2 + 21y + 80
\]
2. Look for two numbers whose product is \(80\) and whose sum is \(21\). These numbers are \(5\) and \(16\) because:
\[
5 \times 16 = 80 \quad \text{and} \quad 5 + 16 = 21
\]
3. Factor the trinomial using these numbers:
\[
y^2 + 21y + 80 = (y + 5)(y + 16)
\]
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Simplify this solution Bonus Knowledge
To rewrite the trinomial in descending powers of one variable, we rearrange it as follows: \[ y^2 + 21y + 80. \] Now, to factor the trinomial, we look for two numbers that multiply to 80 and add up to 21. The numbers 16 and 5 fit the bill because \( 16 \times 5 = 80 \) and \( 16 + 5 = 21 \). So, we can factor the trinomial as \[ (y + 16)(y + 5). \]
