Question
Multiply. \[ (x+11)\left(x^{3}+4 x-7\right) \]
Ask by Christensen Bright. in the United States
Jan 21,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Multiply the polynomials to get \( x^4 + 11x^3 + 4x^2 + 37x - 77 \).
Solution
To multiply the polynomials \((x + 11)\) and \((x^3 + 4x - 7)\), follow these steps:
1. **Distribute each term in the first polynomial to each term in the second polynomial:**
\[
(x + 11)(x^3 + 4x - 7) = x \cdot (x^3) + x \cdot (4x) + x \cdot (-7) + 11 \cdot (x^3) + 11 \cdot (4x) + 11 \cdot (-7)
\]
2. **Perform the multiplication for each term:**
\[
= x^4 + 4x^2 - 7x + 11x^3 + 44x - 77
\]
3. **Combine like terms and arrange them in descending order of degree:**
\[
= x^4 + 11x^3 + 4x^2 + ( -7x + 44x ) - 77
\]
\[
= x^4 + 11x^3 + 4x^2 + 37x - 77
\]
**Final Answer:**
\[
x^4 + 11x^3 + 4x^2 + 37x - 77
\]
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Simplify this solution Bonus Knowledge
To multiply the expressions \((x + 11)(x^3 + 4x - 7)\), we can distribute \(x\) and \(11\) to each term in the second expression. First, distribute \(x\): \[ x \cdot (x^3 + 4x - 7) = x^4 + 4x^2 - 7x \] Next, distribute \(11\): \[ 11 \cdot (x^3 + 4x - 7) = 11x^3 + 44x - 77 \] Now, combine all the terms from both distributions: \[ x^4 + 4x^2 - 7x + 11x^3 + 44x - 77 \] Rearranging and combining like terms gives: \[ x^4 + 11x^3 + 4x^2 + (44 - 7)x - 77 = x^4 + 11x^3 + 4x^2 + 37x - 77 \] Thus, the final result of the multiplication is: \[ \boxed{x^4 + 11x^3 + 4x^2 + 37x - 77} \]
