Question
Find the product when you multiply the polynomials (−4x4+10x)(5x3−1) . (1 point) Responses −20x7+50x4−6x negative 20 x superscript 7 baseline plus 50 x superscript 4 baseline minus 6 x −20x7−54x4−10x negative 20 x superscript 7 baseline minus 54 x superscript 4 baseline minus 10 x −20x7+54x4−10x negative 20 x superscript 7 baseline plus 54 x superscript 4 baseline minus 10 x 20x7+54x4−10x
Answers
GPT-4o mini
To find the product of the polynomials \((-4x^4 + 10x)(5x^3 - 1)\), we will use the distributive property (also known as the FOIL method for multiplying binomials).
1. **Distribute \(-4x^4\)**:
- \((-4x^4) \cdot (5x^3) = -20x^7\)
- \((-4x^4) \cdot (-1) = 4x^4\)
2. **Distribute \(10x\)**:
- \(10x \cdot (5x^3) = 50x^4\)
- \(10x \cdot (-1) = -10x\)
Now, combine all these results:
- From \(-4x^4\): \(-20x^7 + 4x^4\)
- From \(10x\): \(+50x^4 - 10x\)
Combining like terms:
- The \(x^4\) terms: \(4x^4 + 50x^4 = 54x^4\)
Thus, the final result is:
\[
-20x^7 + 54x^4 - 10x
\]
So the correct response is:
\(-20x^7 + 54x^4 - 10x\)
1. **Distribute \(-4x^4\)**:
- \((-4x^4) \cdot (5x^3) = -20x^7\)
- \((-4x^4) \cdot (-1) = 4x^4\)
2. **Distribute \(10x\)**:
- \(10x \cdot (5x^3) = 50x^4\)
- \(10x \cdot (-1) = -10x\)
Now, combine all these results:
- From \(-4x^4\): \(-20x^7 + 4x^4\)
- From \(10x\): \(+50x^4 - 10x\)
Combining like terms:
- The \(x^4\) terms: \(4x^4 + 50x^4 = 54x^4\)
Thus, the final result is:
\[
-20x^7 + 54x^4 - 10x
\]
So the correct response is:
\(-20x^7 + 54x^4 - 10x\)