Find the product when you multiply the polynomials (-4x^4+10x) (5x^3-1)

A.-20x^7+54x^4-10x
B.20x^7+54x^4-10x
C.-20x^7-54x^4-10x
D.-20x^7+50x^4-6x

1 answer

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 binomials) to multiply each term in the first polynomial by each term in the second polynomial.

  1. Multiply \(-4x^4\) by \(5x^3\): \[ -4x^4 \cdot 5x^3 = -20x^7 \]

  2. Multiply \(-4x^4\) by \(-1\): \[ -4x^4 \cdot -1 = 4x^4 \]

  3. Multiply \(10x\) by \(5x^3\): \[ 10x \cdot 5x^3 = 50x^4 \]

  4. Multiply \(10x\) by \(-1\): \[ 10x \cdot -1 = -10x \]

Now we combine all these results: \[ -20x^7 + 4x^4 + 50x^4 - 10x \]

Combine like terms (\(4x^4\) and \(50x^4\)): \[ -20x^7 + (4x^4 + 50x^4) - 10x = -20x^7 + 54x^4 - 10x \]

So, the product of the polynomials \((-4x^4 + 10x)(5x^3 - 1)\) is: \[ -20x^7 + 54x^4 - 10x \]

Thus, the answer corresponds to: A. \( -20x^7 + 54x^4 - 10x \).