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

Question

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

GPT-4o mini · Answer

To find the product of the polynomials $(- 4 x^{4} + 10 x) (5 x^{3} - 1)$ , 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.

Multiply $- 4 x^{4}$ by $5 x^{3}$ : $- 4 x^{4} \cdot 5 x^{3} = - 20 x^{7}$
Multiply $- 4 x^{4}$ by $- 1$ : $- 4 x^{4} \cdot - 1 = 4 x^{4}$
Multiply $10 x$ by $5 x^{3}$ : $10 x \cdot 5 x^{3} = 50 x^{4}$
Multiply $10 x$ by $- 1$ : $10 x \cdot - 1 = - 10 x$

Now we combine all these results: $- 20 x^{7} + 4 x^{4} + 50 x^{4} - 10 x$

Combine like terms ( $4 x^{4}$ and $50 x^{4}$ ): $- 20 x^{7} + (4 x^{4} + 50 x^{4}) - 10 x = - 20 x^{7} + 54 x^{4} - 10 x$

So, the product of the polynomials $(- 4 x^{4} + 10 x) (5 x^{3} - 1)$ is: $- 20 x^{7} + 54 x^{4} - 10 x$

Thus, the answer corresponds to: A. $- 20 x^{7} + 54 x^{4} - 10 x$ .