Question

which polynomial represents the product of 5x-1 and x^2 + 3x - 4?

A. 5x^{3}+3x-4
B. 5x^{3}+15x^{2}-4
C. 5x^{3}+14x^{2}-23x+4
D. 5x^{3}+16x^{2}+17x+4

Answer 1

Answer:

C

Step-by-step explanation:

(5x-1)(x^2+3x-4)

simply expand it

Answer 2

Answer:

$C.\quad 5x^3 + 14x^2 - 23x + 4$

Step-by-step explanation:

To find the product of $(5x - 1)$ and $(x^2 + 3x - 4)$, we can use the distributive property to multiply each term in the first polynomial by each term in the second polynomial and then combine like terms.

$(5x - 1)(x^2 + 3x - 4)$

Multiply each term in the first parenthesis by each term in the second parenthesis:

$5x(x^2+3x-4)-1 (x^2 +3x-4)$

$5x \cdot x^2 + 5x \cdot 3x - 5x \cdot 4 - 1 \cdot x^2 - 1 \cdot 3x - 1 \cdot -4$

Now, simplify each term:

$5x^3 + 15x^2 - 20x - x^2 - 3x + 4$

Combine like terms:

$5x^3 + (15x^2 - x^2) + (-20x - 3x) + 4$

$5x^3 + 14x^2 - 23x + 4$

So, the polynomial that represents the product of $(5x - 1)$ and $(x^2 + 3x - 4)$ is:

$C.\quad 5x^3 + 14x^2 - 23x + 4$