Multiply the following polynomials and write the resulting polynomial in descending order. 3x−82x2+4x−9. What is the value of the coefficient of the x3term?

Answer 1

To multiply the polynomials \( (3x - 8)(2x^2 + 4x - 9) \), we will distribute each term in the first polynomial to each term in the second polynomial.

Starting with \( 3x \):

1. \( 3x \cdot 2x^2 = 6x^3 \)
2. \( 3x \cdot 4x = 12x^2 \)
3. \( 3x \cdot -9 = -27x \)

Next, we multiply \( -8 \):

1. \( -8 \cdot 2x^2 = -16x^2 \)
2. \( -8 \cdot 4x = -32x \)
3. \( -8 \cdot -9 = 72 \)

Now, we combine all the products: \[ 6x^3 + 12x^2 - 27x - 16x^2 - 32x + 72 \]

Next, we combine like terms:

1. For \( x^3 \): \( 6x^3 \)
2. For \( x^2 \): \( 12x^2 - 16x^2 = -4x^2 \)
3. For \( x \): \( -27x - 32x = -59x \)
4. Constant term: \( 72 \)

Putting it all together, we rewrite the polynomial in descending order: \[ 6x^3 - 4x^2 - 59x + 72 \]

The coefficient of the \( x^3 \) term is \( 6 \).

Thus, the final answer for the coefficient of the \( x^3 \) term is: \[ \boxed{6} \]

Answer 2

What is the value of the coefficient of the `x^{2}`term?

Answer 3

From the previous work, we derived the resulting polynomial from the multiplication of the two polynomials \( (3x - 8)(2x^2 + 4x - 9) \):

\[ 6x^3 - 4x^2 - 59x + 72 \]

In this polynomial, the coefficient of the \( x^2 \) term is \( -4 \).

Therefore, the value of the coefficient of the \( x^2 \) term is:

\[ \boxed{-4} \]

Answer 4

What is the value of the coefficient of the x term

Answer 5

From the previously derived polynomial:

\[ 6x^3 - 4x^2 - 59x + 72 \]

We can see that the coefficient of the \( x \) term is \( -59 \).

Therefore, the value of the coefficient of the \( x \) term is:

\[ \boxed{-59} \]

Answer 6

what is the value of the constant

Answer 7

From the previously derived polynomial:

\[ 6x^3 - 4x^2 - 59x + 72 \]

The constant term is \( 72 \).

Therefore, the value of the constant is:

\[ \boxed{72} \]