When (x + 4)(3x + 8)(x) is expressed as a polynomial in
standard form, which statement about the resulting
polynomial is true?
a. the constant term is 3
b. the degree is 2
c. the leading coefficient is 3
d. the number of terms is 2

c. The leading coefficient is 3.

Step-by-step explanation:

To write the polynomial in standard form, you should work step by step. Multiply (x+4)(3x+8) first:

 (x+4)(3x+8)

=x(3x+8) + 4(3x+8)

=3x(x)+8x + 3x*4+8*4

=3x^2+8x + 12x+32

=3x^2+20x+32

Now, mulitply that product by x.

 (3x^2+20x+32)(x)

=(3x^2)(x)+20x(x)+32x

=3x^3+20x^2+32x

That's your polynomial in standard form. Now, let's check all the possible solutions.

a. The constant term is the term not including x. (That's why it's a constant-- it's unaffected by the value of x.) In this polynomial, all the terms have x, so this option can't be correct.

b. The degree is the highest power any variable is raised to in the polynomial. Here, we have x^3, x^2, and x, so the degree is 3. (3>2>1) (When you write a polynomial in standard form, the term with the highest degree has to be at the start anyway, so that's how you can check.)

c.The leading coefficient is the coefficient of the term with the highest degree in the polynomial. 3x^3 is the term with the highest degree, and the coefficient is 3! This option is correct.

d. There are 3 terms in this polynomial: 3x^3, 20x^2, and 32x.

So your answer is c.

Hope I could help!

a

step-by-step explanation: