Question

Drag each label to the correct location on the table. Each label can be used more than once, but not all labels will be used.Simplify the given polynomials. Then, classify each by itsdegree and number of terms.Polynomial 1: (3x – 1/4)(4x + 8)Polynomial 2: (5x^2 + 7x) - 1/2(10x^2– 4)Polynomial 3(8x^2+ 4x – 2) + 6(-4x^2 – 2x + 3)

Answer 1

Okay, here we have this:

Let's solve the table polynomial by polynomial:

Polynomial 1:

We will first find its simplified form:

$\begin{gathered} (3x-\frac{1}{4})(4x+8) \\ =3x\cdot\: 4x+3x\cdot\: 8+\mleft(-\frac{1}{4}\mright)\cdot\: 4x+\mleft(-\frac{1}{4}\mright)\cdot\: 8 \\ =12x^2+24x-x-2 \\ =12x^2+23x-2 \end{gathered}$

Name by degree of the polynomial: quadratic.

Polynomial 2:

Let's simplify it:

$\begin{gathered} \mleft(5x^2+7x\mright)-\frac{1}{2}\mleft(10x^2-4\mright) \\ =5x^2+7x-5x^2+2 \\ =7x+2 \end{gathered}$

Name by number of terms: Binomial

Polynomial 3:

Name by degree of the polynomial: constant

Name by number of terms: Monomial