Question

simplify the given polynomials. then, classify each polynomial by its degree and number of terms
polynomial 1: $(x - \frac{1}{2})(6x + 2)$
polynomial 2: $(7x^{2}+3x)-\frac{1}{3}(21x^{2}-12)$
polynomial 3: $4(6x^{2}-9x + 7)+2(-10x^{2}+18x - 13)$
trinomial $6x^{2}-x - 1$ $6x^{2}+2x - \frac{1}{2}$ constant binomial 6 linear
2

polynomial	simplified form	name by degree	name by number of terms
2	$3x + 4$
3		monomial

Explanation:

Step1: Simplify Polynomial 1

Use FOIL method: $(x-\frac{1}{2})(6x + 2)=x\times6x+x\times2-\frac{1}{2}\times6x-\frac{1}{2}\times2 = 6x^{2}+2x - 3x-1=6x^{2}-x - 1$. It is a quadratic trinomial.

Step2: Simplify Polynomial 2

\[

$$\begin{align*} (7x^{2}+3x)-\frac{1}{3}(21x^{2}-12)&=7x^{2}+3x - 7x^{2}+4\\ &=(7x^{2}-7x^{2})+3x + 4\\ &=3x + 4 \end{align*}$$

\]
It is a linear binomial.

Step3: Simplify Polynomial 3

\[

$$\begin{align*} &4(6x^{2}-9x + 7)+2(-10x^{2}+18x - 13)\\ =&24x^{2}-36x+28-20x^{2}+36x - 26\\ =&(24x^{2}-20x^{2})+(-36x + 36x)+(28 - 26)\\ =&4x^{2}+2 \end{align*}$$

\]
It is a quadratic binomial.

Answer:

Polynomial	Simplified Form	Name by Degree	Name by Number of Terms
2	$3x + 4$	linear	binomial
3	$4x^{2}+2$	quadratic	binomial