Question

simplify the given polynomials. then, classify each polynomial by its degree and number of terms. polynomial 1: (x - 1/2)(6x + 2) polynomial 2: (7x^2 + 3x) - 1/3(21x^2 - 12) polynomial 3: 4(5x^2 - 9x + 7) + 2(-10x^2 + 18x - 13) trinomial 6x^2 - x - 1 6x^2 + 2x - 1/2 constant binomial 6 linear 2 polynomial simplified form name by degree name by number of terms 1 6x^2 - x - 1 quadratic trinomial 2 3x + 4 linear binomial 3 monomial

Explanation:

Step1: Simplify Polynomial 1

Use FOIL method: $(x-\frac{1}{2})(6x + 2)=6x^{2}+2x-3x - 1=6x^{2}-x - 1$. Degree is 2 (quadratic) and number of terms is 3 (trinomial).

Step2: Simplify Polynomial 2

First distribute the $\frac{1}{3}$: $(7x^{2}+3x)-\frac{1}{3}(21x^{2}-12)=7x^{2}+3x - 7x^{2}+4=3x + 4$. Degree is 1 (linear) and number of terms is 2 (binomial).

Step3: Simplify Polynomial 3

Distribute the 4 and 2: $4(5x^{2}-9x + 7)+2(-10x^{2}+18x - 13)=20x^{2}-36x+28-20x^{2}+36x - 26 = 2$. Degree is 0 (constant) and number of terms is 1 (monomial).

Answer:

Polynomial	Simplified Form	Name by Degree	Name by Number of Terms
2	$3x + 4$	linear	binomial
3	$2$	constant	monomial