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 its degree and number of terms. polynomial 1 : (3x - 1/4)(4x + 8) polynomial 2 : (5x² + 7x) - 1/2(10x² - 4) polynomial 3 : 3(8x² + 4x - 2) + 6(-4x² - 2x + 3) table with columns: polynomial, simplified form, name by degree, name by number of terms; rows: polynomial 1 (name by number of terms: trinomial), polynomial 2 (name by degree: linear), polynomial 3 (simplified form: 12)

Explanation:

Step1: Simplify Polynomial 1

Expand using FOIL: $(3x)(4x) + 3x(8) - \frac{1}{4}(4x) - \frac{1}{4}(8) = 12x^2 + 24x - x - 2 = 12x^2 + 23x - 2$

Step2: Classify Polynomial 1

Degree: Highest exponent is 2 (quadratic). Terms: 3 (trinomial)

Step3: Simplify Polynomial 2

Distribute and combine like terms: $5x^2 +7x -5x^2 +2 =7x +2$

Step4: Classify Polynomial 2

Terms: 2 (binomial)

Step5: Classify Polynomial 3

Degree: 0 (constant). Terms:1 (monomial)

Answer:

Polynomial	Simplified Form	Name by Degree	Name by Number of Terms
Polynomial 2	$7x + 2$	linear	binomial
Polynomial 3	$12$	constant	monomial