Question

drag each number to the correct location on the table. each number can be used more than once, but not all numbers will be used.
simplify the given polynomial expressions, and determine the degree and number of terms in each expression.
4 1 6 0 5 3 2
$4x + 2x^2(3x - 5)$
$(-3x^4 + 5x^3 - 12) + (7x^3 - x^5 + 6)$
$(3x^2 - 3)(3x^2 + 3)$
degree
number of terms

Explanation:

Step1: Simplify first expression

Expand and combine like terms:
$4x + 2x^2(3x - 5) = 4x + 6x^3 - 10x^2 = 6x^3 - 10x^2 + 4x$

Step2: Find degree/terms for first expr.

Degree = highest exponent ($3$); Terms = $3$

Step3: Simplify second expression

Combine like terms:
$(-3x^4 + 5x^3 - 12) + (7x^3 - x^5 + 6) = -x^5 - 3x^4 + 12x^3 - 6$

Step4: Find degree/terms for second expr.

Degree = highest exponent ($5$); Terms = $4$

Step5: Simplify third expression

Use difference of squares:
$(3x^2 - 3)(3x^2 + 3) = (3x^2)^2 - 3^2 = 9x^4 - 9$

Step6: Find degree/terms for third expr.

Degree = highest exponent ($4$); Terms = $2$

Answer:

Expression	Degree	Number of Terms
$(-3x^4 + 5x^3 - 12) + (7x^3 - x^5 + 6)$	5	4
$(3x^2 - 3)(3x^2 + 3)$	4	2