Simplify and write in standard form. Then, classify
the polynomial by degree and number of terms.
(9w-4w^2 + 10) + (8w^2 + 7 + 5w)
(9w-4w^2 + 10) + (8w^2 + 7 + 5w)
9w - 4w^2 + 10 + 8w^2 + 7 + 5w
addition is commutative, so
-4w^2 + 8w^2 + 9w + 5w + 10 + 7
multiplication distributes, so
(-4+8)w^2 + (9+5)w + (10+7)
4w^2 + 14w + 17
degree is the highest power of x
terms are separated by + or - signs
To simplify and write the expression in standard form, we need to combine like terms by adding or subtracting them. Let's start by simplifying the expression within each set of parentheses first.
(9w - 4w^2 + 10) + (8w^2 + 7 + 5w)
Within the first set of parentheses: 9w - 4w^2 + 10
Within the second set of parentheses: 8w^2 + 7 + 5w
We'll combine like terms within each set of parentheses:
Combining like terms within the first set of parentheses: 9w - 4w^2 + 10
Combining like terms within the second set of parentheses: 8w^2 + 5w + 7
Now, we'll combine the two simplified expressions:
(9w - 4w^2 + 10) + (8w^2 + 5w + 7)
9w - 4w^2 + 10 + 8w^2 + 5w + 7
Next, we'll further simplify by combining like terms:
-4w^2 + 8w^2 + 9w + 5w + 10 + 7
(8w^2 - 4w^2) + (9w + 5w) + (10 + 7)
4w^2 + 14w + 17
Now, the simplified expression 4w^2 + 14w + 17 is already in standard form, which means the terms are arranged from highest degree to lowest degree.
To classify the polynomial, we need to determine its degree and number of terms:
Degree: The highest power of the variable in the polynomial. In this case, the highest power of w is 2, so the degree is 2.
Number of terms: The number of individual terms in the polynomial. In this case, we have 3 terms: 4w^2, 14w, and 17.
Therefore, we can classify the polynomial 4w^2 + 14w + 17 as a second-degree polynomial (quadratic) with 3 terms (trinomial).