Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms. 2-11x^2-8x+6x^2.
A) -5x^2-8x+2; quadratic trinomial
B) -5x^2-8x; quadratic binomial
C) -6x^2-8x-2; cubic polynomial
D) -8x+2; cubic trinomial
All the answers?!
To write the given polynomial in standard form, we first combine like terms:
2 - 11x^2 - 8x + 6x^2
Combining the like terms -11x^2 and 6x^2, we get:
(6x^2 - 11x^2) - 8x + 2
Simplifying the coefficients of the variable x, we have:
-5x^2 - 8x + 2
Therefore, the polynomial in standard form is -5x^2 - 8x + 2.
Now, let's determine the name of the polynomial based on its degree and number of terms.
The degree of a polynomial is the highest exponent of the variable. In this case, the highest exponent is 2, making it a quadratic term.
The number of terms in the polynomial is simply the number of separate parts in the expression. In this case, there are 3 terms: -5x^2, -8x, and 2.
Putting it together, the polynomial can be named as:
A) -5x^2 - 8x + 2; quadratic trinomial
To write the polynomial in standard form, we rearrange the terms in decreasing order of their exponents.
Given the polynomial 2 - 11x^2 - 8x + 6x^2, we can combine like terms:
-11x^2 + 6x^2 - 8x + 2
Next, we collect the like terms:
(-11 + 6)x^2 - 8x + 2
Simplifying further:
-5x^2 - 8x + 2
Now that we have the polynomial in standard form, let's determine its name based on its degree and number of terms.
The degree of a polynomial is the highest exponent of the variable, which in this case is x. The term with the highest exponent in our polynomial is -5x^2. Hence, the polynomial is of degree 2.
The number of terms in the polynomial is the number of different variable expressions separated by addition or subtraction signs. In our polynomial, there are three separate expressions: -5x^2, -8x, and 2. Therefore, the polynomial has 3 terms.
Based on its degree and number of terms, we can conclude that the polynomial -5x^2 - 8x + 2 is a quadratic trinomial.
So, the correct answer is option A) -5x^2 - 8x + 2; quadratic trinomial.