Write the polynomial in standard from. Then name the polynomial based on its degree and number of terms.
2 - 11x^2 - 8x + 6x^2
a. -5^2 - 8x + 2; quadratic polynomial
b. 5x^2 - 8x - 2; quadratic polynomial
c. -6x^2 - 8x - 2 cubic trinomial
d. 6x^2 - 8x +20 cubic trinomial
To rewrite the polynomial in standard form, combine like terms:
(2 - 11x^2 - 8x + 6x^2)
= (2 - 8x - 11x^2 + 6x^2)
= (-11x^2 + 6x^2 - 8x + 2)
= (-5x^2 - 8x + 2)
The polynomial is: -5x^2 - 8x + 2.
Based on its degree and number of terms, the polynomial is a quadratic polynomial because it has a degree of 2 (the highest exponent is 2) and three terms.
Therefore, the correct answer is option (a): -5x^2 - 8x + 2; quadratic polynomial.