Final answer:
The expression in standard form is 8x² + 9x - 5, and it is classified as a quadratic polynomial. Standard form requires writing terms in order of decreasing degree, and the highest power of x indicates the degree, which is 2 in this case.
Step-by-step explanation:
To write the expression 9x - 5 + 8x² in standard form, we need to order the terms by degree, starting with the highest. The standard form for a polynomial is ordered from the highest power to the lowest. Therefore, the standard form of this expression is 8x² + 9x - 5.
Next, to classify the polynomial, we look at the degree of the polynomial, which is the highest exponent of the variable x. In this case, the degree is 2 (due to the x² term), which makes this a quadratic polynomial.
Polynomials of degree 2 are always called quadratic polynomials, and their graphs are parabolic in shape. To understand the graphing of polynomials, remember that the degree of a polynomial and the leading coefficient (the coefficient of the highest degree term) determine the end behavior and the general shape of the graph.