Question

which polynomial is written in standard form?
$4x^3 + 7x - 9$
$12 + 4x$
$13x + 7x^2 - 9x^3 + 12$
$8x - 11x^2$

Explanation:

Step1: Recall standard form of polynomial

A polynomial in standard form is written with terms in descending order of their degrees (exponents of the variable). The degree of a term is the exponent of the variable in that term.

Step2: Analyze each option

• First option: \(4x^{3}+7x - 9\)
• The degree of \(4x^{3}\) is \(3\), the degree of \(7x\) is \(1\), and the degree of \(- 9\) (constant term, degree \(0\)) is \(0\). The terms are in descending order of degrees (\(3>1 > 0\)).
• Second option: \(12 + 4x\)
• The degree of \(12\) (constant term, degree \(0\)) is \(0\) and the degree of \(4x\) is \(1\). The order is \(0\) then \(1\), which is ascending order, not standard (should be descending).
• Third option: \(13x+7x^{2}-9x^{3}+12\)
• The degree of \(13x\) is \(1\), the degree of \(7x^{2}\) is \(2\), the degree of \(-9x^{3}\) is \(3\), and the degree of \(12\) is \(0\). The degrees are \(1,2,3,0\) which is not in descending order.
• Fourth option: \(8x - 11x^{2}\)
• The degree of \(8x\) is \(1\) and the degree of \(-11x^{2}\) is \(2\). The order is \(1\) then \(2\), which is ascending order, not standard (should be descending, so it should be \(-11x^{2}+8x\)).

Answer:

\(4x^{3}+7x - 9\) (the first polynomial)