Let's determine the type of each polynomial by looking at their degrees:
1. Polynomial a [tex]\( h(x) = 15x + 2 \)[/tex]
- This can be written as [tex]\( h(x) = 15x^1 + 2 \)[/tex].
- The degree of this polynomial is 1 (the highest power of [tex]\(x\)[/tex]).
- A polynomial of degree 1 is called a Linear polynomial.
2. Polynomial b [tex]\( f(x) = x^4 - 3x^2 + 9x^2 \)[/tex]
- First, we need to combine like terms: [tex]\( f(x) = x^4 + ( -3x^2 + 9x^2) = x^4 + 6x^2 \)[/tex].
- The degree of this polynomial is 4 (the highest power of [tex]\(x\)[/tex]).
- A polynomial of degree 4 is called a Quartic polynomial.
3. Polynomial c [tex]\( g(x) = -5x^3 \)[/tex]
- The polynomial is already simplified.
- The degree of this polynomial is 3 (the highest power of [tex]\(x\)[/tex]).
- A polynomial of degree 3 is called a Cubic polynomial.
4. Polynomial d [tex]\( f(x) = 3x^2 - 5x + 7 \)[/tex]
- This polynomial is already in its simplest form.
- The degree of this polynomial is 2 (the highest power of [tex]\(x\)[/tex]).
- A polynomial of degree 2 is called a Quadratic polynomial.
Therefore, the correct match for each polynomial is as follows:
- a: Linear
- b: Quartic
- c: Cubic
- d: Quadratic
