Let f(x)=2x2+3 and g(x)=−x2+6x+2 . Which statements below are true for f(x)⋅g(x) ? Select all that apply.
The x has a coefficient of 1
The resulting polynomial has degree 4
The constant term is 6
The leading term is 2 x to the 4th power
The x3 term has a coefficient of 12
The x2 term has a coefficient of −1
The correct statements are:
- The resulting polynomial has degree 4. This is true because when we multiply two polynomials of degree 2, the resulting polynomial will have a degree equal to the sum of the degrees of the original polynomials.
- The constant term is 6. This is true because when we multiply the constant terms of the two polynomials, we get 3 * 2 = 6.
- The x3 term has a coefficient of 12. This is true because when we multiply the x2 term of f(x) (which is 2x^2) with the x term of g(x) (which is -x), we get: 2x^2 * -x = -2x^3. The coefficient of the x3 term is -2, which is not 12.
So, the correct statements are:
- The resulting polynomial has degree 4.
- The constant term is 6.