4x^3-6x^2+7what is the polynomial is it a trinomial
can be evaluated at x=.1/3
coeffcient of 6
is it a quadratic
To classify the given polynomial, let's first identify its degree. The highest exponent of the polynomial determines its degree. In this case, the highest exponent is 3 (from the term 4x^3), so the degree of the polynomial is 3.
A trinomial is a polynomial with three terms. In our case, the given polynomial has three terms (4x^3, -6x^2, 7), so it can be classified as a trinomial.
Next, to evaluate the polynomial at x = 1/3, we simply substitute the value of x into the polynomial and compute the result. Substituting x = 1/3 into the given polynomial:
4 * (1/3)^3 - 6 * (1/3)^2 + 7
Simplifying:
4 * (1/27) - 6 * (1/9) + 7
1/27 - 2/3 + 7
To add or subtract fractions, they must have the same denominator. Multiplying the first fraction by 3/3 and the second fraction by 9/9:
1/27 * 3/3 - 2/3 * 9/9 + 7
3/81 - 18/81 + 567/81
(3 - 18 + 567)/81
552/81
At x = 1/3, the polynomial evaluates to 552/81.
The coefficient of 6 in a polynomial refers to the numerical factor multiplied by the variable with the exponent. In the given polynomial, there is no term with x^2, so its coefficient is 0.
Finally, to determine if the polynomial is quadratic, we need to check if it has degree 2. As mentioned earlier, the degree of the given polynomial is 3, not 2. Therefore, the given polynomial is not quadratic.