Question

In the following polynomial 5x4 – 6x? + 12x² – 5

a. Name it by degree and the number ofterms.
b. What is the leading coefficient
c. Write a Quadratic trinomial that has aleading coefficient of -9 and a constant term of 15.

Answer 1

The given polynomial is a quartic trinomial. The leading coefficient is 5. An example of a quadratic trinomial with a leading coefficient of -9 and a constant term of 15 is -9x² + 6x + 15.

Step-by-step explanation:

The given polynomial is 5x4 – 6x³ + 12x² – 5a.

Name the polynomial by degree and the number of terms:

A polynomial is named by its highest degree and the number of terms it contains. This polynomial's highest degree term is x4, which makes it a quartic polynomial. Since there are four terms in the expression, it is also called a quartic trinomial.

Find the leading coefficient:

The leading coefficient is the coefficient of the term with the highest power of x. Here, the leading coefficient is 5

Write a quadratic trinomial:

A quadratic trinomial with a leading coefficient of -9 and a constant term of 15 could be written as -9x² + bx + 15, where b is any real number. An example could be -9x² + 6x + 15.