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Classify -3/4x-10 as cubic, quadratic, linear, or trinomial and to what degree.

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2 Answers

the highest power of the variable, in this example the letter x, is 1.
Although the equation has (-3/4)x it is really (-3/4) x1
But we don't need to show the power when the power is 1 because x1 = x
In fact, any number or variable raised to the first power equals itself.
 
So the degree of a polynomial is equal to the highest power of the variable which in this example is 1.
A polynomial of first degree is called linear because its graph is a line.
2nd degree is called quadratic and 3rd degree is called cubic.
 
In addition to describing polynomials by the degree, we also describe them based on how many terms there are. The names are monomial, binomial, trinomial, and polynomial for 4 or more terms.
 
This example is a binomial because (-3/4)x is one term and the constant 10 is a second term.
 
remember that the degree and the number of terms are completely independent of one another.
 
All of the following are monomials:  x, x2, x3, x7 because there is only one term. But notice the degree of each monomial is different.
 
At the same time, x3  and x3 + 2x and x3 + 2x + 4  are all 3rd degree but from left to right we have a monomial, binomial, and trinomial