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(a) Is it a monomial, binomial, or trinomial?

(b) What is its degree?

3x3-10x2+7x+10÷3x+2

Short Answer

Expert verified

The given expression is a trinomial of degree 2.

Step by step solution

01

Step 1. Given information

The given expression is3x3-10x2+7x+10÷3x+2.

02

Part (a) Step 1. Simplify the Polynomial

  • To simplify the polynomial, use the long division method as shown below:

3x+2x2-4x+53x3-10x2+7x+10-(3x3+2x2)-12x2+7x+10-(-12x2-8x)15x+10-(15x10)0

  • So, the simplified polynomial isx2-4x+5.
03

Part (b) Step 1. Count the number of terms

  • The resultant expression has three terms.
  • So, it is a trinomial.
04

Step 4. Find the Highest Power

  • The term with the highest power of the variables is x2and its exponent is 2.
  • So, the degree of the trinomial is 2.

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