Question

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

(b) What is its degree?

$\left(3x^3-10x^2+7x+10\right)÷\left(3x+2\right)$

Short answer

The given expression is a trinomial of degree 2.

Step-by-step solution

Step 1. Given information

The given expression is$\left(3x^3-10x^2+7x+10\right)÷\left(3x+2\right)$.

Part (a) Step 1. Simplify the Polynomial

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

$\begin{array}{cc}3x& +2\end{array}\begin{array}{ccccc}{x}^2& -4x& +5& & \end{array}\begin{array}{ccccc}& 3x^3& -10x^2& +7x& +10\end{array}\begin{array}{ccccc}-& (3x^3& +2x^2)& & \\ & & -12x^2& +7x& +10\\ & -& (-12x^2& -8x)& \\ & & & 15x& +10\\ & & -& (15x& 10)\\ & & & & 0\end{array}$

• So, the simplified polynomial is$x^2-4x+5$.

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

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

Step 4. Find the Highest Power

• The term with the highest power of the variables is $x^2$and its exponent is 2.
• So, the degree of the trinomial is 2.