How to Simplify Polynomials

How to Simplify Polynomials

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As the name suggests, the word “polynomial” can be cut into two words “poly” and “nomial” which means multiple expressions. Therefore, a polynomial refers to an algebraic or a mathematical expression that consists of one or more terms. The expressions in the polynomial terms could be a constant, a variable, or even a mixed term with a co-efficient. Also, in a polynomial, the power of the variable (let’s suppose  x) should be an integer and not a fractional power like a squared root or a cube root.
For example, 2x13 + 3x + 1 is not a polynomial as the first term has a fraction power of x.

Degree of a Polynomial Expression

To know the degree of a single variable expression, follow these steps:

  • First, simplify the polynomial expression.
  • Then, write the polynomial expression in the standard form.
  • Next, you should check and select the highest exponent of the variable term.

Ex: 4x3 + 3x2 + 7 has the degree 3 since the highest exponent of x is 3.

To know the degree of a multivariable polynomial expression, follow these steps:

  • First, simplify the polynomial expression.
  • Then, write the polynomial expression in the standard form.
  • Next, you should check and select the highest exponent of the variable term. Note: you should add the powers of different variables too.

Ex: x3 + 3x2y3 + 4 has the degree 5, since the middle term has the power of x = 2 and y = 3, so the addition comes to 5.

Simplifying Polynomial Expressions

To simplify a polynomial expression, apply the below-mentioned steps:

  • First, simplify the expression by adding/subtracting the like terms.
  • Also, wherever possible, use the distributive property.

Some Examples:

  • 4x3 + 3x3 + 2x2 − x2 + 9 = 7x3 + x2 + 9.
  • 2x3 − 5x3 + 7x2 − x2 + 5 = −3x3 + 6x2 + 5.
  • −x3 + 7x3 − x2 + x2 + 7 = 6x3 + 7.
  • 12x3 + 15x3 − 2x2 −8x2 + 19 = 27x3 − 10x2 + 19.

Free printable Worksheets

Exercises for Simplifying Polynomials

1) 16 + 3x3 − 7x2 − 2=

2) 25 + 7x3 − 5x2 − 4=

3) 18 + 3(−2x3 − 4x2) − 2+x=

4) 3x(x + 5x2 − 2x4)=

5) 18x(x + 6x2 − 7x4)=

6) (−x + 7x2)x=

7) (x − 20x2)(x + 2)=

8) (−x + 14x2)x=

9) (x − 5x2)(x + 3)=

10) (x − 6x2)(x + 3)=

 
1) 16 + 3x3 − 7x2 − 2= 3x3 − 7x2 + 14
2) 25 + 7x3 − 5x2 − 4= 7x3 − 5x2 + 21
3) 18 + 3(−2x3 − 4x2) − 2+x= −6x3 − 12x2 + x + 16
4) 3x(x + 5x2 − 2x4)= −6x4 + 15x3 + 3x2
5) 18x(x + 6x2 − 7x4)= −126x4 + 108x3 + 18x2
6) (−x + 7x2)x= 7x3 − x2
7) (x − 20x2)(x + 2)= −20x3 − 39x2 + 2x
8) (−x + 14x2)x= 14x3 − x2
9) (x − 5x2)(x + 3)= −5x3 − 14x2 + 3x
10) (x − 6x2)(x + 3)= −6x3 − 17x2 + 3x

Simplifying Polynomials Practice Quiz