Polynomial Inequality

Inequality is a statement which means that the two things are not equal. Polynomials are the expressions which have the degree of at least 2 and more. An inequality that has polynomials is known as polynomial inequality. And polynomial inequality is not linear anymore. Solving polynomial inequality is little more complicated when comparing with linear inequalities. We will see how to solve polynomial inequality in the following sections.

Steps to solve polynomial inequality:

The following are the steps involved in solving polynomial inequality

Step 1: Make the inequality to obtain a zero on one side of the inequality

Step 2: The next step is to factor the polynomial which is on the left side of the inequality sign

Step 3: Determine the points at where the polynomial is zero.

Step 4: Graph the points we get in the previous step that is where the polynomial is zero

Step 5: Write down the answer

Example problems on solving polynomial inequality:

1)Solve the polynomial inequality x2 +15 < 8x

Solution:

Step 1: Make the inequality to obtain a zero on one side of the inequality

x2 +15 < 8x

x2-8x+15<0

Step 2: factor the polynomial x2-8x+15

x2-8x+15

x2-3x-5x+15

x(x-3) -5(x-3)

(x-5)(x-3)

Step 3: Determine the points at where the polynomial is zero.

Our polynomial is (x-5)(x-3)

When x= 5 ,

(x-5)(x-3) = (5-5)(5-3)

= 0(2)

=0

When x=3

(x-5)(x-3) = (3-5)(3-3)

= (-2)0

=0

The polynomial gets zero at x=5 and x= 3

Step 4: Graph the points we get in the previous step x=5, x=3 ( where the polynomial is zero )




Step 5: Write down the answer.

The solution of the given polynomial inequality is 3<x<5 .

2) Solve the polynomial inequality (x+2)(x+3) >0

Solution:

Step 1: Make the inequality to obtain a zero on one side of the inequality

Here in our example already there is a zero on the right side of the inequality .

Step 2: Factor the polynomial (x+2)(x+3)

No problem. It is in factored form

Step 3: Determine the points at where the polynomial (x+2)(x+3) is zero.

(x+2)(x+3)

When x= -2 ,

(x+2)(x+3) = (-2+2)(3+3)

=(0)(6)=0

When x= -3,

(x+2)(x+3) = (-2+3)(-3+3) = 0

Our polynomial get 0 at x=-2, x=-3

Step 4: Graph the points we get in the previous step x=-2, x=-3 ( where the polynomial is zero )

Algebra is widely used in day to day activities watch out for my forthcoming posts on Common Factor and solving systems of linear equations by elimination. I am sure they will be helpful.

Step 5: Write down the answer.

The solution for the given polynomial inequality is  -3<x<-2