Solving Polynomials Worksheets
Having the ability to solve polynomials gives us a great deal of power to simplify them into a linear form that makes it much easier to work with. This makes the algebra very manageable, and it also allows us to model all different forms of phenomena with polynomial expressions or equations. The models that we create can help us solve complex real-life events that require higher level thinking. These worksheets and lessons will help students learn how to find all possible values of variables found within complex numbers.
Aligned Standard: HSN-CN.C.8
- Binomial as a Complex Number Step-by-step Lesson- Rewrite the binomial in a complex format.
- Guided Lesson - More polynomial rewrites for you to work with.
- Guided Lesson Explanation - It is really a two step process of rationalizing and factoring in repeated fashion.
- Practice Worksheet - Ten for you to practice on as you get a real handle on the skill.
- Matching Worksheet - Match the polynomials to their complex forms.
- Answer Keys - These are for all the unlocked materials above.
The first sheet is great for students that seeing this skill for the first time.
- Homework 1 - Complex numbers are made up of several parts a real portion and an imaginary portion.
- Homework 2 - Rationalize the whole number as a form of i.
- Homework 3 - These problems usually conclude with you factoring.
We get a great number of teachers telling us how these particular sheets are super helpful.
- Practice 1 - Rewrite the following as complex number: x2 + 32
- Practice 2 - The imaginary portion of a complex number is easy to find, most times, because the i is hanging around it.
- Practice 3 - Breaking these into smaller parts is important.
Math Skill Quizzes
Each quiz mixes all the skills that you will find for this level.
- Quiz 1 - Make these into complex numbers.
- Quiz 2 - The instructions are all the same for you.
- Quiz 3 - A solid review for you to keep.
How Do You Solve Polynomials?
Polynomials are expressions that have many different terms present. There will be times where we are asked to solve polynomials and what that means is that we are look for the roots. Meaning where the function is equal to zero. Our approach to solving polynomials is entirely determined by the degree that is present. The degree is the value of the largest exponent in the polynomial. We really just need to prepare to solve two types of polynomials, in most circumstances:
Linear -These types of polynomials have a degree of 1 because they clearly have variable but lack exponents. Linear follow the form of 2x + 4. These are solved by using simple algebra and rearranging the equation to get the unknown by itself.
Quadratics - These types of polynomials possess a degree of 2 because they contain a squared variable (x2). Quadratics follow the form of 2x2 - 2x + 4. There are three come methods for solving these, but the most common way to approach it is to use the quadratic formula.
You will occasionally run into polynomials that have a degree of 3 meaning that are cube is present or a quartic equation that has a degree of 4. These types of polynomials can be difficult to solve. It is always best to see if you can simplify or breakdown the polynomial into something smaller before you proceed with it.
Regardless of the which form your polynomial takes on, it is always best to check your answer by graphing the polynomial. Where the line crosses the x-axis would indicate an approximation of where your answer should lie.
What are Polynomial Identities?
Dealing with polynomials gets challenging as the highest power of the polynomial keeps on increasing. To make it easy for students to work with polynomials, they are introduced to polynomial identities. These identities help in solving polynomials that defy rationality. These identities are true equations that are a perfect tool to solve polynomials.
There are six most common and useful polynomial identities that help us solve polynomials with ease and without losing our calm.
(a + b)2=a2 + 2ab + b2
(a + b)(c + d) = ac + bd + bc + bd
These are simple ones that we can use. For powers higher than 3, we use the following identities;
Difference of squares: a2-b2=(a + b)(a - b)
Sum and Difference of cubes: a3 ± b3 = (a ± b)(a2 ± ab + b2 )
x2 + (a + b)x + AB=(x + a)(x + b)
For solutions of quadratic equations of the form;
ax2 + bx + c
We use the quadratic formula to solve for the variable;
Quadratic Formula=(- b ± √(b2 - 4ac)) / 2a.