Polynomials are algebraic terms which are two or more in numbers. They are also known as expressions and consist of the variable, constants, and coefficient. Besides this, they are of two types i.e. linear and quadratic polynomials plus they can be high degree and low degree. For solving them, you should be used to factoring methods and basic of algebra. So, let’s start our lessons.
How to solve linear polynomial?
At first, you should know how a linear polynomial looks like? In it, you will see variable with exponents one for example 3x+2. Let’s look at the steps for solving it:
- Sat first you have to set the polynomials in which you have to insert an equal sign in front of it like this 3x+2=0.
- Many people suggest you isolate terms but why to do that when you can give the answer by just looking at the expression.
- What you have to do is to separate like terms like shift 2 to the RHS and 3x to LHS. In other change their sides like this, 3x=0-2. Sort out like terms, and with this simple trick, you can obtain the answer quickly.
- Now, 3x= -2 and now bring three under two as like this x=-2/3.
You should take care of the similar terms, sides, and sign. Guys keep in mind that signs changes when you change the sides of the expression or constants.
How to solve a quadratic equation?
In it, the polynomial is of second degree which means that variables have exponent 2.
- First thing guys, always make sure that the polynomial must be in right order. In other words, higher degree expression should come first or their degree must be in order.
- Now, guys find out the factors of 20 plus you should use these factors in a way that it will give (-8) and will also give 20 when multiplied together.
- You have to multiply one with 20 as the coefficient of is one plus for finding factors, it is an important to step.
- 2, 2 and 5 are its factors so you should simplify it in a way mentioned above. Let’s multiply 5 and 2 to get 10 and leave two alone. It is also known as a grouping of factors.
- Now, write four expressions like this
. Now, divided them from the middle and formed two groups. Do like this: x(x+10)-2(x+10)=0 . Here we have taken x and two as common terms.
- Also, while splinting into expressions, make sure you write signs right. The two group of binomials are visible to you i.e. ( x+10) and (x-2).
- Now, you have to solve it like linear polynomials and get an answer(x=-10,x=2). Again, while using zero in the polynomial, change sings
Algebra is a very easy topic, and polynomials are like basics for other topics like linear or quadratic equations. You can solve another example of polynomials by the steps describe above plus understand properly how to group factors in it?