We will begin with a property that is the converse of the Adding Fractions Property presented in previous sections.
This property allows you to separate the numerator into its individual fractions. This property is used when dividing a polynomial by a monomial.
Let's take a look at a couple of problems that use the Adding Fractions Property:
Using the property above, separate the polynomial into its individual fractions.
Separate the trinomial into its individual fractions and reduce.
Polynomials can also be divided by binomials. However, instead of separating into its individual fractions, we use a process called long division.
Let's look at the process of polynomial long division by solving the following problem:
When we perform division, the expression in the numerator is called the dividend and the expression in the denominator is called the divisor.
To start the division we rewrite the problem in the following form.
Now, bring down 5, the next term in the dividend.
Since there are no more terms from the dividend to bring down, we are done.
Area=wlPlug and chug→x2−2x−24=(w)(x+6)Solve for w →w=x2−2x−24x+6Factor the numerator→w=(x−8)(x+6)x+6Take out common factor→w=x−8
You are being asked to simplify:
You could use long division to find the answer. You can also use patterns of polynomials to simplify and cancel.
Divide the following polynomials.
2x+42 x−4x 5x−355x x2+2x−5x 4x2+12x−36−4x 2x2+10x+72x2 x3−x−2x2 5x4−93x x3−12x2+3x−412x2 3−6x+x3−9x3 x2+3x+6x+1 x2−9x+6x−1 x2+5x+4x+4 x2−10x+25x−5 x2−20x+12x−3 3x2−x+5x−2 9x2+2x−8x+4 3x2−43x+1 5x2+2x−92x−1 x2−6x−125x+4 x4−2x8x+24 x3+14x−1
- Boyle’s Law states that the pressure of a compressed gas varies inversely as its pressure. If the pressure of a 200-pound gas is 16.75 psi, find the pressure if the amount of gas is 60 pounds.
5x3+x2−x−1+8an example of a polynomial? Explain your answer.
- Find the slope of the line perpendicular to
- How many two-person teams can be made from a group of nine individuals?
- Solve for
To see the Review answers, open this PDF file and look for section 12.3.