Sharon1.Rochester@cms.k12.nc.us
Common Polynomials:Quadratic - has the form ax2 + bx + c = 0Highest exponent is two (this is the degree)The most real solutions it has is two.Cubic - has the form ax3 + bx2 + cx + d = 0Highest exponent is three (this is the degree)The most real solutions it has is three.Quartic - has the form ax4 + bx3 + cx2 + dx + e = 0Highest exponent is four (this is the degree)The most real solutions it has is four.Here are the steps required for Solving Polynomials by Factoring:Step 1:Write the equation in the correct form. To be in the correct form, you must remove all parentheses from each side of the equation by distributing, combine all like terms, and finally set the equation equal to zero with the terms written in descending order.Step 2:Use a factoring strategies to factor the problem.Step 3:Use the Zero Product Property and set each factor containing a variable equal to zero.Step 4:Solve each factor that was set equal to zero by getting the x on one side and the answer on the other side.Example 1?– Solve: 3x3?= 12xExample 2?– Solve: x3?+ 5x2?= 9x + 45Example 3?– Solve: 6x3?– 16x = 4x2Example 4?– Solve: 3x2(3x + 4) = 12x(x + 3)Here are the steps required for Solving Polynomials by Graphing:Go to the graph menu on your calculator and type the function into Y1.Graph it and let’s look for places where the graph crosses the x-axis. These are the x-intercepts.If you can’t tell from looking at the graph, go to 2nd Trace and then type 2.Use scroll arrows to go just left of the x-intercept of interest, press ENTER.Use scroll arrows to go just right of the x-intercept of interest, press ENTER.Press ENTER again. You should be given an x value of the bottom of the screen for y=0.Repeat steps 3-6 for all x-intercepts on the graph.Example 1?– Solve: Example 2?– Solve: Example 3?– Solve: ?Example 4?– Solve: ................
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