Download Previous polynomial equations have included

Polynomial Equations
Name: ______________
Previous polynomial equations have included different forms of factoring. Recall that in the
method of factoring
x2 + 4x – 45 = 0
the goal is to find two numbers that multiply to -45, but add to +4.
x
x
+/-
?
x2
+/?
-45
The only possible combination of numbers is 9 and -5, so x2 + 4x – 45 = 0 becomes
(x + 9)(x – 5) = 0.
And you would set each piece equal to zero to solve for x.
BUT, let’s suppose we have the equation
x2 = 25.
Intuition says that to isolate the variable, we use the inverse operation of the square root
on both sides of the equation, giving us x = 5 and -5. Similarly…
x3 = 8
x∙x∙x=8
Ultimately, this equation is asking, “What number, when multiplied by itself three times,
equals 8?” In terms of inverse operations, though, you can use this:
3
: the cube root.
So in solving for x, use the cube root on both sides of the equation
3
x3  3 8
x2
And there we have it! x = 2, but NOT -2. Proof: -2 ∙ -2 ∙ -2 = -8. In general, any negative
number cubed results in a negative number; however, for x4 = 8, we would have two results
since a negative number raised to the fourth power will result in a positive number.
EXAMPLES!
Action Jackson, here we go:
Different powers!
3(x3 – 2) – 4(x3 – 5) = 17
3x3 – 6 – 4x3 – 20 = 17
-x3 – 26 = 17
-x3 = 43
x3 = -43
x ≈ -3.50339806…
DID YOU KNOW…
3
Distribute...
Isolate variables.
CUBE ROOT.
1
3
xx ?
8(2 – x4) + (3x4 – 19) = -2(x4 + 5) Distribute...
16 – 8x4 + 3x4 – 19 = -2x4 – 10
-5x4 – 3 = -2x4 – 10
Isolate variables.
-3x4 = -7
7
x4 =
3
7
FOURTH ROOT.
x= 4
3
** should return two values**
x ≈ ±1.2359309…
Name: ______________
Polynomial Equations
Below are 9 polynomial equations of various types, not only including forms similar to the
examples. Solve for x, and good luck.
1. 3x3 – 5(x3 + 6) – 18 = 6x3
2. 7(x4 – 8) + 2(x4 – 5) = -11
3. 6(x5 – 4) + 10x5 – 3(6 – 2) = 1
4. -3(x3 + 7 – 5x3 – 18 + 2x3) = -23
5. x3 + 5x2 – 14x = 0
6. x4 – 6x2 + 5 = 0
7. x3 – 2x2 + 3x = 6
8. 3x4 – 21x3 + 36x2 = 0
9. 7(x3 + 8) – 10(3 + 2x3) + 2(x3 + 5x3) + 6(-4x3) - 98 + 13x3 – 4(x3 + 4 + 9 + 7x3) = 0