Examples

Find the Equation Given the Roots
-11 , 00 , 11
Step 1
Roots are the points where the graph intercepts with the x-axis (y=0)(y=0).
y=0y=0 at the roots
Step 2
The root at x=-1x=1 was found by solving for xx when x-(-1)=yx(1)=y and y=0y=0.
The factor is x+1x+1
Step 3
The root at x=0x=0 was found by solving for xx when x-(0)=yx(0)=y and y=0y=0.
The factor is xx
Step 4
The root at x=1x=1 was found by solving for xx when x-(1)=yx(1)=y and y=0y=0.
The factor is x-1x1
Step 5
Combine all the factors into a single equation.
y=(x+1)(x)(x-1)y=(x+1)(x)(x1)
Step 6
Multiply all the factors to simplify the equation y=(x+1)(x)(x-1)y=(x+1)(x)(x1).
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Step 6.1
Simplify by multiplying through.
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Step 6.1.1
Apply the distributive property.
y=(xx+1x)(x-1)y=(xx+1x)(x1)
Step 6.1.2
Simplify the expression.
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Step 6.1.2.1
Multiply xx by xx.
y=(x2+1x)(x-1)y=(x2+1x)(x1)
Step 6.1.2.2
Multiply xx by 11.
y=(x2+x)(x-1)y=(x2+x)(x1)
y=(x2+x)(x-1)y=(x2+x)(x1)
y=(x2+x)(x-1)y=(x2+x)(x1)
Step 6.2
Expand (x2+x)(x-1)(x2+x)(x1) using the FOIL Method.
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Step 6.2.1
Apply the distributive property.
y=x2(x-1)+x(x-1)y=x2(x1)+x(x1)
Step 6.2.2
Apply the distributive property.
y=x2x+x2-1+x(x-1)y=x2x+x21+x(x1)
Step 6.2.3
Apply the distributive property.
y=x2x+x2-1+xx+x-1y=x2x+x21+xx+x1
y=x2x+x2-1+xx+x-1y=x2x+x21+xx+x1
Step 6.3
Simplify and combine like terms.
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Step 6.3.1
Simplify each term.
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Step 6.3.1.1
Multiply x2x2 by xx by adding the exponents.
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Step 6.3.1.1.1
Multiply x2x2 by xx.
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Step 6.3.1.1.1.1
Raise xx to the power of 11.
y=x2x+x2-1+xx+x-1y=x2x+x21+xx+x1
Step 6.3.1.1.1.2
Use the power rule aman=am+naman=am+n to combine exponents.
y=x2+1+x2-1+xx+x-1y=x2+1+x21+xx+x1
y=x2+1+x2-1+xx+x-1y=x2+1+x21+xx+x1
Step 6.3.1.1.2
Add 22 and 11.
y=x3+x2-1+xx+x-1y=x3+x21+xx+x1
y=x3+x2-1+xx+x-1y=x3+x21+xx+x1
Step 6.3.1.2
Move -11 to the left of x2x2.
y=x3-1x2+xx+x-1y=x31x2+xx+x1
Step 6.3.1.3
Rewrite -1x21x2 as -x2x2.
y=x3-x2+xx+x-1y=x3x2+xx+x1
Step 6.3.1.4
Multiply xx by xx.
y=x3-x2+x2+x-1y=x3x2+x2+x1
Step 6.3.1.5
Move -11 to the left of xx.
y=x3-x2+x2-1xy=x3x2+x21x
Step 6.3.1.6
Rewrite -1x1x as -xx.
y=x3-x2+x2-xy=x3x2+x2x
y=x3-x2+x2-xy=x3x2+x2x
Step 6.3.2
Add -x2x2 and x2x2.
y=x3+0-xy=x3+0x
Step 6.3.3
Add x3x3 and 00.
y=x3-xy=x3x
y=x3-xy=x3x
y=x3-xy=x3x
Step 7
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