Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
21x3−42x2−84x+168
Evaluate
3(x2−4)×7(x−2)
Multiply the terms
21(x2−4)(x−2)
Multiply the terms
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Evaluate
21(x2−4)
Apply the distributive property
21x2−21×4
Multiply the numbers
21x2−84
(21x2−84)(x−2)
Apply the distributive property
21x2×x−21x2×2−84x−(−84×2)
Multiply the terms
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Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
21x3−21x2×2−84x−(−84×2)
Multiply the numbers
21x3−42x2−84x−(−84×2)
Multiply the numbers
21x3−42x2−84x−(−168)
Solution
21x3−42x2−84x+168
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Factor the expression
21(x−2)2(x+2)
Evaluate
3(x2−4)×7(x−2)
Multiply the terms
21(x2−4)(x−2)
Use a2−b2=(a−b)(a+b) to factor the expression
21(x−2)(x+2)(x−2)
Solution
21(x−2)2(x+2)
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Find the roots
x1=−2,x2=2
Evaluate
3(x2−4)×7(x−2)
To find the roots of the expression,set the expression equal to 0
3(x2−4)×7(x−2)=0
Multiply the terms
21(x2−4)(x−2)=0
Elimination the left coefficient
(x2−4)(x−2)=0
Separate the equation into 2 possible cases
x2−4=0x−2=0
Solve the equation
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Evaluate
x2−4=0
Move the constant to the right-hand side and change its sign
x2=0+4
Removing 0 doesn't change the value,so remove it from the expression
x2=4
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±4
Simplify the expression
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Evaluate
4
Write the number in exponential form with the base of 2
22
Reduce the index of the radical and exponent with 2
2
x=±2
Separate the equation into 2 possible cases
x=2x=−2
x=2x=−2x−2=0
Solve the equation
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Evaluate
x−2=0
Move the constant to the right-hand side and change its sign
x=0+2
Removing 0 doesn't change the value,so remove it from the expression
x=2
x=2x=−2x=2
Find the union
x=2x=−2
Solution
x1=−2,x2=2
Show Solution