Question  
 Simplify the expression
1584x5−792x4−1056x3
Evaluate
(2x2×11x×12)(6x2−3x−4)
Remove the parentheses
2x2×11x×12(6x2−3x−4)
Multiply the terms
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Evaluate
2×11×12
Multiply the terms
22×12
Multiply the numbers
264
264x2×x(6x2−3x−4)
Multiply the terms with the same base by adding their exponents
264x2+1(6x2−3x−4)
Add the numbers
264x3(6x2−3x−4)
Apply the distributive property
264x3×6x2−264x3×3x−264x3×4
Multiply the terms
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Evaluate
264x3×6x2
Multiply the numbers
1584x3×x2
Multiply the terms
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Evaluate
x3×x2
Use the product rule an×am=an+m to simplify the expression
x3+2
Add the numbers
x5
1584x5
1584x5−264x3×3x−264x3×4
Multiply the terms
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Evaluate
264x3×3x
Multiply the numbers
792x3×x
Multiply the terms
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Evaluate
x3×x
Use the product rule an×am=an+m to simplify the expression
x3+1
Add the numbers
x4
792x4
1584x5−792x4−264x3×4
Solution
1584x5−792x4−1056x3
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Find the roots
x1=123−105,x2=0,x3=123+105
Alternative Form
 x1≈−0.603913,x2=0,x3≈1.103913
Evaluate
(2x2×11x×12)(6x2−3x−4)
To find the roots of the expression,set the expression equal to 0
(2x2×11x×12)(6x2−3x−4)=0
Multiply
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Multiply the terms
2x2×11x×12
Multiply the terms
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Evaluate
2×11×12
Multiply the terms
22×12
Multiply the numbers
264
264x2×x
Multiply the terms with the same base by adding their exponents
264x2+1
Add the numbers
264x3
264x3(6x2−3x−4)=0
Elimination the left coefficient
x3(6x2−3x−4)=0
Separate the equation into 2 possible cases
x3=06x2−3x−4=0
The only way a power can be 0 is when the base equals 0
x=06x2−3x−4=0
Solve the equation
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Evaluate
6x2−3x−4=0
Substitute a=6,b=−3 and c=−4 into the quadratic formula x=2a−b±b2−4ac
x=2×63±(−3)2−4×6(−4)
Simplify the expression
x=123±(−3)2−4×6(−4)
Simplify the expression
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Evaluate
(−3)2−4×6(−4)
Multiply
(−3)2−(−96)
Rewrite the expression
32−(−96)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
32+96
Evaluate the power
9+96
Add the numbers
105
x=123±105
Separate the equation into 2 possible cases
x=123+105x=123−105
x=0x=123+105x=123−105
Solution
x1=123−105,x2=0,x3=123+105
Alternative Form
x1≈−0.603913,x2=0,x3≈1.103913
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