Question
Simplify the expression
5x4−10x3−35x2+40x+35
Evaluate
(x2−x−1)(x2−x−7)×5
Use the commutative property to reorder the terms
5(x2−x−1)(x2−x−7)
Multiply the terms
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Evaluate
5(x2−x−1)
Apply the distributive property
5x2−5x−5×1
Any expression multiplied by 1 remains the same
5x2−5x−5
(5x2−5x−5)(x2−x−7)
Apply the distributive property
5x2×x2−5x2×x−5x2×7−5x×x2−(−5x×x)−(−5x×7)−5x2−(−5x)−(−5×7)
Multiply the terms
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Evaluate
x2×x2
Use the product rule an×am=an+m to simplify the expression
x2+2
Add the numbers
x4
5x4−5x2×x−5x2×7−5x×x2−(−5x×x)−(−5x×7)−5x2−(−5x)−(−5×7)
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
5x4−5x3−5x2×7−5x×x2−(−5x×x)−(−5x×7)−5x2−(−5x)−(−5×7)
Multiply the numbers
5x4−5x3−35x2−5x×x2−(−5x×x)−(−5x×7)−5x2−(−5x)−(−5×7)
Multiply the terms
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Evaluate
x×x2
Use the product rule an×am=an+m to simplify the expression
x1+2
Add the numbers
x3
5x4−5x3−35x2−5x3−(−5x×x)−(−5x×7)−5x2−(−5x)−(−5×7)
Multiply the terms
5x4−5x3−35x2−5x3−(−5x2)−(−5x×7)−5x2−(−5x)−(−5×7)
Multiply the numbers
5x4−5x3−35x2−5x3−(−5x2)−(−35x)−5x2−(−5x)−(−5×7)
Multiply the numbers
5x4−5x3−35x2−5x3−(−5x2)−(−35x)−5x2−(−5x)−(−35)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
5x4−5x3−35x2−5x3+5x2+35x−5x2+5x+35
Subtract the terms
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Evaluate
−5x3−5x3
Collect like terms by calculating the sum or difference of their coefficients
(−5−5)x3
Subtract the numbers
−10x3
5x4−10x3−35x2+5x2+35x−5x2+5x+35
Calculate the sum or difference
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Evaluate
−35x2+5x2−5x2
Collect like terms by calculating the sum or difference of their coefficients
(−35+5−5)x2
Calculate the sum or difference
−35x2
5x4−10x3−35x2+35x+5x+35
Solution
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Evaluate
35x+5x
Collect like terms by calculating the sum or difference of their coefficients
(35+5)x
Add the numbers
40x
5x4−10x3−35x2+40x+35
Show Solution

Find the roots
x1=21−29,x2=21−5,x3=21+5,x4=21+29
Alternative Form
x1≈−2.192582,x2≈−0.618034,x3≈1.618034,x4≈3.192582
Evaluate
(x2−x−1)(x2−x−7)×5
To find the roots of the expression,set the expression equal to 0
(x2−x−1)(x2−x−7)×5=0
Use the commutative property to reorder the terms
5(x2−x−1)(x2−x−7)=0
Elimination the left coefficient
(x2−x−1)(x2−x−7)=0
Separate the equation into 2 possible cases
x2−x−1=0x2−x−7=0
Solve the equation
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Evaluate
x2−x−1=0
Substitute a=1,b=−1 and c=−1 into the quadratic formula x=2a−b±b2−4ac
x=21±(−1)2−4(−1)
Simplify the expression
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Evaluate
(−1)2−4(−1)
Evaluate the power
1−4(−1)
Simplify
1−(−4)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
1+4
Add the numbers
5
x=21±5
Separate the equation into 2 possible cases
x=21+5x=21−5
x=21+5x=21−5x2−x−7=0
Solve the equation
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Evaluate
x2−x−7=0
Substitute a=1,b=−1 and c=−7 into the quadratic formula x=2a−b±b2−4ac
x=21±(−1)2−4(−7)
Simplify the expression
More Steps

Evaluate
(−1)2−4(−7)
Evaluate the power
1−4(−7)
Multiply the numbers
1−(−28)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
1+28
Add the numbers
29
x=21±29
Separate the equation into 2 possible cases
x=21+29x=21−29
x=21+5x=21−5x=21+29x=21−29
Solution
x1=21−29,x2=21−5,x3=21+5,x4=21+29
Alternative Form
x1≈−2.192582,x2≈−0.618034,x3≈1.618034,x4≈3.192582
Show Solution
