Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
5j2+2j
Evaluate
j−15j3−3j2−2j
Factor the expression
j−1(j−1)(5j2+2j)
Solution
5j2+2j
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Find the excluded values
j=1
Evaluate
j−15j3−3j2−2j
To find the excluded values,set the denominators equal to 0
j−1=0
Move the constant to the right-hand side and change its sign
j=0+1
Solution
j=1
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Find the roots
j1=−52,j2=0
Alternative Form
j1=−0.4,j2=0
Evaluate
j−15j3−3j2−2j
To find the roots of the expression,set the expression equal to 0
j−15j3−3j2−2j=0
Find the domain
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Evaluate
j−1=0
Move the constant to the right side
j=0+1
Removing 0 doesn't change the value,so remove it from the expression
j=1
j−15j3−3j2−2j=0,j=1
Calculate
j−15j3−3j2−2j=0
Divide the terms
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Evaluate
j−15j3−3j2−2j
Factor the expression
j−1(j−1)(5j2+2j)
Reduce the fraction
5j2+2j
5j2+2j=0
Factor the expression
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Evaluate
5j2+2j
Rewrite the expression
j×5j+j×2
Factor out j from the expression
j(5j+2)
j(5j+2)=0
When the product of factors equals 0,at least one factor is 0
j=05j+2=0
Solve the equation for j
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Evaluate
5j+2=0
Move the constant to the right-hand side and change its sign
5j=0−2
Removing 0 doesn't change the value,so remove it from the expression
5j=−2
Divide both sides
55j=5−2
Divide the numbers
j=5−2
Use b−a=−ba=−ba to rewrite the fraction
j=−52
j=0j=−52
Check if the solution is in the defined range
j=0j=−52,j=1
Find the intersection of the solution and the defined range
j=0j=−52
Solution
j1=−52,j2=0
Alternative Form
j1=−0.4,j2=0
Show Solution