Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
−(x−5)(x−1)
Evaluate
6x−x2−5
Reorder the terms
−x2+6x−5
Rewrite the expression
−x2+(1+5)x−5
Calculate
−x2+x+5x−5
Rewrite the expression
−x×x+x+5x−5
Factor out −x from the expression
−x(x−1)+5x−5
Factor out 5 from the expression
−x(x−1)+5(x−1)
Factor out x−1 from the expression
(−x+5)(x−1)
Solution
−(x−5)(x−1)
Show Solution
Find the roots
x1=1,x2=5
Evaluate
6x−x2−5
To find the roots of the expression,set the expression equal to 0
6x−x2−5=0
Factor the expression
More Steps
Evaluate
6x−x2−5
Reorder the terms
−x2+6x−5
Rewrite the expression
−x2+(1+5)x−5
Calculate
−x2+x+5x−5
Rewrite the expression
−x×x+x+5x−5
Factor out −x from the expression
−x(x−1)+5x−5
Factor out 5 from the expression
−x(x−1)+5(x−1)
Factor out x−1 from the expression
(−x+5)(x−1)
(−x+5)(x−1)=0
When the product of factors equals 0,at least one factor is 0
−x+5=0x−1=0
Solve the equation for x
More Steps
Evaluate
−x+5=0
Move the constant to the right-hand side and change its sign
−x=0−5
Removing 0 doesn't change the value,so remove it from the expression
−x=−5
Change the signs on both sides of the equation
x=5
x=5x−1=0
Solve the equation for x
More Steps
Evaluate
x−1=0
Move the constant to the right-hand side and change its sign
x=0+1
Removing 0 doesn't change the value,so remove it from the expression
x=1
x=5x=1
Solution
x1=1,x2=5
Show Solution