Question
Factor the expression
a(13a2−12a−7)
Evaluate
13a3−12a2−7a
Rewrite the expression
a×13a2−a×12a−a×7
Solution
a(13a2−12a−7)
Show Solution

Find the roots
a1=136−127,a2=0,a3=136+127
Alternative Form
a1≈−0.405341,a2=0,a3≈1.328418
Evaluate
13a3−12a2−7a
To find the roots of the expression,set the expression equal to 0
13a3−12a2−7a=0
Factor the expression
a(13a2−12a−7)=0
Separate the equation into 2 possible cases
a=013a2−12a−7=0
Solve the equation
More Steps

Evaluate
13a2−12a−7=0
Substitute a=13,b=−12 and c=−7 into the quadratic formula a=2a−b±b2−4ac
a=2×1312±(−12)2−4×13(−7)
Simplify the expression
a=2612±(−12)2−4×13(−7)
Simplify the expression
More Steps

Evaluate
(−12)2−4×13(−7)
Multiply
(−12)2−(−364)
Rewrite the expression
122−(−364)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
122+364
Evaluate the power
144+364
Add the numbers
508
a=2612±508
Simplify the radical expression
More Steps

Evaluate
508
Write the expression as a product where the root of one of the factors can be evaluated
4×127
Write the number in exponential form with the base of 2
22×127
The root of a product is equal to the product of the roots of each factor
22×127
Reduce the index of the radical and exponent with 2
2127
a=2612±2127
Separate the equation into 2 possible cases
a=2612+2127a=2612−2127
Simplify the expression
a=136+127a=2612−2127
Simplify the expression
a=136+127a=136−127
a=0a=136+127a=136−127
Solution
a1=136−127,a2=0,a3=136+127
Alternative Form
a1≈−0.405341,a2=0,a3≈1.328418
Show Solution
