Question

Can you factor this completely x^4-16x^3+15x^2

Answer 1

Answer is
x = 0
x = 1
x = 15

Step by step

Given x^4 -16x^3 + 15x^2

First I factored out x^2 from all terms

x^2 (x^2 - 16x +15) = 0
x^2 = 0
√x^2 = √0
x = 0

Now I can factor inside the parentheses

x^2 - 16x +15 = 0

What factor will multiply for product of +15 and also add to sum of -16?
-1 and -15

(x -1) (x - 15) = 0
Solve for each

x - 1 = 0
add 1 to both sides to solve
x -1 +1 = 0 +1
Simplify
x = 1

x - 15 = 0
add 15 to both sides to solve
x -15 + 15 = 0 + 15
Simplify
x = 15

Answer 2

(x-15)(x-1) x²

Explanation:

x² (x²-16x+15)

a+b=-16

ab=15

a=-15

b=-1

x(x²-15)- (x-15)

(x-15)(x-1)

(x-15)(x-1) x²