How do you factor 80x2-5?

Answer 1

5x**2-30x-80

1. Remove common term (and ignore til end):

5(x**2-6x-16)

2. Multiply first and third terms

1*-16=-16

3. Factor product of first and third terms

-16, 1

-8, 2

-4, 4

16, -1

8, -2

4. Choose factors whose sum is equal to second term

-8+2=-6

5. Rewrite equation using factors

x**2-8x+2x-16

6. Halve the expression

x**2-8x

2x-16

7. Factor each half

x**2-8x --> x(x-8)

2x-16 --> 2(x-8)

8. Recombine

x(x-8)+2(x-8)

9. Factor out common term:

(x-8)(x+2)

10. Reintroduce part from beginning

5(x-8)(x+2)

Answer 2

5(4x + 1)(4x - 1)

Answer 3

(r - 5t)(r + 3w)