Question

20. One factor of x^3 + 2x^2 – 23x - 60 is x +4. Find
the remaining factors.

Answer 1

Answer: use x+4 to divide x³+2x²-23x-60

x² -2x-15

__________

x+4 √x³+2x²-23x-60

-(x³+4x²)

-2x²-23x-60

-(-2x²-8x)

-15x-60

-(-15x-60)

Factorize x²-2x-15

x²-5x+3x-15

x(x-5)+3(x-5)

(x-5)(x+3)

Explanation:

Answer 2

x – 5 and x + 3

Explanation:

Knowing that x + 4 is a factor, we can use grouping to factor:

x³ + 2x² – 23x – 60

x³ + 2x² – 8x – 15x – 60

x (x² + 2x – 8) – 15 (x + 4)

x (x – 2) (x + 4) – 15 (x + 4)

(x (x – 2) – 15) (x + 4)

(x² – 2x – 15) (x + 4)

(x – 5) (x + 3) (x + 4)

To use long division, see attached image.