Question

Instructions:Drag the tiles to the correct boxes to complete the pairs. Match each polynomial function with one of its factors. Tiles f(x) = x3 − 3x2 − 13x + 15 f(x) = x4 + 3x3 − 8x2 + 5x − 25 f(x) = x3 − 2x2 − x + 2 f(x) = -x3 + 13x − 12 Pairs x − 2 arrowBoth x + 3 arrowBoth x + 4 arrowBoth x + 5 arrowBoth NextReset

Answer 1

Answer: x + 3 is factor of
`x^3-3x^2-13x+15`,

x + 5 is factor of
`x^4 + 3x^3 - 8x^2 + 5x - 25`,

x - 2 is factor of
`x^3 - 2x^2 - x + 2`

And, x + 4 is factor
`-x^3 + 13x - 12`

Explanation:

Since if for a polynomial f(x), x-a is a factor then f(a)=0, ( because x=a is the zero of the polynomial)

Here, for
`x^3-3x^2-13x+15`,

If x=-3 then
`x^3-3x^2-13x+15= -3^3-3(-3)^2-13* -3+15 =0`

Therefore x-3 is the factor of
`x^3-3x^2-13x+15`.

At x=-5
`x^4 + 3x^3 - 8x^2 + 5x - 25` is equal to zero.

Therefore, x+5 is the factor of
`x^4 + 3x^3 - 8x^2 + 5x - 25`.

At x=2
`x^3 - 2x^2 - x + 2` is equal to zero.

Therefore, x-2 is the factor of
`x^3 - 2x^2 - x + 2`.

At x=-4
`-x^3 + 13x - 12` is equal to zero.

Therefore, x+4 is the factor of
`-x^3 + 13x - 12`.

Answer 2

We have the following functions:
f (x) = x3 - 3x2 - 13x + 15
f (x) = x4 + 3x3 - 8x2 + 5x - 25
f (x) = x3 - 2x2 - x + 2
f (x) = -x3 + 13x - 12
Factoring we have:
f (x) = x3 - 3x2 - 13x + 15 -------> x + 3
f (x) = x4 + 3x3 - 8x2 + 5x - 25 -> x + 5
f (x) = x3 - 2x2 - x + 2 ------------> x - 2
f (x) = -x3 + 13x - 12 -------------> x + 4