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

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

Answer Link

parmesanchilliwack parmesanchilliwack · Answer 2 · 2018-12-03T07:45:12+01:00

Answer: x + 3 is factor of [tex]x^3-3x^2-13x+15[/tex],

x + 5 is factor of [tex]x^4 + 3x^3 - 8x^2 + 5x - 25 [/tex],

x - 2 is factor of [tex]x^3 - 2x^2 - x + 2[/tex]

And, x + 4 is factor [tex]-x^3 + 13x - 12[/tex]

Step-by-step 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 [tex]x^3-3x^2-13x+15[/tex],

If x=-3 then [tex]x^3-3x^2-13x+15= -3^3-3(-3)^2-13\times -3+15 =0[/tex]

Therefore x-3 is the factor of [tex]x^3-3x^2-13x+15[/tex].

At x=-5 [tex]x^4 + 3x^3 - 8x^2 + 5x - 25[/tex] is equal to zero.

Therefore, x+5 is the factor of [tex]x^4 + 3x^3 - 8x^2 + 5x - 25[/tex].

At x=2 [tex]x^3 - 2x^2 - x + 2[/tex] is equal to zero.

Therefore, x-2 is the factor of [tex]x^3 - 2x^2 - x + 2[/tex].

At x=-4 [tex]-x^3 + 13x - 12[/tex] is equal to zero.

Therefore, x+4 is the factor of [tex]-x^3 + 13x - 12[/tex].