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  $-x^3 + 13x - 12$

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   $x^3-3x^2-13x+15$,

If x=-3 then  $x^3-3x^2-13x+15= -3^3-3(-3)^2-13\times -3+15 =0$

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