Question

Drag the tiles to the correct boxes to complete the pairs.

Match each polynomial function with one of its factors.
f(x) = x3 − 3x2 − 13x + 15
f(x) = x4 + 3x3 − 8x2 + 5x − 25
f(x) = x3 − 2x2 − x + 2
f(x) = -x3 + 13x − 12
x − 2
arrowRight
x + 3
arrowRight
x + 4
arrowRight
x + 5
arrowRight

Answer 1

Polynomial 1 = x + 3

Polynomial 2 = x + 5

Polynomial 3 = x - 2

Polynomial 4 = x + 4

Explanation:

We are given with Polynomials and and some factors.

We have to match the correct Pair.

We Map the polynomials on the graph then check which factors matches.

Polynomial 1).

x³ - 3x² - 13x + 15

factors are ( x + 3 ) , ( x - 1 ) , ( x - 5 )

Polynomial 2).

`x^4+3x^3-8x^2+5x-25`

factors are ( x + 5 )

Polynomial 3).

`x^3-2x^2-x+2`

factors are ( x + 1 ) ,( x - 1 ) , ( x - 2 )

Polynomial 4).

`-x^3+13x-12`

factors are ( x + 4 ) ,( x - 1 ) , ( x - 3 )

Therefore,

Polynomial 1 = x + 3

Polynomial 2 = x + 5

Polynomial 3 = x - 2

Polynomial 4 = x + 4

Answer 2

f(x) = x3 − 3x2 − 13x + 15 Factor: x+3

f(x) = x4 + 3x3 − 8x2 + 5x − 25 Factor: x+5

f(x) = x3 − 2x2 − x + 2 Factor: x-2

f(x) = -x3 + 13x − 12 Factor: x+4

Explanation:

f(x) = x^3 − 3x^2 − 13x + 15

Solving:

We will use rational root theorem: -1 is the root of x^3 − 3x^2 − 13x + 15 so, factor out x+1

x^3 − 3x^2 − 13x + 15 / x+1 = x^2-2x-15

Factor: x^2-2x-15 =(x+3)(x-5)

So, factors are: (x+1)(x+3)(x-5)

Factor: (x+5)

f(x) = x^4 + 3x^3 − 8x^2 + 5x − 25

Solving:

We will use rational root theorem: -5 is the root of x^4 + 3x^3 − 8x^2 + 5x − 25, so factour out (x+5)

x^4 + 3x^3 − 8x^2 + 5x − 25 / x+5 = x^3-2x^2 +2x -5

So, factors are (x+5) (x^3-2x^2 +2x -5)

Factor: x+5

f(x) = x^3 − 2x^2 − x + 2

Solving:

x^2(x-2)-1(x-2)

(x-2)(x^2-1)

(x-2) (x-1) (x+1)

Factor: x-2

f(x) = -x^3 + 13x − 12

Solving:

-(x^3 + 13x -12)

We will use rational root theorem:

The 1 is a root of (x^3 + 13x -12) so, factor out x-1

Now solving (x^3 + 13x -12)/x-1 we get (x-3)(x+4)

So, roots are: - (x-1)(x-3)(x+4)

Factor (x+4)