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 + 15f(x) = x4 + 3x3 − 8x2 + 5x − 25f(x) = x3 − 2x2 − x + 2f(x) = -x3 + 13x − 12x − 2arrowRightx + 3arrowRightx + 4arrowRightx + 5arrowRight

Answer 1

The first polynomial is given below as

`\begin{gathered} f(x)=x^3-3x^2-13x+15 \\ x+3=0 \\ x=-3 \\ f(-3)=(-3)^3-3(-3)^2-13(-3)+15 \\ f(-3)=-27-27+39+15 \\ f(-3)=0 \end{gathered}`

Hence,

The first answer is

`\begin{gathered} (x+3) \\ is\text{ a factor of} \\ f(x)=x^(3)-3x^(2)-13x+15 \end{gathered}`

Step 2:

The second function is given below as

`\begin{gathered} f(x)=x^4+3x^3-8x^2+5x-25 \\ x+5=0 \\ x=-5 \\ f(-5)=(-5)^4+3(-5)^3-8(-5)^2+5(-5)-25 \\ f(-5)=625-375-200-25-25 \\ f(-5)=0 \end{gathered}`

Hence,

The final answer is

`\begin{gathered} x+5 \\ is\text{ a factor of } \\ f(x)=x^4+3x^3-8x^2+5x-25 \end{gathered}`

Step 3:

The fourth function is given below as

`\begin{gathered} f(x)=x^3-2x^2-x+2 \\ x-2=0 \\ x=2 \\ f(2)=2^3-2(2^2)-2+2 \\ f(2)=8-8-2+2 \\ f(2)=0 \end{gathered}`

Hence,

The final answer is

`\begin{gathered} (x-2) \\ is\text{ a factor of} \\ f(x)=x^3-2x^2-x+2 \end{gathered}`

Step 4:

`\begin{gathered} f(x)=-x^3+13x-12 \\ x+4=0 \\ x=-4 \\ f(-4)=-(-4)^3+13(-4)-12 \\ f(-4)=64-52-12 \\ f(-4)=0 \end{gathered}`

Hence,

The final answer is

`\begin{gathered} x+4 \\ is\text{ a factor of } \\ f(x)=-x^3+13x-12 \end{gathered}`