G12 3.3 P2 Solving Polynomial Equations

The value 4 is an upper bound for the zeros of the function shown below.

$$f\left(x\right)=4x^3-12x^2-x+15$$

The value 5 is an upper bound for the zeros of the function shown below.

$$f\left(x\right)=x^4+x^3-11x^2-9x+18$$

The value -2 is a lower bound for the zeros of the function shown below.

$$f\left(x\right)=4x^3-12x^2-x+15$$

The value -1 is a lower bound for the zeros of the function shown below.

$$f\left(x\right)=x^4+x^3-11x^2-9x+18$$

Express the polynomial as a product of linear factors.

$$f\left(x\right)=x^3+2x^2-x-2$$ ​ ​ ​ ​ ​

Express the polynomial as a product of linear factors.

$$f\left(x\right)=x^3+4x^2+x-6$$ ​ ​ ​

Find the roots of the polynomial shown. What is the value of the largest root?

$$f\left(x\right)=x^3-8x^2-23x+30$$

(a)  

Find the roots of the polynomial shown. What is the value of the largest root?

$$f\left(x\right)=x^3+2x^2-11x-12$$

(a)  

Find the roots of the polynomial shown. What is the value of the largest root?

$$f\left(x\right)=3x^3+12x^2+3x-18$$

(a)