Factor & Solve Polynomials

What is the degree of the polynomial?

 $f\left(x\right)=3x^8+5x\ +12$  

• 3

• 8

• 5

• 12

What is a degree-2 polynomial known as?

• quintic polynomial

• linear polynomial

• cubic polynomial

• quadratic polynomial

What is a degree-3 polynomial known as?

• quintic polynomial

• quartic polynomial

• cubic polynomial

• quadratic polynomial

According to the Fundamental Theorem of Algebra, how many solutions does the following polynomial have?

 $f\left(x\right)=13x^{20}-101x\ +7$  

• 13

• 20

• 101

• 7

If the zeros of f(x) = 5, 10, -13, then the factors of f(x) are:

• (x + 5)(x + 10)(x - 13)

• (x - 5)(x - 10)(x + 13)

• (x + 5)(x - 10)(x + 13)

• (x - 5)(x - 10)(x - 13)

Solve for all zeros:

 $x\left(x-1\right)\left(x+2\right)\left(3x-5\right)\left(x^2+1\right)\ =\ 0$  

•  $x=-1,\ 2,\ -\frac{5}{3},\ \pm i$  

•  $x=0,\ -1,\ 2,\ -\frac{5}{3},\ \pm i$  
  

•  $x=0,\ 1,\ -2,\ \frac{5}{3},\ \pm i$  

• No solution

If the problem asks you to factor a polynomial knowing that (x - 5) is a factor, what number do you synthetically divide by?

• -5

• 5

•  $5i$  
  

•  $\sqrt{5}$  
  

If the problem asks you to factor a polynomial knowing that x = 7 is a zero, what number do you synthetically divide by?

• -7

• 7

•  $7i$  
  

•  $\sqrt{7}$  
  

Factor the polynomial. 

 One factor is (x - 5).

 $f\left(x\right)=2x^3-9x^2-11x+30$  

•  $\left(x+1\right)\left(x+2\right)\left(x+3\right)$  

•  $\left(x+1\right)\left(x+2\right)\left(x-5\right)$  

•  $\left(2x-3\right)\left(x+2\right)\left(x+3\right)$  

•  $\left(2x-3\right)\left(x+2\right)\left(x-5\right)$  

Factor the polynomial. 

 One zero is x = 1.

 $f\left(x\right)=x^3-2x^2-5x+6$  

•  $x=1,\ 2,\ 3$  

•  $x=-1,\ -2,\ -3$  

•  $x\ =-1,\ 2,\ -3$  
  

•  $x\ =1,\ -2,\ 3$