2.2-2.4 Test Flashcards
Leading Coefficient Test
f(x)=3/4(x⁴+3x²+2)
Left side up
Right side up
Leading Coefficient Test
f(x)=-x²+6x+9
Left side down
Right side down
Finding Zeros
f(x)=2x²+11x-21
0=(2x-3)(x+7)
Zeros; 3/2, -7
Finding Zeros
f(x)=-12x³+20x²
0=-x²(12x-20)
Zeros; 0, 5/3
Finding Zeros
f(t)=t³-3t
0=t(t+√(3))(t-√(3))
Zeros; 0, ±√(3)
Intermediate Value Theorem
f(x)=3x³-x²+3
(-1,0)
Intermediate Value Theorem
f(x)=x⁴-5x-1
(-1,0) (1,2)
Long Division to Divide Polynomials
24x²-x-8)/(3x-2
8x+5+(2/(3x-2))
Long Division to Divide Polynomials
5x³-13x²-x+2)/(x²-3x+1
5x+2
Long Division to Divide Polynomials
X⁴-3x³+4x²-6x+3)/(x²+2
X²-3x+2-(1)/(x²+2)
Using Synthetic Division to Divide Polynomials
6x⁴-4x³-27x²+18x)/(x-(2/3)
6x³-27x
Using Synthetic Division to Divide Polynomials
2x³-19x²+38x+24)/(x-4
2x²-11x-6
Using Synthetic Division to Prove Factors f(x)=20x⁴+9x³-14x²-3x A) x=-1 B) x=3/4 C) x=0 D) x=1
A)yes
B)yes
C)yes
D)no
Using Synthetic Division to Find the Value of the Function
f(x)=x⁴+10x³-24x²+20x+44
A) f(-3)
B) f(-1)
A)-421
B)-9
A) verify given factors
B) find remaining factors
C) use your results to write the complete factorization
D) list all zeros
E) check it by putting the original function and your answer to part c into a graphing utility, and graphing them on the same plane
f(x)=x⁴-4x³-7x²+22x+24
(x+2)(x-3)
A) if you got this far, good job B) (x+1),(x-4) C) f(x)=(x+2)(x+1)(x-4)(x-3) D) -2,-1,4,3 E) I could really care less
A) verify given factors
B) find remaining factors
C) use your results to write the complete factorization
D) list all zeros
E) check it by putting the original function and your answer to part c into a graphing utility, and graphing them on the same plane
f(x)=x³+4x²-25x-28
(X-4)
A) good job for getting this far! B) (x+7),(x+1) C) f(x)=(x+7)(x+1)(x-4) D) -7, -1, 4 E) do it if you care to
Write the complex number in standard form
3-√(-25)
3-5i
Write the complex number in standard form
-5i+i²
-1-5i
Perform the operation. Result in standard form.
(√(2)/2)-(√(2)/2)i)-((√(2)/2)+(√(2)/2)i
-i√(2)
Perform the operation. Result in standard form.
1+6i)(5-2i
17+28i
Perform the operation. Result in standard form.
i(6+i)(3-2i)
9+20i
Perform the operation. Result in standard form.
3+2i)/(5+i
(17/26)+(7/26)i
Perform the operation. Result in standard form.
1/(2+i))-(5/(1+4i
(9/85)+(83/85)i
Write a polynomial given the zeros
0,10
x(x-10)
Or
x²-10x
Write a polynomial given the zeros
2,-6
(x-2)(x+6)
Or
x²+4x-12
Write a polynomial given the zeros
0,-2,-3
x(x+2)(x+3)
Or
x³+5x²+6x
Write a polynomial given the zeros
4,-3,3,0
x(x-4)(x+3)(x-3)
Or
x⁴-4x³-9x²+36x
Write a polynomial given the zeros
1+√(3),1-√(3)
x²-2x-2
Find a polynomial of degree n with given zeros
Zeros=-2
N=2
x²+4x+4
Find a polynomial of degree n with given zeros
Zeros=-3,0,1
N=3
x³+2x²-3x
Find a polynomial of degree n with given zeros
Zeros=0,√(3),-√(3)
N=3
x³-3x
Find a polynomial of degree n with given zeros
Zeros=-5,1,2
N=4
x⁴+x³-15x²+23x-10
Find a polynomial of degree n with given zeros
Zeros=0,-4
N=5
x⁵+16x⁴+96x³+256x²+256x
what are the equations for finding the square roots of complex numbers?
(a+bi)²=x+yi
a²-b²=x
a²+b²=√(x²+y²)
