5.1,5.2,5.4,5.7 Flashcards
(25 cards)
Steps for Finding Zeroes
1.Divide GCF 2.Factor or Quadratic Equation 3.Set each factor=0 and solve
Quadratic equation
When finding zeros the X, X squared, x cubed etc. divided out…
Must be put to zero additionally resulting in
1 zero, 2 zeroes, 3 zeroes, etc. respectively
Remember, the square roots of certain numbers results in
+ or - the number, ex. the square root of one results in (x+1) (x-1)
Multiplicity Symbol
an m in a circle followed by the number of times it is repeated
Find Polynomial Equation:Steps
- write solution into factored form (x+#) (x-#)
- multiply factors together, foil 2 at a time
- simplify
End Behavior
Directions arrows point
Turning points
and steps to find it on the calculator
where direction changes (top of hill, bottom of trough)
Calculate Menu-Min/Max
Intervals
I=Increasing
D=Decreasing
∞=All Positive Numbers
-∞= All Negative Numbers
<x>
</x>
Domain
Does the Graph Span all the Way from Lef to Right
Yes:All real #s
No:an inequality=
right- x>or=#
left-x<or>
</or>
Range
Does the Graph Span all the Way Up and Down
Yes:All real #s
No:an inequality=
Up-x><or>
</or>
X intercepts
Where the graph intercepts the x-axis
Synthetic Division lowers the degree of a polynomial by
One
In synthetic divisions if any power is missing in the sequence
add zeroes as place holders
Synthetic Division:Steps
1.Set the factor equal to zero and solve for x
Write the coefficients of the dividend
- Bring the first coefficient down to the bottom line.
- Multiply the coefficient by the divisor. Put this product underneath the second coefficent and add these two numbers.
- Continue multiplying and adding through the last coefficient.
The final sum is the remainder.
In synthetic division if the remainder is zero
the divisor is a factor
(the divisor is the (x+2) not the x squared+2x-2, that is the dividend)
Binomial Theorem Steps
- The power of the binomial corresponds to the second numer in each row of Pascal’s triangle. Thr numbers of the row are the coefficients of the expansion.
- The exponents of the first of the expansion count down beginning with the power of the binomials and decrease until you reach zero. The exponenets of the second term of the expansion count up beginning with zero and increase until you reach the power of the binomial. (multiply power before coefficient) (only multiply the coefficient with the first number) (combine both numbers into one number)
- Simplify all terms to write the expansion in standard form (add them)
A polynomial has a zero at x=b. Find one of its factors.
(x-b)
The term 126cto4dto5 appears in the expansion of (c+d)to n. What is n?
126c4d5=4+5=9
Graph a quadratic equation. What is the most solutions this function could have?
Quadratic equation is degree 2. So at most 2 solutions. (it looks like a U, so when both arms cross the x axis. If the bottom of the tough touches the x axis= 1 solution, if the xa sis is not touched= zero soultions.)
Can a graph still have an interval if there are no turning points ?
Yes, a graph with no turning points would simply be increasing or decreasing throughout the entire graph.
Remainder Theorem
Put the number in ths box without changing the sign. Solution P(#)=#
How do you find if a something is a factor
use synthetic division and if there is no remainder it is, if there is, then it is not
State the number of terms in (x-y)to the 15th
16 terms, there is always one more term than power
