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| A polynomial is a factor of a.... |
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Definition
| polynomial F(x) if there is a polynomial Q(x) such that F(x)=D(x)*Q(x) |
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| Finite Sequence of precise steps that leads to the solution of a problem |
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| F(x)/D(x) Is Improper if.... |
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| F(x) is greater than or equal to Degree of D(x) |
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| R(x)/D(x) Is Proper if..... |
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| R(x) is less than Degree of D(x) |
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Dividend=Divisor + Quotient
or
Dividend=Divisor*Quotient+Remainder |
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| The Dividend is Divided by the.... |
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| What is Divided by the Divisor? |
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| What is the first step to Long Division of Polynomials? |
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| Write the terms in the dividend and the divisor in descending powers of the variable |
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| What is the second step to Long Division of Polynomials? |
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| Insert terms with zero coefficients in the dividend for any missing powers of the variable |
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| What is the third step to Long Division of Polynomials? |
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| Divide the first term in the dividend by the first term in the divisor to obtain the first term in the quotient |
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| What is the fourth step to Long Division of Polynomials? |
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| Multiply the divisor by the first term in the quotient and subtract the product from the dividend |
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| What is the fifth step to Long Division of Polynomials? |
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Definition
| Treat the remainder obtained in Step 4 as a new dividend and repeat steps three and four. Continue this process until a remainder is obtained that is a lower degree than the divisor |
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| What is the sixth step to Long Division of Polynomials? |
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| Write the quotient and the remainder |
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| What are the steps to long division of polynomials? |
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Definition
1.)Write the terms in the dividend and the divisor in descending powers of the variable
2.)Insert terms with zero coefficients in the dividend for any missing powers of the variable
3.)Divide the first term in the dividend by the first term in the divisor to obtain the first term in the quotient
4.)Multiply the divisor by the first term in the quotient and subtract the product from the dividend
5.)Treat the remainder obtained in Step 4 as a new dividend and repeat steps three and four. Continue this process until a remainder is obtained that is a lower degree than the divisor
6.)Write the quotient and the remainder |
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| What is the Objective of Polynomial Synthetic Division? |
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Definition
| Divide a polynomial F(x) by x-a |
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| What is the objective of polynomial long division? |
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| Find the quotient and remainder when one polynomial is divided by another |
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| What is the first step to polynomial synthetic division? |
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Definition
| Arrange the coefficients of F(x) in order of descending powers of x, supplying zero as the coefficient of each missing power |
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| Let f(x) be a polynomial a is a zero of p, if |
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Definition
f(a)=0
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a is a root of f
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(a,0) is an x-intercept of the graph of f |
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| How to find the zeroes of a function |
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| Set the function to equal zero, find the solution set for each x that will make the function equal zero |
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| A unit is a solution set that comes from a factored polynomial that had an exponent, has a multiplicity of that exponent. |
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| What is the second step to polynomial synthetic division? |
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| Replace the divisor x-a with a. Place a in the position to the left of the coefficients. |
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| What is the third step to polynomial synthetic division? |
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Definition
Bring the leftmost coefficient down below the line.
Multiply it by a and write the product one column to the right and above the line. |
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| What is the fourth step to polynomial synthetic division? |
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Definition
| Add the product obtained in the previous step to the coefficient directly above it and write the resulting sum directly below it and below the line. The sum is the newest number below the line. |
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| What is the fifth step to polynomial synthetic division? |
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Definition
| Multiply the newest number below the line by a, write the resulting product one column to the right and above the line, and repeat step 4. |
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| What is the sixth step to polynomial synthetic division? |
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| Repeat step 5 until a product is added to the constant term. Separate the last number below the line with a short vertical line |
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| What is the seventh step to polynomial synthetic division? |
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| The last number below the line is the remainder, and the other numbers reading left to right, are the coefficients of the quotient, which has a degree one less than the dividend F(x) |
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| If a polynomial F(x) is divided by x-a, then the remainder is given by R=F(a) |
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| A polynomial F(x) has (x-a) as a factor if and only if F(a)=0 |
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