Polynomials and linear factors
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The document discusses polynomials and their linear factors. It provides examples of polynomial functions with positive integer exponents like Ax^n+bx^n-1+cx^n-2. It also gives examples of specific polynomial functions like F(x)=1/2x^2+2x-3. The document notes that polynomials must have coefficients in descending order and defines what is not a polynomial, like functions with non-positive exponents. It also discusses finding the zeros of polynomials and defines vocabulary terms like degree and standard versus factored form.
Polynomials and linear factors
- 1. Polynomials and Linear FactorsBy: Daniel Yeiser
- 2. Example of a polynomial functionAx^n+bx^n-1+cx^n-2……………………if a,b, andc are real numbers n is a positive integer.
- 3. More examplesF(x)=1/2x^2+2x-3F(x)=6x^4-3x^2+2x-5F(x)=X^7-2F(x)=X^12The coefficients of the terms have to be put into a descending order.
- 4. Not PolynomialsF(x)=X^-2+5F(x)=2x^1/2+3x-4These are not polynomials because the exponents are not positive whole numbers
- 5. Zeros of polynomialsy=x-4. the zero of this one is 4Y=x+5. the zero of this one is -5Y=x^4-14x^2+30x this problem has 3 distinct zerosY=x^4-2x^3. this problem has exactly two zeros
- 6. Vocab. TermsDegree- highest power of x in standard formStandard form- everything in the problem is multiplied togetherFactored form looks like- f(x)=(x-r1) (x-r2)(x-r3)……….