6-2 Polynomials and Linear Factors

6-2 Polynomials and Linear Factors

Standard and Factored Form • Standard form means to write it as a simplified (multiplied out) polynomial starting with the highest degree term and working down to the constant term. 3x2 + 2x – 7 • Factored form means to write it as the product of two or more factors by factoring. (remember GCF first!) (x – 4)(x + 2)(x + 1)

Zeros • A zero is a (solution or x-intercept) to a polynomial function. • If (x – a) is a factor of a polynomial, then a is a zero (solution) of the function. • If a polynomial has a repeated solution, it has a multiple zero. • The number of repeats of a zero is called its multiplicity.

Finding Zeros • To find the zeros of a polynomial, we can either graph or we can factor. (2x – 1)(2x – 1)(x + 5)(x – 5)

Finding Zeros • To find the zeros of a polynomial, we can either graph or we can factor. (2x – 1)(2x – 1)(x + 5)(x – 5) 2x – 1=0

Finding Zeros • To find the zeros of a polynomial, we can either graph or we can factor. (2x – 1)(2x – 1)(x + 5)(x – 5) 2x =1

Finding Zeros • To find the zeros of a polynomial, we can either graph or we can factor. (2x – 1)(2x – 1)(x + 5)(x – 5) x = ½

Finding Zeros • To find the zeros of a polynomial, we can either graph or we can factor. (2x – 1)(2x – 1)(x + 5)(x – 5) x = ½ (multiplicity 2)

Finding Zeros • To find the zeros of a polynomial, we can either graph or we can factor. (2x – 1)(2x – 1)(x + 5)(x – 5) x = ½

Finding Zeros • To find the zeros of a polynomial, we can either graph or we can factor. (2x – 1)(2x – 1)(x + 5)(x – 5) x = ½, -5

Finding Zeros • To find the zeros of a polynomial, we can either graph or we can factor. (2x – 1)(2x – 1)(x + 5)(x – 5) x = ½, -5, 5

Remember • The following are equivalent statements: • -4 is a solution of x2 + 3x – 4 • -4 is an x-intercept of x2 + 3x – 4 • -4 is a zero of y = x2 + 3x – 4 • x + 4 is a factor of x2 + 3x – 4

6-2 Polynomials and Linear Factors