Why do you think it is necessary to express polynomials as a product and as factors? Give examples.
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Why do you think it is necessary to express polynomials as a product and as factors? What are some examples?
Indeed, polynomials can be written in two different forms:
a) As sum of terms: integrating and differentiating is easier with this form.
b) As product of factors: finding the roots is easier with this form.
As example, the same polynomial p(x) can be written as:
a) p(x) = x^2 + x - 6 ; sum of three terms
b) p(x) = (x + 3)(x - 2) ; product of two factors
Form a) tells me that p(x) crosses the y-axis at y=-6
the y-intercept p(0) can be directly found as it’s the last constant term
Form b) tells me that p(x) crosses the x-axis at x=-3 and x=2
p(x)=0; a product is 0 when one of the factors is 0
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