Answer:
[tex]x^3-8x^2+5x+14[/tex]
Step-by-step explanation:
We have been given the zeroes of polynomial which are -1,2,7
That means the factors are (x+1) (x-2) (x-7)
When we want to a polynomial from zeroes we multiply the factors
[tex](x+1)(x-2)(x-7)[/tex]
[tex](x+1)(x^2-7x-2x+14)[/tex]
[tex](x+1)(x^2-9x+14)[/tex]
[tex](x^3-9x^2+14x+x^2-9x+14[/tex]
[tex]x^3-8x^2+5x+14[/tex]
Hence, the required polynomial is:
[tex]x^3-8x^2+5x+14[/tex]
The polynomial function that has a zero at -1,2, and 7 in its standard form is [tex]P(x)=x^3-8x^2+5x+14[/tex]
Given the zeros of a polynomial to be -1, 2 and 7. The factors in "x" will be (x+1), (x-2) and (x-7)
In order to get the required polynomial, we will have to multiply the factors as shown:
[tex]P(x) = (x+1)(x-2)(x-7)\\P(x) = (x^2-2x+x-2)(x-7)\\P(x) = (x^2-x-2)(x-7)\\P(x) = x^3-7x^2-x^2+7x-2x+14\\P(x)=x^3-8x^2+5x+14[/tex]
Hence the polynomial function that has a zero at -1,2, and 7 in its standard form is [tex]P(x)=x^3-8x^2+5x+14[/tex]
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