Mathematics: Write a polynomial in standard form with the zeros -4,0, 1, and 4. A. x4 – x3 - 8x2 + 16x B. x4 – x3 – 16x2 + 16x C. X4 - 7x3 + 8x2 + 16x D. x4-9x3 + 24x2 – 16x

3x+4=7x for the top one4x-1= 3x for the bottom...

Write a polynomial in standard form with the zeros

Ответ:

MalikaJones

31.01.2022

Mathematics

x^4-x^3-16x^2+16x

Step-by-step explanation:

Factor theorem : If x=a is a zero of a polynomial p(x) then (x-a) is a factor of p(x).

Given: Zeroes of polynomial : -4,0, 1, and 4.

Then Factors = (x-(-4)), (x-0), (x-1) and (x-4) [By factor theorem ]

=(x+4), (x-0), (x-1) and (x-4)

Multiplying these factors to get polynomial in standard form.

$(x+4)\times(x-0)\times(x-1)\times(x-4) \\\\= x(x+4)(x-4)(x-1)\\\\= x(x^2-4^2)(x-1)\\\\= x(x^2-16)(x-1)\\\\= x(x^2-16)(x-1)\\\\=x(x^2x+x^2\left(-1\right)+\left(-16\right)x+\left(-16\right)\left(-1\right))\\\\= x(x^3-x^2-16x+16)\\\\=x^4-x^3-16x^2+16x$

Hence, B is the correct option.

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Write a polynomial in standard form with the zeros -4,0, 1, and 4. A. x4 – x3 - 8x2 + 16x
B. x4 – x3 – 16x2 + 16x
C. X4 - 7x3 + 8x2 + 16x
D. x4-9x3 + 24x2 – 16x

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