Form a polynomial whose zeros and degree are given. Zeros: −2, 2, 8; degree: 3 Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below.

Question

Form a polynomial whose zeros and degree are given.   ​Zeros:  −2​,  2​,  8​;  ​ degree: 3  Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below.

Jenny Sheppard · Accepted Answer

Step 1  We have to find the polynomial whose zeros and degree are as follows -   Zeros = -2, 2, 8  Degree = 3  And leading coefficient is 1.  The general form of a polynomial function is as follows-   f(x)=a(x−c1)(x−c2)(x−c3)…(x−cn)  Step 2  Given that the zeros are -2, 2, 8 therefore the factors of the required polynomial are - (x+2), (x-2) and (x-8).  Since the degree is 3 and the leading coefficient is 1, therefore, the required polynomial is written as -   f(x)=1(x+2)(x-2)(x-8)  f(x)=(x2−4)(x−8)  f(x)=x3−8x2−4x+32  This is the required polynomial.

vicki331g8 · Accepted Answer

Let f(x)=x(x+2)(x-2)(x-8)  Since leading coefficient  ∴f(x)=(x+2)(x−2)(x−8)  =(x2−4)(x−8)  =x3−8x2−4x+32

Vasquez · Accepted Answer

Given, a polynomial f(x) with zeros -2,2,8. ⇒f(x)=(x−(−2))(x−2)(x−8)=(x+2)(x−2)(x−8)=(x2−4)(x−8)=x2(x−8)−4(x−8)f(x)=x3−8x2−4x+32 This is the required polynomial.

Form a polynomial whose zeros and degree are given. Zeros: −2, 2, 8;

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