Analizing the polynomial y=(x−1)(3x−2)(x+3) a) Determine the roots of the polinomial b) Determine the end behaviors c) Determine how many turning points

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Analizing the polynomial  y=(x−1)(3x−2)(x+3)  a) Determine the roots of the polinomial  b) Determine the end behaviors  c) Determine how many turning points

Sally Cresswell · Accepted Answer

Step 1 Explanation: Given that, y=(x−1)(3x−2)(x+3) a) Determine the roots of the polynomial. To find the roots, put y=0 and solve for x (x−1)(3x−2)(x+3)=0 x−1=0 x=1 3x−2=0 x=32 x+3=0 x=−3 Roots are: −3, 1, 32 Step 2 b) Determine end behaviour. Write the polynomial in standard form. y=(x−1)(3x−2)(x+3) y=3x3+4x2−13x+6 Here we see that, leading coefficient is +3 that is positive. and degree of the polynomial is 3. Rule says, When degree is odd and leading coefficient is positive end behaviour of the polynomial is: f(x)→−∞, as x→−∞ f(x)→∞, as x→∞ c) Determine the number of turning points. A polynomial of degree n will have at most n−1 turning points. Here degree of given polynomial is 3 Number of turning points =3−1=2

Analizing the polynomial y=(x-1)(3x-2)(x+3) a) Determine the roots of the polinomial b) Determine

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