For each polynomial function, one zero is given. Find all rational zeros and factor the polynomial. Then graph the function. f(x)=3x^{3}+x^{2}-10x-8, zero:2

illusiia 2020-12-06 Answered

For each polynomial function, one zero is given. Find all rational zeros and factor the polynomial. Then graph the function. f(x)=3x3+x210x8, zero:2

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sovienesY
Answered 2020-12-07 Author has 89 answers

Step 1 Since 2 is a zero of f(x)=3x3+x210x8 The quotient is 3x2+7x+4
f(x)=(x2)(3x2+7x+4) Factor the trinomial 3x2+7x+4=(3x+4)(x+1) So, the function in factored form is f(x)=(x2)(3x+4)(x+1) Set each factor equal to zero x2=0 or 3x+4=0 or x+1=0 So, all rational zeros are 2,42,1 Step 2 Since, all rational zeros are 2,43,1 So, the graph of the function crosses the x-axis at (2,0),(43,0),(1,0) To find the y-intercept evaluate f(0) f(x)=3x3+x210x8
f(0)=3(0)3+(0)210(0)8 Substitute 0 for x =8 The leading coefficient is 3 (positive), and the function of degree 3 (odd) So, the end behavior is x,f(x) x,f(x) See the graph of f(x) image

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