Graph each polynomial function.f(x)=2x^{3) - 7x^{2} + 2x + 3given that 3 is a zero.

Tammy Todd 2021-02-05 Answered

Graph each polynomial function. f(x)=2x3  7x2 + 2x + 3 given that 3 is a zero.

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Expert Answer

Velsenw
Answered 2021-02-06 Author has 91 answers

Step 1 To find the y-intercept evalute f(0) f(x)=2x3  7x2 + 2x + 3
f(0)=2(0)3  7(0)2 + 2(0) + 3 Substitute 0 for x =3 Simplify So, the y-intercept is (0, 3)

Step 2 f(x)=2x3  7x2 + 2x + 3 given that 3 is a zero Use synthetic division image The quotient is 2x2  x  1
2x2  x  1=0
(2x + 1)(x  1)=0 Factor the trinomial
2x + 1=0 or x  1=0 Solve each factor equal to 0
x= 12 or x=1 Solve each equation So, 12 and 1 are zeros of f(x) The graph of f(x) crosses the x-axis at (3, 0), (12, 0), and(1, 0) Plot the points (1, 8) and (2, 5) See the graph below. image

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