The illustration below is a graph of the polynomial function P(x). The graph crosses the x-axis 2 times and touches the x-axis once at the point (4, 0).

Question

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Answer 1

Synthetic division by root x=-2: 2x^2+3x-2=(2x-1)(x+2). Factors: P(x)=((x+2)^2)(2x-1) Solution: x=-2 (multiple), x=1/2. These are the zeroes. Note that the graph touches the x axis at x=-2 and crosses it at x=1/2.

-2 | 2..7..4 -4

......2 -4 -6..4

......2..3 -2 | 0

y intercept is -4 (when x=0). Degree of polynomial is 3. For x<-2, as x becomes more negative the graph heads towards minus infinity. For x>1/2 the graph heads towards plus infinity as x gets larger.