Question

What polynomial has a graph that passes through the given points? (–4, 89), (–3, 7), (–1, –1), (1, –1), (4, 329) a)y = 2x3 – 3x2 – 2x + 1 b)y = 1x4 – 2x3 – 3x2 + 2x + 1 c)y = x4 – 2x3 + 3x2 + 2x – 1. d)y = x4 + 2x3 – 3x2 – 2x + 1

Answer 1

Let

`A (-4, 89) B (-3, 7)C (-1, -1) D (1, -1)E (4, 329)`

Using a graph tool

case a)
`y = 2x^(3)-3x^(2)-2x + 1`

see the attached figure N
`1`

The polynomial is not the solution

case b)
`y = x^(4)-2x^(3)-3x^(2) + 2x+1`

see the attached figure N
`2`

The polynomial is not the solution

case c)
`y = x^(4)-2x^(3)+3x^(2) + 2x-1`

see the attached figure N
`3`

The polynomial is not the solution

case d)
`y = x^(4)+2x^(3)-3x^(2) - 2x+1`

see the attached figure N
`4`

The polynomial pass through all the points

therefore

the answer is the polynomial

d)
`y = x^(4)+2x^(3)-3x^(2) - 2x+1`

Answer 2

The way to answer this problem given different points and different equations in the choices is to do substitution and trial and error. In this regard, we substitute for example 4 to x in the equations and check which of them yields 89. The answer is D.