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.