Question

The partial graph of a 4th-degree polynomial function P(x) is shown. The leading coefficient is 1 and the x-intercepts of the graph are integers

Answer 1

If the polynomial function is written in the form P(x) = c(x − a)2(x − b)(x + d), where a, b, c, and d are all positive integers, then what is the value of d?

Answer 2

and you want the polynomial right?

Answer 3

the zeros are there for you to see from your eyeballs
one (the one where the graph touches but does not cross) has multiplicity 2

Answer 4

what are the zeros (where the graph crosses the x axis)?

Answer 5

(0,4) and (0, -3) ?

Answer 6

you have it backwards

Answer 7

the x is the first coordinate, the zero is the y coordinate

Answer 8

also include the point where it touches

Answer 9

oops sorry (4,0) and (-3,0)

Answer 10

yeah and also \((1,0)\)

Answer 11

which means you know how to factor it
\[(x+3)(x-4)(x-1)^2\]

Answer 12

on account of if \(r\) is a zero, then one factor of the polynomial is \((x-r)\)

Answer 13

Just make a comparison to find d
\(P(x) = c(x-\color{blue}{a})^\color{red}{2}(x-\color{green}{b})(x+\color{orange}{d})\)
to your polynomial above
\(1(x-\color{blue}{1})^\color{red}{2}(x-\color{green}{4})(x+\color{orange}{3})\)
Hence \(\color{orange}{d}\) is?