Question

Write an expression in factored form for the polynomial of least possible degree graphed below

Answer 1

Factoring a polynomial involves writing the polynomial in a simpler form

The factored form of the polynomial is: $y = (x + 3)(x + 2)(x - 1)(x -3)$

How to factor the polynomial

From the graph, the zeros of the graph are:

x = -3

x = -2

x = 1

x = 3

Equate the above equations to 0

x + 3 = 0

x + 2 = 0

x - 1 = 0

x - 3 = 0

Multiply the equations

$(x + 3)(x + 2)(x - 1)(x -3) = 0 *0*0*0$

This gives

$(x + 3)(x + 2)(x - 1)(x -3) = 0$

Express as a function

$y = (x + 3)(x + 2)(x - 1)(x -3)$

Hence, the factored form of the polynomial is:

$y = (x + 3)(x + 2)(x - 1)(x -3)$

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