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Caelan

Answered question

2021-04-02

Find all rational zeros of the polynomial, and write the polynomial in factored form.

P (x) = 2 x^{3} - 3 x^{2} - 2 x + 3

Arham Warner

Skilled2021-04-04Added 102 answers

Step 1

P (x) = 2 x^{3} - 3 x^{2} - 2 x + 3

All rational zeros = ?
Factored form = ?

P (x) = x^{2} (2 x - 3) - 2 (2 x - 3)

P (x) = (2 x - 3) (x^{2} - 2)

P (x) = (2 x - 3) (x - \sqrt{2}) (x + \sqrt{2})

The polynomial in factored form:

P (x) = (2 x - 3) (x - \sqrt{2}) (x + \sqrt{2})

Step 2
To find rational zeros:
Put P(x) = 0

(2 x - 3) (x - \sqrt{2}) (x + \sqrt{2}) = 0

2 x - 3 = 0 \Rightarrow x = \frac{3}{2}

x - \sqrt{2} = 0 \Rightarrow x = \sqrt{2}

x + \sqrt{2} = 0 \Rightarrow x = - \sqrt{2}

The rational zeros are:

- \sqrt{2}, \sqrt{2}

and

\frac{3}{2}

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