3 years ago

Can someone plz help me with this math equation!

1 answer:

5 0

Answer:

x² + 2x + 9 - $\frac{7}{x+3}$

Step-by-step explanation:

Using Synthetic division

- 3 | 1 5 15 20

↓ - 3 - 6 - 27

----------------------------

1 2 9 - 7 ← remainder r(x)

Quotient Q(x) = x² + 2x + 9

Thus

x³ + 5x² + 5x + 20 = x² + 2x +9 - $\frac{7}{x+3}$

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sammy [17]

Using the rational root theorem, it is found that your friend is correct.

<h3>What is the rational root theorem?</h3>

It is a theorem that states that for a polynomial with integer coefficients, with q being the factors of the leading coefficient and p being the factors of the constant, every <u>possible rational root</u> is the format $\frac{p}{q}$ .

In this problem:

The leading coefficient is 1, hence it's only factor is $q = 1$ , thus guaranteeing that every possible rational zero is an integer, which means that your friend is correct.