manuels division is shown. manuel did not write the remainder. what is the remainder over the divisor? a + 3…

Explanation:

Step1: Perform polynomial long - division

We have the division of (a^{2}-4a + 3) by (a + 3). First, divide the leading term of the dividend (a^{2}-4a + 3) (which is (a^{2})) by the leading term of the divisor (a+3) (which is (a)). We get (a). Multiply (a + 3) by (a) to get (a^{2}+3a), and subtract it from (a^{2}-4a + 3): ((a^{2}-4a + 3)-(a^{2}+3a)=a^{2}-4a + 3 - a^{2}-3a=-7a + 3).

Step2: Continue the division

Now divide the leading term of (-7a + 3) (which is (-7a)) by the leading term of (a + 3) (which is (a)). We get (-7). Multiply (a + 3) by (-7) to get (-7a-21), and subtract it from (-7a + 3): ((-7a + 3)-(-7a-21)=-7a + 3+7a + 21 = 24). The divisor is (a + 3) and the remainder is (24). The remainder over the divisor is (\frac{24}{a + 3}).

Answer:

(\frac{24}{a + 3})