Question

Find ((f/g)(x)) using long division for (f(x)=x^2+7x+13) and (g(x)=x+3).

a) The quotient is (x+4), the remainder is (1).

b) The quotient is (x+4), the remainder is (-3).

c) The quotient is (x+5), the remainder is (2).

d) The quotient is (x+3), the remainder is (4).

Answer 1

The correct answer to find (f/g)(x) using long division for f(x)=x^2+7x+13 and g(x)=x+3 is option a, which states that the quotient is (x+4) and the remainder is (1). The long division process shows that dividing f(x) by g(x) results in a quotient with an additional term 'x' and a constant '4'.

Step-by-step explanation:

To find (f/g)(x) using long division for f(x)=x^2+7x+13 and g(x)=x+3, you would set up the long division by writing x^2+7x+13 inside the division box and x+3 outside. Divide the first term of the dividend (x^2) by the first term of the divisor (x), which gives you x. Multiply x+3 by x to subtract from the dividend, yielding a new dividend of 4x+13. Repeat the division step by dividing 4x by x to get 4, and the process ends with a remainder of 1 when you subtract the product of 4(x+3) from 4x+13. So, the quotient is x+4, and the remainder is 1, which corresponds to option a: The quotient is (x+4), the remainder is (1).