Final answer:
To evaluate the expression (6x²+24x+13)-:(x+3), divide each term inside the parentheses by (x+3) using long division. Combine the resulting terms to obtain the quotient a, which is 54x + 13.
Step-by-step explanation:
To evaluate the expression (6x²+24x+13)-:(x+3), we need to divide the expression inside the parentheses by (x+3). This can be done by using the distributive property of division. First, divide each term inside the parentheses by (x+3) and then simplify the expression.
The expression inside the parentheses is a quadratic expression, so we can divide each term by (x+3) using long division. Divide the first term, 6x², by (x+3) to get 6x. Then, multiply (x+3) by 6x to get 6x²+18x. Subtract this from the original quadratic expression to get 6x²+24x - (6x²+18x) = 6x²+24x - 6x² - 18x = 6x + 6x + 24x - 18x = 30x.
The second term, 24x, is already divisible by (x+3), so it remains the same.
The third term, 13, is not divisible by (x+3), so it remains the same as well.
The resulting expression after dividing each term by (x+3) is 30x + 24x + 13. Combining like terms, we get 54x + 13. Therefore, the quotient a is equal to 54x + 13.