An expression of the fifth degree with a leading coefficient of seven and a constant term of six is correctly written as 7x^5 + 2x^2 + 6.

The expression you've provided, 7x^5 + 2x^2 + 6, is indeed an expression of the fifth degree due to the highest power of x being five (x^5). The leading coefficient is the coefficient of the term with the highest power, which in this case is seven (7), as indicated in the term 7x^5. And finally, the constant term, which is the term without a variable, is six (6). Therefore, your expression meets the criteria you've specified: a fifth degree expression with a leading coefficient of seven and a constant term of six.

Extra: In algebra, polynomial expressions are made up of terms combined by addition or subtraction. Each term in a polynomial contains a coefficient (the numerical factor) and often a variable raised to a power. The degree of the polynomial is determined by the highest power of the variable present in the expression. For instance, a fifth degree polynomial, also called a quintic polynomial, will have its highest variable term in the form of x^5.

The leading coefficient of a polynomial is the coefficient of the term with the highest degree. It is significant because it influences the end behavior of the polynomial's graph. For example, if the leading coefficient is positive, as x approaches infinity, the polynomial will tend toward positive infinity as well.

The constant term is the term that does not contain a variable. It can affect the y-intercept of the graph when the polynomial is plotted on a standard (x,y) coordinate plane. The y-intercept is the point where the graph crosses the y-axis, which occurs when x equals zero. For the expression above, when x=0, the value of the polynomial is 6, indicating that the y-intercept is at (0, 6).