Given:
A quadratic monomial with a leading coefficient of 6.
A linear binomial with a leading coefficient of 2.
To find:
The mathematical terms for the given statements.
Solution:
Monomial: The expression with single term.
Binomial: The expression with two terms.
Quadratic: Highest power of the variable is 2.
Linear: Highest power of the variable is 1.
Coefficient: In the product of a number and a variable, the number is known as the coefficient of that variable.
The first statement is "A quadratic monomial with a leading coefficient of 6".
Quadratic monomial means single term with degree 2. The leading coefficient of 6. So, the term is [tex]6x^2[/tex].
The second statement is "A linear binomial with a leading coefficient of 2".
Linear binomial means [tex]ax+b[/tex], where a and b are real values. The leading coefficient is 2. So, [tex]a=2[/tex].
Let [tex]b=1[/tex], then the required linear binomial is [tex]2x+1[/tex].
Therefore, a quadratic monomial with a leading coefficient of 6 is [tex]6x^2[/tex].
A linear binomial with a leading coefficient of 2 is [tex]2x+1[/tex].
