Question

A quadratic monomial with a leading coefficient of 6

Answer 1

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 $6x^2$.

The second statement is "A linear binomial with a leading coefficient of 2".

Linear binomial means $ax+b$, where a and b are real values. The leading coefficient is 2. So, $a=2$.

Let $b=1$, then the required linear binomial is $2x+1$.

Therefore, a quadratic monomial with a leading coefficient of 6 is $6x^2$.

A linear binomial with a leading coefficient of 2 is $2x+1$.