Question

A quadratic monomial with a leading coefficient of 6

A linear binomial with a leading coefficient of 2

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`.