Question

When the polynomial is written in standard form, what are the values of the leading coefficient and the constant?

5x + 2 – 3x2

The leading coefficient is 5, and the constant is 2.
The leading coefficient is 2, and the constant is 5.
The leading coefficient is –3, and the constant is 2.
The leading coefficient is 2, and the constant is –3.

Answer 1

We have been provided with the following polynomial 5x + 2 - 3x²

The polynomial is a quadratic polynomial since the maximum power of the variable x is 2.

If we compare the provided polynomial with the general form of the polynomial we can clearly understand that it's not in the general form.

We know the general form of quadratic polynomial is :

• $\sf{\red{ax^2 + bx + c = 0 }}$

How do we identify the leading coefficient?

- Actually, whenever a polynomial is written in such a way that the powers are in descending order, we say that the polynomial is in its general form.

So, yeah now let's head towards the leading coefficient. The coefficient of the leading term is called the leading coefficient.

What is a leading term?

- The term having the highest degree is called the leading term.

What is a constant?

- A number in a polynomial which is not multiplied by a variable is called the constant.

Now, in the provided polynomial let's find the leading coefficient and the constant.

So, let's first write the provided polynomial in the general form.

General form :

• $\sf{\blue{-3x^2 + 5x + 2 = 0}}$

We can see, the variable is x and the highest power is 2.

-3 is the coefficient with highest power of x.

•°• We infer that the leading coefficient is -3.

Also, 2 is the term which isn't multiplied by any variable.

So as per the definition of constant, 2 becomes the constant of the polynomial.

So, we can say that from the provided option, the third one which states, the leading coefficient is -3 and the constant is 2 is correct.

Answer 2

Answer: The answer is C. The leading coefficient is -3, and the constant is 2.

explanation: I just took the test.