Question Video: Finding the Value of a Parameter by Multiplying a Binomial and a Trinomial | Nagwa Question Video: Finding the Value of a Parameter by Multiplying a Binomial and a Trinomial | Nagwa

Question Video: Finding the Value of a Parameter by Multiplying a Binomial and a Trinomial Mathematics • First Year of Preparatory School

Join Nagwa Classes

Attend live Mathematics sessions on Nagwa Classes to learn more about this topic from an expert teacher!

If (π‘₯ + π‘˜)(π‘₯Β² βˆ’ 4π‘₯ + 9) = π‘₯Β³ βˆ’ 11π‘₯Β² + 37π‘₯ βˆ’ 63, find the value of parameter π‘˜.

02:04

Video Transcript

If π‘₯ plus π‘˜ multiplied by π‘₯ squared minus four π‘₯ plus nine equals π‘₯ cubed minus 11π‘₯ squared plus 37π‘₯ minus 63, find the value of parameter π‘˜.

In this question, we have been given a product of a binomial and a trinomial, where the binomial includes an unknown parameter, π‘˜. We have that this product is equal to a cubic expression. In order to find the value of π‘˜, we can expand the product and compare it to the cubic.

Using the distributive property of multiplication over addition, we multiply each of the terms in the trinomial by the binomial. We must be careful to remember the negative sign in front of the four π‘₯ term. Next, we expand each of the products and then combine the like terms.

Now, we have fully expanded the left-hand side. In order to find the value of π‘˜, we can compare this expanded form with the cubic on the right-hand side. We need to compare the coefficients of these two expressions. We can equate any of these three coefficients to find π‘˜. For the π‘₯ squared term, we have π‘˜ minus four equals negative 11. For the π‘₯-term, we have nine minus four π‘˜ equals 37. And for the constant term, we have nine π‘˜ equals negative 63.

We can solve any of these equations to find π‘˜. But for the purpose of this video, we shall solve all three. All three equations rearrange to the same solution, which is that π‘˜ equals negative seven.

Now that we have solved the question, let’s look at another quicker method we could have used to reach our solution.

If we look at the constant terms in the binomial and trinomial on the left-hand side of the equation, we know that their product must be equal to the constant term on the right-hand side, since every other term from the left-hand side will have some power of π‘₯ in it. By comparing the constant terms in this way, we obtain that π‘˜ multiplied by nine is equal to negative 63. This rearranges to give us the same solution of π‘˜ equals negative seven.

Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

  • Interactive Sessions
  • Chat & Messaging
  • Realistic Exam Questions

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy