Question Video: Determining the Coefficient of a Given Term in an Algebraic Expression Mathematics

What is the coefficient of 𝑣⁴ in the expression 𝑣⁴ βˆ’ 2𝑣³?

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Video Transcript

What is the coefficient of 𝑣 to the fourth power in the expression 𝑣 to the fourth power minus two 𝑣 cubed?

In this question, we’re asked to determine the coefficient of 𝑣 to the fourth power in the expression 𝑣 to the fourth power minus two 𝑣 cubed. We can start by noticing 𝑣 to the fourth power is a term on its own in this expression. So to determine the coefficient of this term, let’s start by recalling what we mean by a coefficient.

And there are many different definitions of a coefficient. It’s a constant factor or constant multiplier of the term. And we do need to be careful with this definition because if we look at the expression, it appears that there is no constant multiple or constant factor of 𝑣 to the fourth power. However, it’s not correct to say that this value is zero because multiplying 𝑣 to the fourth power by zero is just equal to zero.

Instead, we need to recall that we can rewrite this as one times 𝑣 to the fourth power. Then we can see that this constant factor is one. Therefore, we were able to show the coefficient of 𝑣 to the fourth power in the expression 𝑣 to the fourth power minus two 𝑣 cubed is one.

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