Video Transcript
Factor the expression two multiplied by 𝑝 minus one plus 𝑥 multiplied by 𝑝 minus one completely.
In this question, we are asked to completely factor a given algebraic expression. And to do this, we need to find all of the common factors of the two terms.
We can start by checking the coefficients. However, we see that the second term has a coefficient of one, so the greatest common factor of the coefficients is one. We can then note that both of the terms share a factor of 𝑝 minus one. So we can take this factor out by using the distributive property. Taking out the factor of 𝑝 minus one gives us 𝑝 minus one multiplied by two plus 𝑥.
We now have two linear factors. We check each factor to see if there are any common factors among the terms. We note that the highest common factor of 𝑝 and negative one is one. So we leave this factor as it is. Similarly, the highest common factor of two and 𝑥 is one and the coefficient of 𝑥 is positive. So we will leave this factor unchanged.
It is worth noting that it is standard practice to write the variable before the constant. So we will reorder the terms in the second factor. This gives us a final answer of 𝑝 minus one multiplied by 𝑥 plus two.
