I'm following video tutorials on factoring quadratic polynomials. So I'm given the polynomial:
$$x^2 + 3x – 10$$
And I'm given the task of finding the values of $a$ and $b$ in:
$$(x + a) (x + b)$$
Obviously the answer is:
$$(x + 5)(x – 2)$$
However the answer can be also:
$$(x – 2) (x + 5)$$
I just want to make sure if the question asks for the values of '$a$' and '$b$', then '$a$' can be either $5$ or $-2$, and '$b$' can be either $5$ or $-2$.
Therefore if a question asks what are the values of '$a$' and '$b$' both the following answers are correct:
Answer $1$
$a = -2$
$b = 5$
or
Answer $2$
$a = 5$
$b = -2$
I'm sure this is a completely obvious question, but I'm just a beginner in this.
Best Answer
.Yes, you are correct. Since $(x+5)(x-2) = (x-2)(x+5) = x^2 + 3x-10$, we note that $a$ and $b$ may either take the values $(5,-2)$ or $(-2,5)$.
I would consider providing just one of the two solutions to be insufficient, since the question itself ask for the values of $a$ and $b$, but nowhere mentions that they are unique. However, any question saying "find the values of $a$ and $b$" is wrong with the word "the" : they are assuming uniqueness of $a$ and $b$, which is not the case.The question as quoted by you includes the word "the" , and this is misleading.