Video Transcript
Factorize fully negative 𝑥 squared plus 𝑥 plus 12.
In this question, we are asked to fully factor a given algebraic expression. If we look at the given algebraic expression, we can first note that the only variable is 𝑥. And the powers of 𝑥 that appear in the expression are two and one. So, this is a single-variable quadratic in 𝑥.
To factor the expression, we want to try and write it as the product of binomials. We can begin by looking at the leading coefficient. In this case, it is negative one. We could factor this expression directly. However, we can also take this factor of negative one out of the expression to obtain a monic quadratic. We get negative one multiplied by 𝑥 squared minus 𝑥 minus 12.
To factor a monic quadratic, we need to find two numbers whose sum is the coefficient of 𝑥 and whose product is the constant term. This means we want to find two numbers whose sum is negative one and whose product is negative 12. One way of doing this is to consider the factor pairs of 12. We can then see that three times negative four is equal to negative 12 and three plus negative four is equal to negative one.
Therefore, our value of 𝑎 is negative four and our value of 𝑏 is three, giving us negative one times 𝑥 minus four times 𝑥 plus three. Each binomial factor cannot be simplified further. So, the expression is now fully factored.
