Question

How do you factor $ - {x^2} + x + 42$?

Answer 1

Hint: According to given in the question we have to determine the factor of the given quadratic expression which is $ - {x^2} + x + 42$ as given in the question. So, to determine the factor of the given quadratic expression first of all we have to determine the coefficient of ${x^2}$ and same as we have to determine the constant term.
Now, we have to determine the L.C.M of the coefficient of ${x^2}$ and the constant term to determine the coefficient of x for the given quadratic expression.
Now, we have to take the variables or integers as common variables of integers which can be taken as common variables or integers in the expression obtained.
Now, on solving the expression we will obtain two factors of the given quadratic expression $ - {x^2} + x + 42$ which is as asked in the question.

Complete step by step answer:
Step 1: First of all we have to determine the coefficient of ${x^2}$ and the same as we have to determine the constant term. Hence,
coefficient of ${x^2}$= -1,
Constant term = 42
Step 2: Now, we have to determine the L.C.M of the coefficient of ${x^2}$ and the constant term to determine the coefficient of x for the given quadratic expression.
L.C.M of coefficient of ${x^2}$ and the constant term $ \Rightarrow (2 \times 3 \times 7)$
$
   \Rightarrow - {x^2} + x(7 - 6) + 42 \\
   \Rightarrow - {x^2} + 7x - 6x + 42 \\
 $
Step 3: Now, we have to take the variables or integers as common variables of integers which can be taken as common variables or integers in the expression obtained. Hence,
$ \Rightarrow - x(x - 7) - 6(x - 7)$
Step 4: Now, on solving the expression we will obtain two factors of the given quadratic expression $ - {x^2} + x + 42$ which is as asked in the question. Hence,
$ \Rightarrow ( - x - 6)(x - 7)$

Hence, we have determined the factor of the given quadratic expression which are $ \Rightarrow ( - x - 6)(x - 7)$.

Note: It is necessary that we have to determine the L.C.M of the coefficient of the constant term and ${x^2}$to determine the coefficient of x.
To obtain the factor of the quadratic expression it is necessary that we have to take the terms which can be taken as the common terms.