Question

How do you factor the trinomial ${x^2} - 11x + 18?$

Answer 1

Hint:
According to the question we have to determine the factor of the given quadratic expression which is${x^2} - 11x + 18$. So, first of all to determine the solution or we can say that to determine the roots of the given quadratic expression we have to determine the coefficient of ${x^2}$ and the constant term.
Now, with the help of the coefficient of ${x^2}$ and the constant term we have to determine the coefficient of x by finding the factors of the product of ${x^2}$ and the constant term.
Now, have to take the terms common which can be taken as the common term in the expression obtained.

Complete step by step solution:
Step 1: first of all to determine the solution or we can say that to determine the roots of the given quadratic expression we have to determine the coefficient of ${x^2}$and the constant term. Hence,
Coefficient of ${x^2}$= 1 and the constant term = 18
Step 2: Now, with the help of coefficient of ${x^2}$and the constant term we have to determine the coefficient of x by finding the factors of the product of ${x^2}$and the constant term. Hence,
$
   \Rightarrow {x^2} - (9 + 2)x + 18 \\
   \Rightarrow {x^2} - 9x - 2x + 18 \\
 $
Step 3: Now, have to take the terms common which can be taken as the common term in the expression obtained. Hence,
$
   \Rightarrow x(x - 9) - 2(x - 9) \\
   \Rightarrow (x - 2)(x - 9) \\
 $
Hence, we have determined the required factor for the given quadratic expression which is $ \Rightarrow (x - 2)(x - 9)$.

Note:
1) It is necessary that we have to determine the coefficient of x with the help of the product of the coefficient of ${x^2}$and the constant term.
2) On solving a quadratic expression only two possible roots/zeroes can be obtained which will satisfy the given quadratic expression mean on placing these in place of x the whole expression becomes 0.