Answer
Practice 2a (Answer)
$x^{2} - 23x + 22$
$=(x - 1)(x - 22)$
Practice 2b (Answer)
$x^{2} - 27x + 50$
$= (x - 2)(x - 25)$
Work Step by Step
Practice 2a (Solution)
Factor : $x^{2} - 23x + 22$
To begin by writing the first terms of the binomial factors
(x + $\triangle$)(x + $\square$)
Next, to look for two numbers whose product is +22 and whose sum is -23. As the two numbers must have a positive product and a negative sum, pairs of negative factors of 22 are to be investigated only.
Factors of 22 $\Longleftrightarrow$ Sum of Factors
-1,-22 $\Longleftrightarrow$ -23 (Correct sum, so the numbers are -1 and -22)
-2,-11 $\Longleftrightarrow$ -13
Thus, $x^{2} - 23x + 22 = (x - 1)(x - 22)$
Practice 2b (Solution)
Factor : $x^{2} - 27x + 50$
To begin by writing the first terms of the binomial factors
(x + $\triangle$)(x + $\square$)
Next, to look for two numbers whose product is +50 and whose sum is -27. As the two numbers must have a positive product and a negative sum, pairs of negative factors of 50 are to be investigated only.
Factors of 50 $\Longleftrightarrow$ Sum of Factors
-1,-50 $\Longleftrightarrow$ -51
-2,-25 $\Longleftrightarrow$ -27 (Correct sum, so the numbers are -2 and -25)
-5,-10 $\Longleftrightarrow$ -15
Thus, $x^{2} - 27x + 50 = (x - 2)(x - 25)$
