factorise x square - 32x+135
Answers
Answer:
(x−27)(x−5)
Step-by-step explanation:
x²−32x+135
Factor the expression by grouping. First, the expression needs to be rewritten as x²+ax+bx+135. To find a and b, set up a system to be solved.
a+b=−32
ab=1×135=135
Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 135.
−1,−135
−3,−45
−5,−27
−9,−15
Calculate the sum for each pair.
−1−135=−136
−3−45=−48
−5−27=−32
−9−15=−24
The solution is the pair that gives sum −32.
a=−27
b=−5
Rewrite x² −32x+135 as (x²−27x)+(−5x+135).
(x²−27x)+(−5x+135)
Factor out x in the first and −5 in the second group.
x(x−27)−5(x−27)
Factor out common term x−27 by using distributive property.
(x−27)(x−5)
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