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Q.

Factorise x 2 −14x+13 and choose the option which represents the product of the factors correctly.


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a

(x−1)(x−13)

b

(x+1)(x+13)  

c

(x+1)(x−13)

d

(x−1)(x+13)

answer is A.

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Detailed Solution

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The given expression is as follows,
x 2 −14x+13 .
It can be observed that above equation is of the form x 2 +bx+c , where b = -14 and c = 13.
To factorise such an algebraic expression, we need to find two factors, say p and q such that the following conditions are satisfied,
c=pq
p+q=b
According to the above conditions, the product of first and last constant term of the expression will be 13×1=13 .
Next, we will have to find the factors of the product, i.e., 13 in such a way that their sum or difference is equal to the middle term.
So, we have the factors as −1×−13=13 , which is the product of the first and last terms of the equation, while their sum, i.e., −1+(−13)=−14 is the middle term.
Now, we will factorise the expression using the factors and splitting the middle term as follows,
x 2 −14x+13= x 2 −x−13x+13 =x(x−1)−13(x−1) =(x−1)(x−13)
So, the factored form of x 2 −14x+13 is (x−1)(x−13) .
Hence, the correct option is (1).
 
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