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Question

Factorize the followingx2âˆ’14x+24

A
(x2)(x12)
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B
(x+2)(x12)
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C
(x2)(x+12)
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D
None of these
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Solution

The correct option is A (x−2)(x−12)In the given polynomial x2−14x+24,The first term is x2 and its coefficient is 1.The middle term is −14x and its coefficient is −14.The last term is a constant term 24.Multiply the coefficient of the first term by the constant 1×24=24.We now find the factor of 24 whose sum equals the coefficient of the middle term, which is −14 and then factorize the polynomial x2−14x+24 as shown below:x2−14x+24=x2−12x−2x+24 =x(x−12)−2(x−12)=(x−2)(x−12)Hence, x2−14x+24=(x−2)(x−12).

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