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1.What are the factors of x 3 + 4x 2 – 11x – 30 ? 2.If x = 111…1 (20 digits), y = 333…3 (10 digits) and z = 222…2 (10 digits), then what is x – y 2 / z equal to?

1.What are the factors of x3 + 4x2 – 11x – 30 ?
 2.If x = 111…1 (20 digits), y = 333…3 (10 digits) and z = 222…2 (10 digits), then what is x – y2/ z equal to?

Grade:12th pass

1 Answers

Snehal Jadhav
54 Points
5 years ago
In the first question we have to split the terms to obtain the factors:
 
The equation:
x3 + 4x2 – 11x – 30
can be written as:
 
x3 + 5x2 – x2 – 5x – 6x – 30
 
Further, by combining similar terms:
 
x2(x + 5) – x(x + 5) – 6(x + 5)
 
(x2 – x – 6)(x + 5)
 
Further, by factorising the first term:
 
[ x(x – 3) + 2(x – 3)](x + 5)
 
Lastly, the final expression is:
 
(x + 2)(x – 3)(x + 5)
 

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