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(X + 5) is a Factor of 2x3 + 5x2 – 28x – 15. Hence, Factorise the Expression 2x3 + 5x2 – 28x – 15 Completely. - ICSE Class 10 - Mathematics

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Question

(x + 5) is a factor of 2x3 + 5x2 – 28x – 15. Hence, factorise the expression 2x3 + 5x2 – 28x – 15 completely.  

Solution

Let f(x)=`2x^3+5x^2-28x-15` 

`x+5=0 ` ⇒ x=-5  

∴ Remainder = f(-5)  

=`2(-5)^3+5(-5)^2-28(-5)-15`  

=`-250+125+140-15` 

=`-265+265` 

=`0` 

Hence, (x+5)is a factoor of f(x) 

Now, we have, 

  

∴ `2x^3+5x^2-28x-15=(x+5) (2x^2-5x-3)` 

=`(x+5)[2x^2+6x+x-3]` 

=`(x-5)[2x(x-3)+1(x-3)]` 

=`(x+5) (2x+1) (x-3)` 

 

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Solution (X + 5) is a Factor of 2x3 + 5x2 – 28x – 15. Hence, Factorise the Expression 2x3 + 5x2 – 28x – 15 Completely. Concept: Factor Theorem.
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