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factorize(x+1)(x+2)(x+3)(x+6)-3x2

ajinkya bhole , 15 Years ago

Grade 10

2 Answers

Jitender Singh

Last Activity: 10 Years ago

Ans:
Hello Student,
Please find answer to your question

$f(x) = (x+1)(x+2)(x+3)(x+6) - 3x^2$
$f(x) = (x^2+4x+6)(x^2+8x+6)$
$f(x) = (x^2+4x+6)(x^2+4x+4x+6)$
Use simple quadratic formulas now
$f(x) = -(x+\sqrt{10}+4)(-ix+\sqrt{2}-2i)(ix+\sqrt{2}+2i)(-x+\sqrt{10}-4)$

mycroft holmes

Last Activity: 10 Years ago

Given expression equals $(x^2+4x+3)(x^2+8x+12)- 3x^2$

Now we have $$3x^2 = 6(x^2+4x+3)-3(x^2+8x+12)+18$

Hence if $$A =(x^2+4x+3), B=(x^2+8x+12)$ ,

the given expression can be written out as AB-6A+3B-18 = (A+3)(B-6)

which on substituting back for A and B equals

$$(x^2+4x+6)(x^2+8x+6)$

Both expressions are irreducible over integers and hence you can leave the factorization at this stage

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