Thread: need help for some factoring problems?

1. need help for some factoring problems?

the first question is : (21.22.23.24+1)^(1/2) =? (without using calculator)

A few more questions has been added to the end. thnx for all answers.

2. Originally Posted by ibirsen
the first question is : (21.22.23.24+1)^(1/2) =? (without using calculator)
is this the expression you posted? please clarify ...

$\displaystyle \left(21 \cdot 22 \cdot 23 \cdot 24 + 1\right)^{\frac{1}{2}}$

3. Originally Posted by skeeter
is this the expression you posted? please clarify ...

$\displaystyle \left(21 \cdot 22 \cdot 23 \cdot 24 + 1\right)^{\frac{1}{2}}$
If it is, then use $\displaystyle \left(a+b\right)^n = a^n + 2ab + b^n$ so substitute $\displaystyle \left(21 \cdot 22 \cdot 23 \cdot 24\right)$ for a, 1 for b and 1/2 for n.

4. Originally Posted by skeeter
is this the expression you posted? please clarify ...

$\displaystyle \left(21 \cdot 22 \cdot 23 \cdot 24 + 1\right)^{\frac{1}{2}}$
If it is, then use $\displaystyle \left(a+b\right)^n = a^n + 2ab + b^n$ so substitute $\displaystyle \left(21 \cdot 22 \cdot 23 \cdot 24\right)$ for a, 1 for b and 1/2 for n.

5. Originally Posted by Manfriedthetalkingpinata
If it is, then use $\displaystyle \left(a+b\right)^n = a^n + 2ab + b^n$ so substitute $\displaystyle \left(21 \cdot 22 \cdot 23 \cdot 24\right)$ for a, 1 for b and 1/2 for n.
This is incorrect. $\displaystyle (a+ b)^n= a^n+ 2ab+ b^n$ only if n= 2, which is not the case here.

If we call that number "x", then $\displaystyle 21(22)(23)(24)+ 1= x^2$ so that $\displaystyle x^2- 1= (x- 1)(x+ 1)= 21(22)(23)(24)$. Now notice that 21(24)= 504 and 22*23= 506.

6. Originally Posted by HallsofIvy
This is incorrect. $\displaystyle (a+ b)^n= a^n+ 2ab+ b^n$ only if n= 2, which is not the case here.

If we call that number "x", then $\displaystyle 21(22)(23)(24)+ 1= x^2$ so that $\displaystyle x^2- 1= (x- 1)(x+ 1)= 21(22)(23(24)$. Now notice that 21(24)= 504 and 22*23= 506.
Thank you for this very good solution

7. I'm trying to solve the questions of factorization so i have got afew questions. I also wanted to continue here in order to avoid a new topic.
$\displaystyle y^3+1=3y^2$
$\displaystyle 3y-2=x^3$ find y-x?
A) -2 B) -1 C) 0 D) 1 E) 2
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find the one of the factor of function $\displaystyle 2x^2+y^2+3xy+y-2$

A) x+y+1 B) x+y-1 C) 2x+y+1 D) 2x+y-2 E) x+y+2

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a , b ,c ∈ R and they r different eachother ;
find the a+b+c if
$\displaystyle 2a+b=3c$
$\displaystyle 2a^3 + b^3 =3c^3$
A) -2 B) -1 C) 0 D) 1 E)-2