Factoring and Simplifying.

[paulxzt]

I'm not that great in math and I have a few review Alg2 Problems. I would really appreciate if anyone can help. Thanks in advance.

Factor and Simplify. Express your answer as a fraction w/o negative exponents.

1) 3x(2x+5)^-1/2 + 3(2x+5)^1/2

2) Multiply: (x^5/2 + 3/root(2))^2

Thanks.

 

[stapel]

1) There really isn't anything to factor out, and nothing you do is going to make this much "simpler" than it already is. (And, no, it isn't terribly simple. Radical expressions are frequently nasty, and there's nothing you can do about it. Pet peeve....)

You've got:

. . . . .(3x)/(sqrt[2x + 5]) + 3 sqrt[2x + 5]

In some crude sense, "sqrt[2x + 5]" is probably what they're referring to as the "common factor". Except that it isn't....

To deal with this, rationalize the first fraction (because you can't have the radical in the denominator). This will "create" a "common factor":

. . . . .(3x sqrt[2x + 5])/(2x + 5) + 3 sqrt[2x + 5]

. . . . .(3 sqrt[2x + 5]) ( x/(2x + 5) + 1 )

And that's the "simplification".

2) Try writing this as "(sqrt[x⁵] + 3/sqrt[2])²", and then do the multiplication "vertically". That's usually simpler, for this sort of exercise.

Eliz.

 

[skeeter]

3x(2x+5)^-1/2 + 3(2x+5)^1/2

factor out 3(2x+5)^-1/2 ...

3(2x+5)^-1/2[x + (2x+5)] = 3(2x+5)^-1/2(3x+5)

 

[paulxzt]

2) Try writing this as "(sqrt[x⁵] + 3/sqrt[2])²", and then do the multiplication "vertically". That's usually simpler, for this sort of exercise.

Eliz.

Can you sorta explain what to do because im lost on both the problems. Should I try to factor it since it is squared? Sorry for any inconvenience and i appreciate the help!

 

[stapel]

Try writing this as "(sqrt[x⁵] + 3/sqrt[2])²", and then do the multiplication....

Should I try to factor it since it is squared?

It already is factored. You need to multiply it out.

Are you not familiar with polynomial multiplication?

Eliz.

 

[paulxzt]

Try writing this as "(sqrt[x⁵] + 3/sqrt[2])²", and then do the multiplication....

Should I try to factor it since it is squared?

It already is factored. You need to multiply it out.

Are you not familiar with polynomial multiplication?

Eliz.

Oh yeah that's what i meant, multiply it out but the root x^5 is confusing the **** out of me:

[ [sqrt(x^5)] + 3/sqrt(2) ] [ [sqrt(x^5)] + 3/sqrt(2) ]

x^5 + 3/sqrt(2) * sqrt(x^5) + 3/sqrt(2) * sqrt(x^5) + 9/2

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I think im doing something wrong with the sqrt*x^5.. lol sorry, help is appreciated.

 

[stapel]

[ [sqrt(x^5)] + 3/sqrt(2) ] [ [sqrt(x^5)] + 3/sqrt(2) ]

x^5 + 3/sqrt(2) * sqrt(x^5) + 3/sqrt(2) * sqrt(x^5) + 9/2

Now carry on with the simplification:

. . . . .x⁵ + (6 sqrt[x⁵])/sqrt[2] + 9/2

Rationalize the denominator in the second term and simplify the radical to get 3x² sqrt[2x], and I think you're done. (Your instructor might prefer "3sqrt[2]x^5/2". Check your book and/or notes for advice in this area.)

Eliz.

 

[paulxzt]

[ [sqrt(x^5)] + 3/sqrt(2) ] [ [sqrt(x^5)] + 3/sqrt(2) ]

x^5 + 3/sqrt(2) * sqrt(x^5) + 3/sqrt(2) * sqrt(x^5) + 9/2

Now carry on with the simplification:

. . . . .x⁵ + (6 sqrt[x⁵])/sqrt[2] + 9/2

Rationalize the denominator in the second term and simplify the radical to get 3x² sqrt[2x], and I think you're done. (Your instructor might prefer "3sqrt[2]x^5/2". Check your book and/or notes for advice in this area.)

Eliz.

Sorry for all these silly questions but could you show me how you simplified the radical ?

 

[stapel]

Sorry for all these silly questions but could you show me how you simplified the radical ?

I rationalized the denominator, and then cancelled off the common factor of "2".

Eliz.