​is there a common factor for all terms in the polynomial x2+16x+64?

label Algebra
account_circle Unassigned
schedule 1 Day
account_balance_wallet \$5

is there a common factor for all terms in the polynomial x2+16x+64?

Mar 23rd, 2015

When looking for factors, you want to first look at the first and last terms.

To get x^2, the only possibilities are x * x.

For 64 there are many more factors, 1*64, 2*32, 4*16 and 8*8 and each of these containing two negative numbers.

The next thing you would want to do is find one of the factors that would sum to the middle number.  In this case we are looking for two numbers that would add to 16.  We can automatically get rid of any factors with negative numbers.  The only factors that add to 16 are 8 + 8.

The factors are (x+8)(x+8) or (x + 8)^2.

Mar 23rd, 2015

how many terms exist in the polynomial x2+16x+64?

Mar 23rd, 2015

3.  Each part separated by addition or subtraction is considered a term.  So the terms are as follows, x^2, 16x and 64

Mar 23rd, 2015

are the first and last terms perfect squares? if so what are their respective square roots? in x2+16x+64

Mar 23rd, 2015

They are perfect squares.

sqrt(x^2) = x

and

sqrt(64) = 8

Mar 23rd, 2015

Notice that the trinomial of the form a2 +2ab+b2. What is the value of a? and b?

Mar 23rd, 2015

In this case a is x and b is 8.

Mar 23rd, 2015

Use the formula a2+2ab+b2=(a+b)2 for factoring a perfect-square trinomial

Mar 23rd, 2015

is it possible to factor x2+8x+32 in a similar manner? explain.

Mar 23rd, 2015

Is there a common factor for all terms in the polynomial x2+8x+15?

Mar 23rd, 2015

Please, if you have questions unrelated to the original post, post them separately.  I will not answer unrelated questions in the solution to a previous one.  Or if you have several questions to be answered, post them together as a paid question.

Mar 23rd, 2015

ok sorry.

Use the formula a2+2ab+b2=(a+b)2 for factoring a perfect-square trinomial

Mar 23rd, 2015

I have already used that formula to factor in the original answer.

Mar 23rd, 2015

ok. Factor the polynomial using the formula for factoring a trinomial that is not a perfect square. x2+8x+15

Mar 23rd, 2015

You cannot use the formula to factor something that is not a perfect square.  It doesn't work that way.  The formula is only for use with perfect sqaures.

Mar 23rd, 2015

factor out the GCF of the first group terms x3+7x2+2x+14

Mar 23rd, 2015

That is a completely seperate question and needs to be posted seperately.

Mar 23rd, 2015

write the polynomial using the the factored groups of terms x3+7x2+2x+14

Mar 23rd, 2015

...
Mar 23rd, 2015
...
Mar 23rd, 2015
Oct 17th, 2017
check_circle