how do you factor x^2 + 10x + 21?

Question

mathmale · Answer

Smiley:  What are factors of 21?  List all of them, if you can.  Next, look for any pair of factors that add up to 10.  Hope this hint helps.

abbles · Answer

(x + ?)(x + ?)
You need to figure out what the two other numbers are.  To do that look at all the factors of 21.
(x + 7 )(x + 3)
If you multiply this out, you get the correct solution.

anonymous · Answer

ah, yes! thank you so much!

whpalmer4 · Answer

Here's the whole procedure for factoring something of the form
$$ax^2+bx+c$$such as you have here:

Multiply $a*c$.  Now find a pair of factors of $a*c$ that sums to $b$.  Call them $f_1,f_2$  $$f_1+f_2 = b$$

Rewrite the original polynomial, splitting the middle term into two pieces using $f_1,f_2$:

$$ax^2+f_1x+f_2x + c$$Now group them as two pairs
$$(ax^2+f_1x)+(f_2x+c)$$At this point, you should be able to factor each pair, and you'll have a common factor to each pair.  Hard to illustrate that with the letters, so I'll demonstrate:

$$x^2+10x+21$$$$1*21=21$$factors of $21$ that add to $10$ are $3,7$
$$x^2+3x+7x+21$$$$(x^2+3x)+(7x+21)$$$$x(x+3)+7(x+3)$$$$(x+3)(x+7)$$

anonymous · Answer

Smiley: also try the IAM method which means 
that the factors would equal 10 and would be multiples of 21.
But this only works if x= 1
you could also try the x factor method as well