Question

explain how a trinomial of the form 2x2 + 13x + 15 can be turned into a four term polynomial suitable for factoring by grouping. Use complete sentences.

Answer 1

(2x+3)(x+5)

Answer 2

\[ac = (\frac{b}{2}+d)(\frac{b}{2}-d)\]

Answer 3

solve for d

Answer 4

(2x+3)(x+5)

Answer 5

\[30 = (\frac{13}{2}+d)(\frac{13}{2}-d)\]

Answer 6

\[30 = \frac{169}{4}-d^2\]

Answer 7

\[d^2 = \frac{169}{4} - 30\]

Answer 8

\[d^2 = \frac{169}{4}-\frac{120}{4}\]

Answer 9

\[d = \sqrt{\frac{49}{4}}\]

Answer 10

\[d = \frac{7}{2}\]

Answer 11

\[(\frac{13}{2} + \frac{7}{2})(\frac{13}{2}-\frac{7}{2})\]

Answer 12

\[(10)(3)\]

Answer 13

Those are your two middle numbers

Answer 14

thanks 4 being so detailed

Answer 15

So now, write it like this:

\[2x^2+10x + 3x + 15\]

Answer 16

Then factor out what's common to the first two terms and what's common to the last two terms

Answer 17

\[2x(x+5)+3(x+5) = (x+5)(2x+3)\]

Answer 18

You should be able to make plenty sentences out of that

Answer 19

Make sure you start off saying to set \[a = (\frac{b}{2}+d)\] and \[b = (\frac{b}{2}-d)\]

Answer 20

Your teacher will probably be intrigued by all this.