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# How do you factor the trinomial 2p^2-3p-54

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How do you factor the trinomial 2p^2-3p-54

Annabelle  Apr 1, 2015

#1
+91919
+10

\$\$2p^2-3p-54\$\$

first I would look for 2 numbers that mult to 2*-54=-108

since it mult to a negative one must be positive and the other one negative.

BUT they also have to add to -3    So the 'bigger' one will be neg and they must be close together. (3 apart.)

Now i am just going to 'play' with the factors of 108.

108=4*27 = 4*3*3*3=9*12      BINGO

-12 and +9

NOW

I will split -3p up into  -12p+9p

\$\$\\2p^2-3p-54\\
=2p^2-12p+9p-54\\
\$now factorise in pairs\$\\
=2p(p-6)+9(p-6)\\
=(2p+9)(p-6)\\\$\$

And that is it :)

Melody  Apr 1, 2015
Sort:

#1
+91919
+10

\$\$2p^2-3p-54\$\$

first I would look for 2 numbers that mult to 2*-54=-108

since it mult to a negative one must be positive and the other one negative.

BUT they also have to add to -3    So the 'bigger' one will be neg and they must be close together. (3 apart.)

Now i am just going to 'play' with the factors of 108.

108=4*27 = 4*3*3*3=9*12      BINGO

-12 and +9

NOW

I will split -3p up into  -12p+9p

\$\$\\2p^2-3p-54\\
=2p^2-12p+9p-54\\
\$now factorise in pairs\$\\
=2p(p-6)+9(p-6)\\
=(2p+9)(p-6)\\\$\$

And that is it :)

Melody  Apr 1, 2015

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