# SAT Math: Identifying the Most Sensible Route to Divide a Polynomial

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If , what is C + D equal to?

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### Transcript

they'll be easier to find if we replace nine x

squared over three x minus one with its quotient Right

So let's do that C plus de plus one over

three x minus one sure looks like c plus d

and three x plus one are best friends So what

do you think Answer d and a simple hard to

catch division mistake that could lead to three x minus

one like in number See Well if you're not a

huge fan of long division in o who is other

than a calculator here there's another way to tackle this

problem But it's kind of error prone to So take

another quick look at the starting equation We got nine

x squared over three x minus one equals c plus

de plus one of three x minus one Well sneaky

way to create the fraction one over three x minus

one on the left side of the equation Do this

not x squared plus one minus one over three ex

money's one And then we kind of sim fly out

the ones that we got Nine x squared minus one

over three x minus one plus one over three x

minus one walk Adding in subtracting one is the same

thing is adding zero so it doesn't change the overall

value of the expression from here Do some quick factoring

and then i'll get the expression into a form we

can compare c plus the two and that gets you

three x plus one times quantity here through x minus

one over three x minus one plus twenty one over

three x minus one And then that's what it looks

like when you simplified terms out Three x plus one

plus one over three x minus one See we ended

up in the same position as before Oh and there's

even a third way to approach this problem If you're

not asleep yet with plain old algebra just subtract one

over three x minus one from both sides of the

equation You know we could have done that That's what

it would look like and well looks awfully familiar It's

a bit easier to work with tio Maybe we should

have started off with this one instead It would've been 00:04:02.635 --> [endTime] a whole lot quicker All right we're done