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TSI Math: Factoring a Multivariable Trinomial 3 Views
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Description:
Factor completely.
3x² + 4xy – 4y²
- Intermediate Algebra and Functions / Expressions, Equations, and Functions Involving Powers, Roots, and Radicals
- Test Prep / TSI
- TSI / TSI Math
- TSI / TSI Mathematics
- Intermediate Algebra and Functions / Expressions, Equations, and Functions Involving Powers, Roots, and Radicals
- TSI Mathematics / Intermediate Algebra and Functions
- Test Prep / TSI
- TSI Math / Intermediate Algebra and Functions
Transcript
- 00:03
Okay sy mash bumpers Next up Two words for you
- 00:07
Factor completely That's beef flank The new james bond movie
- 00:13
titles So let's just dive right in Well there are
- 00:16
legends about its existence stories of unicorns dragons But nothing
- 00:20
is prepared us for the sighting of a creature as
Full Transcript
- 00:22
elusive as the multi variant Try no meal That's what
- 00:25
that thing is face the ferocious creature by attacking the
- 00:28
variables first Well the x squared the y squared terms
- 00:31
break into their individual factors of x times x and
- 00:34
white times Why Pretty easily there right Well placing the
- 00:37
variables in the first and last terms And each binomial
- 00:39
naturally creates the x y term in the middle of
- 00:42
the tri no meal while unlike the heads of the
- 00:44
infamous greek hydra the regrown variables of this flavour Good
- 00:48
Okay last term is negative so that by no meals
- 00:51
must have opposite signs Okay so see this is minus
- 00:55
and that's a plus thinking Yeah well the coefficients of
- 00:57
the tri no meal or handled as usual The first
- 00:59
coefficient is a prime and has only two factors One
- 01:02
and three in the last coefficient for their has factor
- 01:04
Pairs of one and four in two and two Right
- 01:06
Well start With little trial and error to find the
- 01:08
right combo here nobody gets this right off the bat
- 01:11
usually and let's try on all three Acts and money's
- 01:14
4 times x plus y is that work Well Is
- 01:16
the proposed factor pair valiant enough to pass the first
- 01:19
trial Well it's multiply the binomial tze and find out
- 01:22
so we got three exponents for why'd times x plus
- 01:25
y so inside and an outside then we had the
- 01:27
middle Remember how all that works so let's Think about
- 01:29
this gives us three acts times quantity x plus y
- 01:33
minus for why Tens quantity x plus y we've got
- 01:37
three x squared plus three x y bonnie's for x
- 01:39
y minus four y squared and yeah that gets us
- 01:42
three expert minus x y monies for y squared b
- 01:46
there that one's close but it's not quite right Switching
- 01:49
the signs makes the middle term positive See the positive
- 01:52
one there and switching the placement of the four and
- 01:55
the one makes the middle term too large We can't
- 01:58
do that So strategy change Send the factor pair two
- 02:01
times two in the battle instead So what we have
- 02:03
here Well Let's see we've got dead this x and
- 02:06
that's Why i'm thinking all right so we got three
- 02:07
explaining to why times x plus two why and that
- 02:11
pull out the three x there and that gets us
- 02:13
x plus two y minus two times exposed to why
- 02:16
and then the factors there Three x squared plus six
- 02:19
wide minus two Excellent on movements that kid says three
- 02:22
x squared plus for x y minus four y squared
- 02:25
Yeah there we go make like hercules and be proud
- 02:27
are great mathematical feats Leave us with the factors Three
- 02:30
x minus two why and Acts plus 2 like so
- 02:34
the answer is d
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