anonymous
  • anonymous
.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
split the middle term, do you know how to do that?
anonymous
  • anonymous
kind of but could you please walk me through the steps
anonymous
  • anonymous
I'll try when you split the middle term of a quadratic polynomial \[p(x)=ax^2+bx+c\] you are looking to split b into two numbers say, f and g such that \[b=f+g\] and \[f \times g =a \times c\] Do you understand this?

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anonymous
  • anonymous
yes
anonymous
  • anonymous
Ok now calculate \[a \times c\] for the polynomial u r given
anonymous
  • anonymous
|dw:1438524585865:dw|
anonymous
  • anonymous
okay keep going i understand
anonymous
  • anonymous
can u find the product of a and c for me
anonymous
  • anonymous
-12
anonymous
  • anonymous
ok good, now what is your b?
anonymous
  • anonymous
-4
anonymous
  • anonymous
great, now can you think of two numbers u can split b(that is -4 in this case) into, such that the product of those numbers will equal -12 and adding those numbers will give u back -4
anonymous
  • anonymous
-6 and 2
anonymous
  • anonymous
good job!! now just split b and work it out as \[12x^2+(-6+2)x-1=12x^2-6x+2x-1\]
anonymous
  • anonymous
factorize first 2 terms together and last 2 terms together
anonymous
  • anonymous
what two terms
anonymous
  • anonymous
|dw:1438524844892:dw|
anonymous
  • anonymous
take out as much factors out as u can from the first 2 terms
anonymous
  • anonymous
|dw:1438524921185:dw| What does that say?
anonymous
  • anonymous
it's 6x, for the first 2 terms what can u take out??what is common in 12x^2 and -6x ??
anonymous
  • anonymous
6x(2x-1)
anonymous
  • anonymous
good, now so now we have \[6x(2x-1)+(2x-1)\] Now we have two terms, you can take 2x-1 out, what are you left with?
anonymous
  • anonymous
6x
anonymous
  • anonymous
nope, you are missing something!! \[(2x-1)(6x+??)\]
anonymous
  • anonymous
1?
anonymous
  • anonymous
yep! and there you have your factors, nice and clean \[(2x-1)(6x+1)\] Just to verify, let's open these up \[(2x \times 6x)+( -1 \times 6x)+(2x \times 1)+(-1 \times 1)=12x^2-6x+2x-1=12x^2-4x-1\]
anonymous
  • anonymous
12x^2-4x-1
anonymous
  • anonymous
Thanks

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