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split the middle term, do you know how to do that?
kind of but could you please walk me through the steps
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?
Ok now calculate \[a \times c\] for the polynomial u r given
okay keep going i understand
can u find the product of a and c for me
ok good, now what is your b?
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
-6 and 2
good job!! now just split b and work it out as \[12x^2+(-6+2)x-1=12x^2-6x+2x-1\]
factorize first 2 terms together and last 2 terms together
what two terms
take out as much factors out as u can from the first 2 terms
|dw:1438524921185:dw| What does that say?
it's 6x, for the first 2 terms what can u take out??what is common in 12x^2 and -6x ??
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?
nope, you are missing something!! \[(2x-1)(6x+??)\]
yep! and there you have your factors, nice and clean \[(2x-1)(6x+1)\] Just to verify, let's open these up \[(2x \times 6x)+( -1 \times 6x)+(2x \times 1)+(-1 \times 1)=12x^2-6x+2x-1=12x^2-4x-1\]