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Explain how to factor the following trinomials forms: x2 + bx + c and ax2 + bx + c. Is there
more than one way to factor this? Show your answer using both words and
mathematical notation.
 2 years ago
 2 years ago
Explain how to factor the following trinomials forms: x2 + bx + c and ax2 + bx + c. Is there more than one way to factor this? Show your answer using both words and mathematical notation.
 2 years ago
 2 years ago

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HeroBest ResponseYou've already chosen the best response.4
Yeah, this is always an interesting topic of discussion. Technically, there's really only one way to factor it. But there are two different approaches to the same thing. Now, however, there are indeed several ways of solving each.
 2 years ago

HeroBest ResponseYou've already chosen the best response.4
As you may already know...
 2 years ago

HeroBest ResponseYou've already chosen the best response.4
Clearly your instructor must want you to write some long and lengthy explanation for this.
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
ax^2+bx+c I always do: Find two factors of a*c that have product a*c and that have sum b. Say that the we find two factors of a*c and lets call them m and n. Let's assume m and n have product a*c and have sum b. If there are no such m and n then ax^2+bx+c is not factorable over the integers. So if there exist such m and n, then we do the following: Replace bx with mx+nx. We can do this since b=m+n. So now we have ax^2+mx+nx+c. Then we would factor by grouping. (ax^2+mx)+(nx+c) Look to see what the first two terms have in common and then factor that out. Look to see what the second two terms have in common and the factor that out. Then you should have the same binomial times something for each of the two grouping we made. So we would factor this binomial out creating our two factors. Now here is example: 3x^22x5 a=3 b=2 c=5 a*c=3(5) b=2=35 bx=3x5x 3x^2+3x5x5 3x(x+1)5(x+1) (x+1)(3x5) here m=a and n=c that is not always the case so how about another example: 12x^2+2x2 a=12 b=2 c=2 a*c=12(2)=24=(6)(4) b=2=64 bx=2x=6x4x 12x^2+2x2 12x^2+6x4x2 3x(4x+2)(4x+2) (4x+2)(3x1) 2(2x+1)(3x1) and of course we could had factor out a 2 at the beginning
 2 years ago

HeroBest ResponseYou've already chosen the best response.4
Okay, and that's one way to factor....But the other way is still the same way...so there is only ONE way to factor....just two different approaches...and there's still multiple ways of solving...i.e. factoring, quadratic formula, graphing, solving for x, etc...
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
so at the very beginning of all of this you can say is there a greatest common factor and factor that out at the beginning
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
greatest common factor of the three terms*
 2 years ago

HeroBest ResponseYou've already chosen the best response.4
Also, complete the square but that's just the long form of the quadratic formula.
 2 years ago

HeroBest ResponseYou've already chosen the best response.4
Which still isn't factoring
 2 years ago
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