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 Explain how to factor the following trinomials forms: `x^2 + bx +c` and `ax^2 + bx...

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yissy | Student, College Freshman | Honors

Posted November 15, 2012 at 2:24 PM via web

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 Explain how to factor the following trinomials forms: `x^2 + bx +c` and `ax^2 + bx +c`

Is there more than one way to factor this? Show your answer using both words and mathematical notation.

Tagged with algebra, factor, math, quadratic

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mathsworkmusic | (Level 3) Associate Educator

Posted November 15, 2012 at 3:13 PM (Answer #1)

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Use the quadratic formula to factorise the expressions

So if  `y = Ax^2+ Bx + C`

the factors satisfy

`x = (-B +- sqrt(B^2 - 4AC))/(2A)`

However, when you factorise `y = Ax^2+ Bx + C`

the term in `x^2` must equal `A`

We can factorise the expression then as

`y = (Ax/h - (A/h)(-B-sqrt(B^2 - 4AC))/(2A))(hx - h(-B+sqrt(B^2 -4AC))/(2A))`

where `h` is any real number (plug in `A=1` to factorise y = x^2 +bx + c) answer

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