Factorise x squared + 8x -12 ?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to remember that you may write the factored form of a polynomial when you know its roots, hence you need to find the roots of quadratic `x^2 + 8x - 12 = 0` .

You should use the quadratic formula such that:

`x_(1,2) = (-b+-sqrt(b^2 - 4ac))/(2a)`

The coefficients a,b,c occur in the standard form of quadratic `ax^2 + bx + c = 0` .

Comparing the given quadratic to the standard form yields a=1, b=8, c=-12.

You need to substitute 1 for a, 8 for b and -12 for c in the quadratic formula such that:

`x_(1,2) = (-8+-sqrt(64 + 48))/2`

`x_(1,2) = (-8+-sqrt112)/2`

`` `x_(1,2) = (-8+-4sqrt7)/2 =gt x_(1,2) = (-4+-2sqrt7)`

Hence, evaluating the roots of quadratic you may write the factored form of quadratic such that: `x^2 + 8x - 12 = (x+ 4 - 2sqrt7)(x + 4+ 2sqrt7) = (x+4)^2 - 28` .

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