Find the constant a, P and Q such
that 3x²-12x+16=a(x+p) +q​

Step-by-step explanation:

Rewrite 3x²-12x+16 as follows:

3(x^2 - 4x) + 16

Complete the square of x^2 - 4x; it is (x - 2)^2 - 4.  We then have:

3( (x - 2)^2 - 4) + 16, or:

3(x - 2)^2 - 12 + 16, or

3(x - 2)^2 + 4

Then a = 3, p = -2 and q = 4

Completing the square of x^2 - 4x is done as follows:

1.  Identify the coefficient of x:  It is -4.

2.  Take half of this result:  It is -2

3.  Square this, and then add the square to x^2 - 4x, and then subtract it:

    x^2 - 4x = x^2 - 4x + 4 - 4

4.  Rewrite this result in the form (x - a)^2 - c:

    (x - 2)^2 - 4  

5.  Now follow the remainder of the problem solution (given above)

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step-by-step explanation: