If (x-2)(x-p)= x2 - ax + 6, then the value of (a-p) is
2
Let's expand the left-hand side of the equation (x-2)(x-p):
Using the distributive property (also known as the FOIL method for binomials), we have:
\((x-2)(x-p) = x^2 - px - 2x + 2p\)
Simplify this to:
\(x^2 - (p+2)x + 2p\)
We are given that this is equal to \(x^2 - ax + 6\).
By comparing the coefficients of the corresponding terms, we get two equations:
- From the coefficient of \(x\): \(-a = -(p+2)\), which simplifies to \(a = p+2\)
- From the constant term: \(2p = 6\), giving \(p = 3\)
Substitute \(p = 3\) into the equation \(a = p+2\):
\(a = 3 + 2 = 5\)
Now, find \(a - p\):
\(a - p = 5 - 3 = 2\)
Thus, the value of \(a-p\) is \(2\).
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