When the expression \((x+p)(x+5)\) is expanded and simplified, the coefficient of x in the result is 12. This information is used to find the missing consta...
Question 1 Report
When the expression \((x+p)(x+5)\) is expanded and simplified, the coefficient of x in the result is 12. This information is used to find the missing constant p.
Find the value of p. (3)
Answer Details
Expanding \((x+p)(x+5)\) using the standard method of multiplying each term in the first bracket by each term in the second: \(x^{2}+5x+px+5p\), which collects to \(x^{2}+(p+5)x+5p\). [1 mark]
The coefficient of \(x\) in this expansion is \(p+5\). Since this is given as \(12\): \(p+5=12\). [1 mark]
Subtracting \(5\) from both sides gives \(p=7\). [1 mark]
Comparing coefficients like this, matching the \(x\) term in the general expanded form to the given numerical value, works because the expansion is an identity that holds for every value of \(x\), so the coefficients themselves must match exactly.
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