QQuestionMathematics
QuestionMathematics
"Find the value of c that makes the expression a perfect square trinomial.
x² + 4x + c
Responses
A 22
B 44
C 88
D 16"
10 months agoReport content
Answer
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Step 1:: Identify the form of the perfect square trinomial.
To make this a perfect square trinomial, we need to find a value of $c$ such that there exists an $a$ and $b$ where the equation holds true.
Step 2:: Compare the given expression with the perfect square trinomial formula.
By comparing the given expression $x^2 + 4x + c$ with the perfect square trinomial formula $(a+b)^2 = a^2 + 2ab + b^2$, we can see that $a = x$ and $2ab = 4x$.
Step 3:: Solve for $b$ in terms of $a$.
2ab = 4x \Rightarrow b = \frac{4x}{2a} = \frac{4}{2} \cdot \frac{1}{x} = \frac{2}{x}
Step 4:: Substitute the value of $b$ into the perfect square trinomial formula.
(a+b)^2 = a^2 + 2ab + b^2 \Rightarrow \left(x + \frac{2}{x}\right)^2 = x^2 + 2 + \frac{4}{x^2}
Step 5:: Compare the derived expression with the given expression.
By comparing the derived expression with the given expression, we can see that $c = 2$.
Final Answer
The value of $c$ that makes the expression $x^2 + 4x + c$ a perfect square trinomial is $1$.
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