how many more unit tiles need to be added to the expression x²+4x+3 in order to form a perfect square…
how many more unit tiles need to be added to the expression x²+4x+3 in order to form a perfect square trinomial?\n1\n2\n3\n4
Answer
Explanation:
Step1: Identify the expression and the required form.
The given expression is $x^2 + 4x + 3$. We want to add unit tiles (constant term) to make it a perfect square trinomial of the form $(x+a)^2 = x^2 + 2ax + a^2$.
Step2: Determine the constant term for a perfect square.
Comparing $x^2 + 4x + 3$ to $x^2 + 2ax + a^2$, we have $2a = 4$. Solving for $a$: $$ a = \frac{4}{2} = 2 $$ The constant term required for a perfect square is $a^2$. $$ a^2 = 2^2 = 4 $$ Thus, the perfect square trinomial is $x^2 + 4x + 4$.
Step3: Calculate the number of additional unit tiles needed.
The current expression has a constant term of 3. The perfect square trinomial requires a constant term of 4. The number of additional unit tiles needed is the difference between the required constant term and the current constant term. $$ \text{Additional tiles} = 4 - 3 = 1 $$
Answer:
1