QuestionMarch 3, 2026

A perfect square trinomial can be represented by a square model with equivalent length and width.. Which polynomial can be represented by a perfect square model? x^2-6x+9 x^2-2x+4 x^2+5x+10 x^2+4x+16

A perfect square trinomial can be represented by a square model with equivalent length and width.. Which polynomial can be represented by a perfect square model? x^2-6x+9 x^2-2x+4 x^2+5x+10 x^2+4x+16
A perfect square trinomial can be represented by a square model with equivalent length and width.. Which polynomial can be represented by a perfect square model? x^2-6x+9 x^2-2x+4 x^2+5x+10 x^2+4x+16

Solution
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Answer

x^{2} - 6x + 9 Explanation 1. Identify condition for perfect square trinomial A perfect square trinomial has the form x^2 \pm 2ax + a^2. 2. Check each polynomial 1. x^2 - 6x + 9: Here 2a = 6 \Rightarrow a = 3, and a^2 = 9 matches → perfect square. 2. x^2 - 2x + 4: 2a = 2 \Rightarrow a = 1, but a^2 = 1 \neq 4 → not perfect square. 3. x^2 + 5x + 10: 2a = 5 \Rightarrow a = 2.5, a^2 = 6.25 \neq 10 → not perfect square. 4. x^2 + 4x + 16: 2a = 4 \Rightarrow a = 2, a^2 = 4 \neq 16 → not perfect square.

Explanation

1. Identify condition for perfect square trinomial <br /> A perfect square trinomial has the form $x^2 \pm 2ax + a^2$. <br />2. Check each polynomial <br /> 1. $x^2 - 6x + 9$: Here $2a = 6 \Rightarrow a = 3$, and $a^2 = 9$ matches → perfect square. <br /> 2. $x^2 - 2x + 4$: $2a = 2 \Rightarrow a = 1$, but $a^2 = 1 \neq 4$ → not perfect square. <br /> 3. $x^2 + 5x + 10$: $2a = 5 \Rightarrow a = 2.5$, $a^2 = 6.25 \neq 10$ → not perfect square. <br /> 4. $x^2 + 4x + 16$: $2a = 4 \Rightarrow a = 2$, $a^2 = 4 \neq 16$ → not perfect square.
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