Question

How do you determine whether `4x^2-3x+9` is a perfect square trinomial?

Answer 1

`4x^2-3x+9` is not a perfect trinomial.

Explanation:

Let us discuss the identity `(a+-b)^2=a^2+-2ab+b^2`

Observe the RHS. While

• `a^2` is the square of the first term `a`
• `b^2` is the square of the second term `b`
• sign of `a^2` and `b^2` is same and is positive
• `2ab` is twice the product of two terms `a` and `b` and its sign is `+` or `-` depending on its sign in `(a+-b)^2`

In `4x^2-3x+9`, while `4x^2=(2x)^2` and `9=3^2`,

but (leaving the sign) middle term is not `2xx2x xx3` which is `12x` but is `3x`

Hence, `4x^2-3x+9` is not a perfect trinomial.