which is the completely factored form of $4x^2 + 28x + 49$?\n○ $(x + 7)(4x + 7)$\n○ $4(x + 7)(x + 7)$\n○…
which is the completely factored form of $4x^2 + 28x + 49$?\n○ $(x + 7)(4x + 7)$\n○ $4(x + 7)(x + 7)$\n○ $(2x + 7)(2x + 7)$\n○ $2(x + 7)(x + 7)$
Answer
Explanation:
Step1: Recall perfect square trinomial
A perfect square trinomial has the form (a^2 + 2ab + b^2=(a + b)^2). For (4x^{2}+28x + 49), we can rewrite (4x^{2}=(2x)^{2}) and (49 = 7^{2}).
Step2: Check the middle term
The middle term should be (2ab). Here, (a = 2x) and (b=7), so (2ab=2\times(2x)\times7 = 28x), which matches the middle term of the given trinomial.
Step3: Factor the trinomial
So (4x^{2}+28x + 49=(2x + 7)^{2}=(2x + 7)(2x + 7)).