Simplify the polynomial, then evaluate for \( x=-1 \) \( 3 x^{2}-4+2 x-1+x^{2} \) \( 3 x^{2}+3 x-5 ;-5 \) \( 6 x^{2}-5 ; 1 \) \( 4 x^{2}+2 x-5 ;-3 \) \( 4 x^{2}+2 x-5 ;-11 \)
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Let's simplify the polynomial step by step. Starting with: \[ 3x^{2} - 4 + 2x - 1 + x^{2} \] We combine like terms: 1. For \( x^{2} \) terms: \( 3x^{2} + x^{2} = 4x^{2} \) 2. For \( x \) terms: \( 2x \) 3. For constant terms: \( -4 - 1 = -5 \) Combining everything gives us: \[ 4x^{2} + 2x - 5 \] Now, we need to evaluate it for \( x = -1 \): \[ 4(-1)^{2} + 2(-1) - 5 = 4(1) - 2 - 5 = 4 - 2 - 5 = -3 \] So, the simplified polynomial is \( 4x^{2} + 2x - 5 \) and its evaluation at \( x = -1 \) gives us \( -3 \).