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Simplify the polynomial, then evaluate for [tex]x=3[/tex].

[tex]\[x^2 + 2x - 3 - 2x^2 + x + 4\][/tex]

A. [tex]\(-x^2 + 3x + 1 ; 19\)[/tex]
B. [tex]\(-x^2 + 3x + 1 ; 1\)[/tex]
C. [tex]\(2x^2 + 1 ; 19\)[/tex]
D. [tex]\(3x^2 + 3x + 1 ; 37\)[/tex]

Sagot :

GinnyAnsweridn
Let's simplify the given polynomial and then evaluate it for [tex]\( x = 3 \)[/tex].

### Step 1: Simplify the Polynomial
The given polynomial is:
[tex]\[ x^2 + 2x - 3 - 2x^2 + x + 4 \][/tex]

First, let's combine the like terms. The polynomial has the terms:
[tex]\[ x^2 \][/tex]
[tex]\[ 2x - 2x^2 + x \][/tex]
[tex]\[ -3 + 4 \][/tex]

Combining these, we get:
[tex]\[ (x^2 - 2x^2) + (2x + x) + (-3 + 4) \][/tex]

Let's simplify each type separately:
[tex]\[ (x^2 - 2x^2) = -x^2 \][/tex]
[tex]\[ (2x + x) = 3x \][/tex]
[tex]\[ (-3 + 4) = 1 \][/tex]

So, the simplified polynomial is:
[tex]\[ -x^2 + 3x + 1 \][/tex]

### Step 2: Evaluate the Simplified Polynomial for [tex]\( x = 3 \)[/tex]
Now, we need to evaluate this simplified polynomial at [tex]\( x = 3 \)[/tex]:
[tex]\[ -x^2 + 3x + 1 \][/tex]

Substitute [tex]\( x = 3 \)[/tex] into the polynomial:
[tex]\[ -(3)^2 + 3(3) + 1 \][/tex]

Calculate each term:
[tex]\[ -(3)^2 = -9 \][/tex]
[tex]\[ 3(3) = 9 \][/tex]
[tex]\[ 1 = 1 \][/tex]

Now add these values together:
[tex]\[ -9 + 9 + 1 = 1 \][/tex]

### Conclusion
The simplified polynomial is:
[tex]\[ -x^2 + 3x + 1 \][/tex]

And the value of the polynomial when [tex]\( x = 3 \)[/tex] is:
[tex]\[ 1 \][/tex]

So, the correct answer is:
[tex]\[ -x^2 + 3x + 1; 1 \][/tex]
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