Answered

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What is the sum of the given polynomials in standard form?

[tex]\left(x^2 - 3x\right) + \left(-2x^2 + 5x - 3\right)[/tex]

A. [tex]-3x^2 + 8x - 3[/tex]

B. [tex]-x^2 - 2x - 3[/tex]

C. [tex]3x^2 - 8x + 3[/tex]

D. [tex]-x^2 + 2x - 3[/tex]

Sagot :

GinnyAnswer
Certainly! Let's add the given polynomials step-by-step:

The given polynomials are:
[tex]\[P_1(x) = x^2 - 3x\][/tex]
[tex]\[P_2(x) = -2x^2 + 5x - 3\][/tex]

To find the sum, we add the corresponding coefficients of each polynomial.

1. Add the \(x^2\) terms:
[tex]\[ 1x^2 + (-2x^2) = 1 - 2 = -1x^2 \][/tex]

2. Add the \(x\) terms:
[tex]\[ -3x + 5x = 5 - 3 = 2x \][/tex]

3. Add the constant terms:
[tex]\[ 0 + (-3) = -3 \][/tex]

Putting it all together, we get the resulting polynomial:
[tex]\[ -x^2 + 2x - 3 \][/tex]

Therefore, the sum of the given polynomials in standard form is:
[tex]\[ -x^2 + 2x - 3 \][/tex]

Hence, the correct answer from the given options is:
[tex]\[ -x^2 + 2x - 3 \][/tex]
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