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

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

Sure, let's find the sum of the given polynomials step-by-step. The polynomials given are:

[tex]\[ P(x) = x^2 - 3x \][/tex]
[tex]\[ Q(x) = -2x^2 + 5x - 3 \][/tex]

To find the sum, we need to combine like terms. Like terms are the terms that contain the same power of [tex]\(x\)[/tex]. Let's align the terms according to their powers:

[tex]\[ \left(x^2 - 3x + 0\right) + \left(-2x^2 + 5x - 3\right) \][/tex]

Now, add the coefficients of like terms:

1. [tex]\(x^2\)[/tex] terms:
[tex]\[ 1x^2 + (-2x^2) = 1 - 2 = -1 \][/tex]
So, the coefficient of [tex]\(x^2\)[/tex] is [tex]\(-1\)[/tex].

2. [tex]\(x\)[/tex] terms:
[tex]\[ -3x + 5x = -3 + 5 = 2 \][/tex]
So, the coefficient of [tex]\(x\)[/tex] is [tex]\(2\)[/tex].

3. Constant term:
[tex]\[ 0 + (-3) = -3 \][/tex]
So, the constant term is [tex]\(-3\)[/tex].

Combining these results, the sum of the polynomials is:

[tex]\[ P(x) + Q(x) = -1x^2 + 2x - 3 \][/tex]

So, the sum of the given polynomials in standard form is:

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

Thus, the correct answer is:

[tex]\[ \boxed{-x^2 + 2x - 3} \][/tex]