High School

Which expression is equivalent to [tex]\left(-11 x^2+1.4 x-3\right)+\left(4 x^2-2.7 x+8\right)[/tex]?

A. [tex]-7 x^2-1.3 x+5[/tex]
B. [tex]-7 x^2+1.3 x+5[/tex]
C. [tex]7 x^2-1.3 x+5[/tex]
D. [tex]7 x^2+1.3 x+5[/tex]

Answer :

To solve the given problem, we need to add the two polynomials together by combining like terms. Let's start by writing down the two polynomials:

1. [tex]\(-11x^2 + 1.4x - 3\)[/tex]
2. [tex]\(4x^2 - 2.7x + 8\)[/tex]

Now, we'll follow these steps:

1. Combine the [tex]\(x^2\)[/tex] terms:
- From the first polynomial: [tex]\(-11x^2\)[/tex]
- From the second polynomial: [tex]\(4x^2\)[/tex]
- Adding them together: [tex]\( -11x^2 + 4x^2 = -7x^2 \)[/tex]

2. Combine the [tex]\(x\)[/tex] terms:
- From the first polynomial: [tex]\(1.4x\)[/tex]
- From the second polynomial: [tex]\(-2.7x\)[/tex]
- Adding them together: [tex]\(1.4x - 2.7x = -1.3x\)[/tex]

3. Combine the constant terms:
- From the first polynomial: [tex]\(-3\)[/tex]
- From the second polynomial: [tex]\(8\)[/tex]
- Adding them together: [tex]\(-3 + 8 = 5\)[/tex]

Putting it all together, we get the combined expression:

[tex]\[ -7x^2 - 1.3x + 5 \][/tex]

Therefore, the expression that is equivalent to [tex]\(\left(-11x^2 + 1.4x - 3\right) + \left(4x^2 - 2.7x + 8\right)\)[/tex] is:

[tex]\(\boxed{-7x^2 - 1.3x + 5}\)[/tex]

So, the correct answer is:

A. [tex]\(-7x^2 - 1.3x + 5\)[/tex]

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