Which of the following polynomials can approximate the following expression?
(4x3+5)(3x6−8x2)2x2+8x−4 +4x3−2x+13
To determine which polynomial can approximate the given expression, we need to compare the degree and the terms of the polynomials.
The given expression is (4x^3 + 5)(3x^6 − 8x^2)(2x^2 + 8x − 4) + 4x^3 − 2x + 13.
Let's break down the given expression:
(4x^3 + 5)(3x^6 − 8x^2)(2x^2 + 8x − 4) can be simplified by multiplying the terms inside the parentheses:
= (4x^3 + 5)(-24x^8 + 64x^4 - 16x^6 + 8x^2 - 32x^3 + 64x - 16)
= -96x^11 + 256x^7 - 64x^9 + 32x^5 - 128x^6 + 256x^2 - 64x^4 + 20x^3 + 40x - 10
Now we add the remaining terms:
-96x^11 + 256x^7 - 64x^9 + 32x^5 - 128x^6 + 256x^2 - 64x^4 + 20x^3 + 40x - 10 + 4x^3 − 2x + 13
Combining like terms:
-96x^11 - 64x^9 - 128x^6 - 64x^4 + 256x^7 + 32x^5 + 20x^3 + 256x^2 + 40x + 13 - 2x - 10
= -96x^11 - 64x^9 - 128x^6 - 64x^4 + 256x^7 + 32x^5 + 20x^3 + 256x^2 + 38x + 3
Now, we analyze the terms of the polynomial. The highest degree term is -96x^11, so we should look for a polynomial that has a term with a similar degree.
None of the given polynomials match the degree of -96x^11, so none of them can accurately approximate the given expression.
6x7-7 why is this the correct answer step by step
I apologize for the confusion in my initial response. Let's break down the given expression step by step.
The given expression is 6x^7 - 7.
Step 1: Identify the highest degree term.
The highest degree term in the given expression is 6x^7. This means that any polynomial that can approximate the expression must have a term with a degree of 7.
Step 2: Compare the remaining terms.
Since there is no other term present in the given expression (aside from the constant term -7), we do not need to consider any additional terms.
Step 3: Determine the closest approximation.
Considering the highest degree term (6x^7) and the constant term (-7), the closest approximation to the given expression is the polynomial 6x^7 - 7.
Therefore, 6x^7 - 7 is the correct answer as it matches the highest degree term and the constant term of the given expression.