Which of the following polynomials can approximate the following expression?
((4x^3+5)(3x^6-8x^2)/2x^2+8x-4)+4x^3-2x+13
6x^7+15
6x^7-7
6x^7+13
12x^7-27
The polynomial that can approximate the given expression is 6x^7+13.
To determine which of the given polynomials can approximate the expression ((4x^3+5)(3x^6-8x^2)/2x^2+8x-4)+4x^3-2x+13, we can compare the degrees of the terms.
The term with the highest degree in the given expression is 6x^7, so we need to find a polynomial with a 6x^7 term.
Looking at the options:
1) 6x^7 + 15: This polynomial has a 6x^7 term, but the constant term is 15, not 13 as in the given expression.
2) 6x^7 - 7: This polynomial also has a 6x^7 term, but the constant term is -7, not 13 as in the given expression.
3) 6x^7 + 13: This polynomial matches the given expression in terms of the degree of the highest term (6x^7) and the constant term (13). So, this polynomial can approximate the given expression.
4) 12x^7 - 27: This polynomial has a 12x^7 term, which is higher than the 6x^7 term in the given expression. Additionally, the constant term is -27, not 13 as in the given expression.
Therefore, the polynomial that can approximate the given expression is 6x^7 + 13.
To determine which polynomial can approximate the given expression, we need to match the highest degree term and simplify the expression.
The given expression:
((4x^3 + 5)(3x^6 - 8x^2) / (2x^2 + 8x - 4)) + 4x^3 - 2x + 13
First, let's simplify the expression by performing the multiplication of the terms (4x^3 + 5) and (3x^6 - 8x^2).
(4x^3 + 5) * (3x^6 - 8x^2)
= 12x^9 - 32x^5 + 15x^6 - 40x^2
Now, we can rewrite the given expression with the simplified terms:
(12x^9 - 32x^5 + 15x^6 - 40x^2) / (2x^2 + 8x - 4) + 4x^3 - 2x + 13
This expression has the highest degree term of 12x^9. Looking at the options provided, we can see that only one of them has a similar highest degree term:
6x^7 + 15
6x^7 - 7
6x^7 + 13
12x^7 - 27
Among the options, 6x^7 + 15 matches the degree of the term 12x^9. Therefore, 6x^7 + 15 is the polynomial that can approximate the given expression.