Question

lesson 17.2 checkpoint□ once you have completed the above problems and checked your solutions, complete the lesson checkpoint below.□ complete the lesson reflection above by circling your current understanding of the learning goal.write an expression equivalent to the following problems using the fewest number of terms.1. $(4x^{4}+x^{3}+2x^{2})$ and $(3x^{3}+x^{2}+4x)$2. $(ab^{2}+13b-4a)$ and $(3ab^{2}+a+7b)$3. $(n^{3}+12n^{2}-2n)$ and $(-n^{4}+3n^{3}-4n^{2})$model the situation with the sum of polynomials. then simplify the sum.4. the width of a rectangle is represented by $4x$, and its length is represented by $(3x + 2)$. write a polynomial for the perimeter of the rectangle.

Explanation:

Step1: Combine like terms (Problem1)

$4x^4 + (x^3+3x^3) + (2x^2+x^2) + 4x$

Step2: Simplify each term group (Problem1)

$4x^4 + 4x^3 + 3x^2 + 4x$

Step3: Combine like terms (Problem2)

$(ab^2+3ab^2) + (13b+7b) + (-4a+a)$

Step4: Simplify each term group (Problem2)

$4ab^2 + 20b - 3a$

Step5: Combine like terms (Problem3)

$-n^4 + (n^3+3n^3) + (12n^2-4n^2) - 2n$

Step6: Simplify each term group (Problem3)

$-n^4 + 4n^3 + 8n^2 - 2n$

Step7: Use perimeter formula (Problem4)

$Perimeter = 2\times(length + width) = 2[(3x+2)+4x]$

Step8: Simplify inside parentheses (Problem4)

$2(7x + 2)$

Step9: Distribute the 2 (Problem4)

$14x + 4$

Answer:

1. $4x^4 + 4x^3 + 3x^2 + 4x$
2. $4ab^2 + 20b - 3a$
3. $-n^4 + 4n^3 + 8n^2 - 2n$
4. $14x + 4$