Question

5 which expression is equivalent to (x² + 6x + 3)+(-2x² + 5x - 3)? a -x² + 11x b 3x² + 11x + 6 c 6x² - 5x + 4 d -x² + 13x + 6 6 given the figure below, which expression represents the perimeter of the polygon 4x + 1 7x - 3 5x² 4x² + 9x + 5 a x²+11x + 3 b 5x²+16x + 3 c 8x²+16x + 3

Explanation:

Step1: Remove parentheses

$(x^{2}+6x + 3)+(-2x^{2}+5x - 3)=x^{2}+6x + 3-2x^{2}+5x - 3$

Step2: Combine like - terms

For $x^{2}$ terms: $x^{2}-2x^{2}=(1 - 2)x^{2}=-x^{2}$
For $x$ terms: $6x+5x=(6 + 5)x = 11x$
For constant terms: $3-3 = 0$
So the result is $-x^{2}+11x$.

For question 6, to find the perimeter of the polygon, we add up the lengths of all its sides:

Step1: Set up the sum

Perimeter$=(7x - 3)+(4x + 1)+5x^{2}+(4x^{2}+9x + 5)$

Step2: Combine like - terms

For $x^{2}$ terms: $5x^{2}+4x^{2}=9x^{2}$
For $x$ terms: $7x+4x+9x=(7 + 4+9)x=20x$
For constant terms: $-3 + 1+5=3$
So the perimeter is $9x^{2}+20x + 3$.

Answer:

A. $-x^{2}+11x$