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Greatest garden Calculations!!!

Greatest garden Calculations!!!. By: Lauren Brace, Amanda Stone, Ali Cuteri. Our 1st goal!. Our 1st goal of the project was to find all the possible factored pairs of binomials that could make up the possible length and width of our rectangle garden with the dimensions of 12x^2+36x+24.

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Greatest garden Calculations!!!

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  1. Greatest garden Calculations!!! By: Lauren Brace, Amanda Stone, Ali Cuteri

  2. Our 1st goal! • Our 1st goal of the project was to find all the possible factored pairs of binomials that could make up the possible length and width of our rectangle garden with the dimensions of 12x^2+36x+24. • We accomplished this goal by factoring.

  3. Factoring • There are only a few easy steps to factoring. • Find you’re a, b, and c points • A= the x^2 term • B= the x term • C= the number that stands alone • In this case 12x^2=a, 36x= b, and 24=c • First, multiply 12*24 (drop the x^2 term)= 288 • To find all possible lengths and widths, you must find multiplies of 288, however they must add to get your b term or 36.

  4. Binomials • The first pair of common multiples of 288 is 12 and 24, therefore we plugged those numbers in, and they replaced the b term. • Therefore, we ended up with the equation 12x^2 + 12x +24x + 24. • Using the first two numbers divide by the common multiple (12x), resulting in 12x(x+1) • Do the same with the other two numbers, common multiple 24, therefore 24(x+1) • Use the outside numbers as another parenthesis…. Final Answer= (x+1) (12x+24) • 1st pair of binomials, there are five left

  5. Binomials continued • To find the other pairs of binomials, we found common numbers that 12 and 24 (excluding 1) are divisible by. You MULTIPLY the first parenthesis (x+1) by the common number, and DIVIDE the second parenthesis (12x+24). • Therefore, our other five final results were… • (3x+3) (4x+8) • (4x+4) (3x+6) • (12x+12) (1x+2) • (2x+2) (6x+12) • (6x+6) (2x+4)

  6. Our 2nd goal! • Our second goal of the project was to find the dimensions of length and width that uses the most fencing and the least fencing if x=4. • We accomplished this goal by finding the perimeter, adding all four sides of the rectangle.

  7. Perimeter • Tofind the perimeter, we used all the binomial pairs. • For example our first binomial pair was (x+1) (12x+24). • We plugged this into the rectangle, then added the like terms. • When we added the like terms we got an answer of 26x+50, then we plugged 4 in for x. Resulting in 104+50=154. Therefore, the perimeter of this binomial pair is 154. 12x+24 X+1 X+1 12x+24

  8. Perimeter continued • After we found the perimeter for the first pairs of binomials, we found the other 5. • 78 • 76 • 132 • 92 • 84

  9. Most & least fencing • The dimensions of length and width that uses the most fencing is (x+1) (12x+24). • The dimensions of length and width that uses the least fencing is (3x+6) (4x+4).

  10. Area=0 • For area to equal 0, we used the quadratic formula, -b+or- • Our x values came out to be, -1 and -2 B^2-4 ac 2a

  11. THE END!!!! :) :) :) :) :) :)

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