An algebra tile configuration. There are 3 large tiles, 5 tiles each half the size of a large tile, and 8 tiles each one-quarter the size of a large tile. Two of the large tiles are labeled plus x squared and 1 is labeled negative x square. Two smaller tiles are labeled plus x and 3 are labeled negative x. Six of the smallest tiles are labeled + and 2 are labeled minus.
Which polynomial is represented by the algebra tiles?
x2 – x – 4
x2 – x + 4
3x2 – 5x + 8
3x2 – 5x – 8
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Answer:
k = 13The smallest zero or root is x = -10
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Work Shown:
note: you can write "x^2" to mean "x squared"
f(x) = x^2+3x-10
f(x+5) = (x+5)^2+3(x+5)-10 ... replace every x with x+5
f(x+5) = (x^2+10x+25)+3(x+5)-10
f(x+5) = x^2+10x+25+3x+15-10
f(x+5) = x^2+13x+30
Compare this with x^2+kx+30 and we see that k = 13
Factor and solve the equation below
x^2+13x+30 = 0
(x+10)(x+3) = 0
x+10 = 0 or x+3 = 0
x = -10 or x = -3
The smallest zero is x = -10 as its the left-most value on a number line.
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