Question 1173745: Hey, I need help with this ASAP if someone could help me with this that would be very much appreciated. Thank you:)
a)find all values of b so that x^2 +bx +10 can be factored over the integers
b) find all values of b so that 4y^2 +by +5 can be factored over the integers
c) write an algebraic expression for the shaded area. Then write the expression in factored form.
P.S the shaded area is a square the perimeter is x+2 by x+1 and then there is a smaller square inside of that which is 4 by 3.
Found 2 solutions by ikleyn, Boreal:
Answer by ikleyn(52835)   (Show Source):
You can put this solution on YOUR website! .
1)
Start noticing that 10 = 1*10 = 2*5 = (-1)*(-10) = (-2)*(-5).
It gives you all possible values b = 1 + 10 = 11;
2 + 5 = 7;
(-1) + (-10) = -11;
(-2) + (-5) = -7.
Answer by Boreal(15235)  (Show Source):
You can put this solution on YOUR website! (x+5)(x+2), b=7 look at factors of 10.
(x-5)(x-2), b=-7
(x+1)(x+10) b=11
(x-1)(x-10) b=-11
make the discriminant b^2-4ac a perfect square: b^2-40 is a perfect square
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b^2-80 is a perfect square: b=9,12,21
(2y+1)(2y+5) b=12
(2y-1)(2y-5) b=-12
(4y+1)(y+5) b=21 and the negative
(4y+5)(y+1) b=9 and the negative
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I'm not clear on the last part.
A perimeter is 2L + 2W, if these are length and width. But in a square they are equal.
Same with a square inside that can't be 4 by 3, at least the way I interpret the statement.
If these are rectangles inside a square with those areas, that needs to be clarified. Something x+2 by x+1 has area x^2+3x+2 and if the 4 by 3 inside is subtracted from the area, the remaining area is x^2+3x-10 which factors into (x+5)(x-2).
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