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w^2+5w-50=
GCF = 1
-1*50=-50 -1 50 -2 25 -5 10 -25 2 -10 5 -50 1
-5 10
w^2-5w+10w-50 w(10+w) -5(10+w) (10+w)(-5+w)
5s^5-95s^4+420s^3
GCF = 5
5s^3(s^2 -19s + 84)
-7 and -12 sum to -19 and multiply together to 84
5s^3(s-7)(s-12)
5x^3y + 44x^2y^2+63xy^3
xy(5x^2+44xy+63y^2)
5 * 63 = 315
15 * 21
21 * 15
5 * 63
63 * 5
105 * 3
35 * 9
9 * 35
9 + 35 = 44
xy(5x^2+9xy+35xy+63y^2)
xy(5x^2+9xy)(35xy+63y^2)
xy(x(5x+9y)7y(5x+9y)
xy(x+7y)(5x+9y)
q^2-18q+81 GCF 1 AC - 181 = 81 -9-9=81 -9-9 = -18 q^2-9q-9q+81 q(q-9)-9(q-9) (q-9)^2
108x^3+180x^2m+75xm^2 GCF 3 3x(36x^2+60xm+25m^2)
36*25 = 900 factors of 900: 1 2 3 4 5 6 9 10 12 15 18 20 25 30 36 45 50 60 75 90 100 150 180 225 300 450 900
30 * 30 = 900 30 + 30 = 60
3x(36x^2 + 30xm + 30xm +25m^2) 3x(x(36x+30m) + m(30x + 25m)) gave up on this one, symbolab showed me it requires the “perfect square rule” which we have not been shown
9y^4 -12y^2z^3+4z^6 GCF 1
9 * 4 = 36 factors of 36: 6 * 6
-6 + -6 = -12 -6 * -6 = 36
9y^4 -6y^2z^3 -6y^2z^3 + 4z^6 3y^2(3y^2-2z^3) + 2z^3(-3y^2 + 2z^3) 3y^2(3y^2-2z^3) - 2z^3(3y^2 - 2z^3) (3y^2-2z^3)+(3y^2-2z^3) (3y^2-2z^3)
49r^2-81 (7r)^2-(9)^2 (7r-9)(7r+9)
98p^4-50t^6 gcf 2 2(49p^4-25t^6) 2(7p^2)^2-((5t^3)^2) 2(7p^2-5t^3)(7p^2+5t^3)
16x^4-81 gcf 9 9(2x^4-9)
(4x^2)^2-(9)^2 (4x^2+9)(4x^2-9) (4x^2+9)(2x+3)(2x-3)
20z^4+30z^3-180z^2-270z GCF is 10z 10z(2z^3+3z^2-18z-27)
2z^3+3z^2-18z-27 (2z^3)(3z^2) (-18z-27) z^2(2z+3) -9(2z-3) (2z+3)(z+3)(z-3) 10z(2z+3)(z+3)(z-3)
(k^2-3)^2-6(k^2-3)+5 k^2-3 = u u^2-6u+5 gcf 1 1 * 5 = 5 x 6 * -1 = -6 x 6 - 1 = 5 x u^2 -6u+1u +5 x u(u-6) + (u+5) x x means i did wrong thing (u^2-u)+(-5u+5) u(u-1)-5(u-1) (u-1)(u-5) ((k^2-3)-1)((k^2-3)-5) (k^2-4)(k^2-8) (k+2)(k-2)(k^2-8)
-20d^3+82d^2-42d GCF 2 2d(-10d^2+41d-21) -10 * -21 = 210 1 2 3 4 5 6 7 8 9 10 14 15 21 30 35 42 70 105 210 6 * 35 = 210 6 + 35 = 41 2d(-10d^2+6d+35d-21) x 2d(-2d(5d-3)+7(5d-3)) x 2d((-2d+7)(5d-3)) 2d(-(2d-7)(5d-3)) -2d(2d-7)(5d-3)
2d(-10d^2+41d-21) 2d * -(10d^2-41d+21) 2d * -(10d^2+6d+35d-21) 2d * -(2d(5d-3) - 7(5d-3)
|t+5|=3 t+5=3 t=-2 t+5=-3 t=-8
|t+5|=0 -5
|t+5|=-4 empty set
3|2x+7|+5=17 3|2x+7|=12 |2x+7|=4 2x+7=4 2x=-3 x=-1.5 2x+7=-4 2x=-11 x=-5.5
-|t+8|+1 = -5 -|t+8|= -6 |t+8| = 6 t+8 = 6 t=-2 t + 8 =-6 t=-14
4=7+|10z+3| -3=|10z+3| no set
|c+2|+3=6 |c+2|=3 c+2=3 c=1 c+2=-3 c=-5
|c+2|+3⇐6 |c+2|⇐3 c+2⇐3 c⇐1 c+2⇐-3 c⇐5
2|7-x|+3<13 2|7-x|<10 |7-x|<5
7-x<5 7<5+x 2<x 7-x>-5 7>-5+x 12>x
2|8+z|-2>=16 2|8+z|>=18 |8+z|>=9 8+z>=9 z>=1 8+z⇐-9 z⇐-17
-1⇐1-|2y+8| -2⇐-|2y+8| 2⇐|2y+8| -2 ⇐ 2y+8 ⇐ 2 -10 ⇐ 2y ⇐ -6 -5 ⇐ y ⇐ -3
10 < |-2y-4| +3 7 < |-2y-4|
7 < -2y-4 11 < -2y -5.5 < y
-7 > -2y-4 -3 > -2y 1.5 > y
|(t-7)/5|<5 -5 < |(t-7)/5| < 5 -25 < t-7 < 25 -18 < t < 32
15⇐3-|y+3| -|y+3|>=12 |y+3|>=-12 |8w-1|+7⇐4 |8w-1|⇐-3
|9-4x|+18>2 |9-4x|>-16
|5x+2|+7<3 |5x+2|←4
-1.83(6)+212
191=-1.83(x)+212 -21=-1.83(x) 11.475=x
162.55x+99 162.55(20)+99 2537.25 = 162.55x+99 2438.25 = 162.55x 15 = x
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