 2)*(w - 1)/4
Let b be 424/318 + 22/(-3) + 78/9. Determine n, given that 0 + 2/3*n**2 + b*n = 0.
-4, 0
Let k(y) be the third derivative of 1/12*y**4 + 0 + 2*y**3 + 0*y - 24*y**2 - 1/30*y**5. Factor k(q).
-2*(q - 3)*(q + 2)
Let h = -34070 + 34072. Determine o, given that 2/5*o**3 - 4/5 + 1/5*o**4 - 3/5*o**h - 8/5*o = 0.
-2, -1, 2
Let l = -1043 - -1043. Determine k, given that 0*k + 0*k**2 + 1/5*k**3 + l = 0.
0
Let w = 37 + -7. Let b = 29 - w. Let q(n) = -n**4 - n**3 + 2*n**2 + 2*n. Let x(i) = i**5 + i**4 - i**3 + i. Let y(a) = b*q(a) + x(a). Factor y(p).
p*(p - 1)*(p + 1)**3
Suppose 0 = 8*a - 8 - 8. Factor -10 - 2 + 12 + 6*c**2 - a*c**3.
-2*c**2*(c - 3)
Let g(n) = -4*n**2 - 22*n - 11. Let k(i) = i**2 + 10*i + 6. Let w(m) = -3*g(m) - 7*k(m). Factor w(s).
(s + 1)*(5*s - 9)
Let w(c) = -8*c**2 - 48*c - 45. Let k(f) = 4*f**2 + 24*f - 12 + 0*f**2 + 34. Let y(p) = 5*k(p) + 2*w(p). Let y(b) = 0. What is b?
-5, -1
Suppose 3*v = 23 - 14. Factor 12*q**3 + 8 - 32*q + 14*q**4 - 11*q**5 + 50*q**2 + 9*q**5 - 50*q**v.
-2*(q - 2)**2*(q - 1)**3
Suppose 13*v - 16*v - 15 = 0. Let k be (-16 - -16) + v/((-10)/4). Suppose -72/5*z + 81/5*z**4 - 729/5*z**5 - 93/5*z**k + 12/5 + 801/5*z**3 = 0. Calculate z.
-1, -1/3, 2/9, 1
Let l(u) = -3*u**2 + 3*u + 3. Let v = -5 + 4. Let k(w) = -1 - 1 + 3. Let b(d) = v*l(d) + 3*k(d). Suppose b(m) = 0. What is m?
0, 1
Suppose 5*t - 5 = 10. Let j(z) = 8*z**3 + 17*z**2 + 12*z + 3. Let p(d) = -65*d**3 - 135*d**2 - 95*d - 25. Let o(x) = t*p(x) + 25*j(x). What is q in o(q) = 0?
-3, -1, 0
Let k(w) be the first derivative of -4*w**3/3 - 10*w**2 + 56*w - 52. Find q, given that k(q) = 0.
-7, 2
Suppose -2*z + 3*i = -49 + 29, -i = -4*z + 20. Let p(c) be the second derivative of 7*c + c**z + 3*c**2 - 3/20*c**5 - 5/2*c**3 + 0. Suppose p(o) = 0. What is o?
1, 2
Let r be 1701/4374 - 4/18. Suppose 1/3*h**4 + 0 - 4/3*h**2 - r*h**5 + 1/2*h**3 + 2/3*h = 0. Calculate h.
-2, 0, 1, 2
Let d(a) = 4*a**2. Let m be d(-2). Suppose -8 = 2*n, 4*f - m = -n + 2*n. Factor -3*p + f - 3 + 6*p**2 - 3*p**3 + 0.
-3*p*(p - 1)**2
Let -25*q + 4*q**3 - 7*q + 4*q**4 + 10*q + 102*q - 64*q**2 = 0. Calculate q.
-5, 0, 2
Let v(l) be the second derivative of -23*l + 0 + 1/16*l**4 - 3/8*l**3 - 3/2*l**2. Determine x so that v(x) = 0.
-1, 4
Let w(g) be the second derivative of g**6/75 - 23*g**5/50 - 49*g**4/30 - 5*g**3/3 - g - 10. Suppose w(x) = 0. Calculate x.
-1, 0, 25
Let z = -128943/1610 - -557/7. Let k = -2/115 - z. Factor 0 + 0*g - k*g**4 - g**2 - 3/2*g**3.
-g**2*(g + 1)*(g + 2)/2
Let x(u) be the first derivative of u**6/57 + 2*u**5/19 + 3*u**4/19 - 84. Let x(h) = 0. Calculate h.
-3, -2, 0
Let o(m) be the first derivative of -m**6/3600 + 7*m**5/300 - 49*m**4/60 + 4*m**3 - 18. Let l(q) be the third derivative of o(q). Factor l(n).
-(n - 14)**2/10
Let z = 607 - 1820/3. Let s(r) be the first derivative of 1/18*r**6 + 11/30*r**5 + 11/12*r**2 + 23/24*r**4 + 23/18*r**3 + 7 + z*r. Solve s(o) = 0.
-2, -1, -1/2
Factor -1730*q**2 + 3925*q**2 - 45*q**3 - 3640*q + 10*q**3 - 1220.
-5*(q - 61)*(q - 2)*(7*q + 2)
Let s(x) be the first derivative of -x**4/16 + x**3/12 + 2*x**2 + 5*x - 132. Factor s(i).
-(i - 5)*(i + 2)**2/4
Factor 12 - z**2 - 5*z**2 - 3*z + 4*z**2 + z.
-2*(z - 2)*(z + 3)
Factor 52*p - 2/5*p**2 - 1690.
-2*(p - 65)**2/5
Let r be (-3 - (-6 - 0)) + 0. Let v be (6 - 3)*(1 - -1). Factor 2*a + 5*a**3 - 3*a**r + v*a**3 - 2 + 10*a**2 - 2*a**3.
2*(a + 1)**2*(3*a - 1)
Suppose 3*r - 4 = -r. Let k be r/(-3)*-9*2/2. Factor -15*v**5 - 12/5*v + 42*v**4 + 84/5*v**2 + 0 - 207/5*v**k.
-3*v*(v - 1)**2*(5*v - 2)**2/5
Let v be (86/(-70) + ((-860)/50 - -18))*-2. Factor 2/7*q**4 - 4*q**2 - v - 22/7*q - 12/7*q**3 + 2/7*q**5.
2*(q - 3)*(q + 1)**4/7
Let n be (-75)/(-45)*108/60. Solve 1/3*x**n + 7*x**2 + 343/3 + 49*x = 0.
-7
Let r(i) be the second derivative of i**8/1680 - i**6/180 + 11*i**4/12 - 12*i. Let v(h) be the third derivative of r(h). Factor v(a).
4*a*(a - 1)*(a + 1)
Let w = -14 - -37. What is q in -9*q**2 - 20*q**3 + 40*q**3 - w*q**3 = 0?
-3, 0
Let x = -73 - -73. Suppose -2*z = -2*c - 17 + 11, -4*z - 2*c + 18 = x. Determine u, given that -3/4 + 0*u**2 + 3/4*u**z + 3/2*u - 3/2*u**3 = 0.
-1, 1
Let o(c) = c**3 - 5*c + 3. Let m be o(3). Factor -7 + 45*l + m*l - 45*l**2 - 13.
-5*(3*l - 2)**2
Factor 34/15*p**2 + 0 - 4/3*p**3 + 2/15*p**4 - 16/15*p.
2*p*(p - 8)*(p - 1)**2/15
Let g = -13 + 9. Let i(p) = -p**3 - 7*p**2 - 12*p + 2. Let c be i(g). Factor 0 - 1/4*t**c - 1/4*t.
-t*(t + 1)/4
Suppose -2 = -2*q, 4*q + 2 = a + 2*a. Factor -18*u + u + 100 - 11*u - 12*u + 4*u**a.
4*(u - 5)**2
Let x be (19536/(-259))/((-15)/7 - -2). Let n be 228/x - ((-6)/(-33))/1. Determine y so that n*y**2 - 1/2 - 1/4*y = 0.
-1, 2
Suppose -29*g + 65*g = 144. Let v(a) be the second derivative of 2/3*a**3 - g*a - 1/20*a**5 + 0 - 1/6*a**4 + 4*a**2. Factor v(d).
-(d - 2)*(d + 2)**2
Suppose 3*v + t - 22 = -3*t, -4*v + 4*t + 20 = 0. Let p be 4/v + 70/84. Factor -3/2*r + p - 3/2*r**2 + 3/2*r**3.
3*(r - 1)**2*(r + 1)/2
Let c(f) = -6*f**2 + 4*f - 10. Let n = -11 + 19. Suppose -2*s = -n + 6. Let a(x) = x**2 + x + 1. Let w(v) = s*c(v) + 4*a(v). Factor w(q).
-2*(q - 3)*(q - 1)
Let t = 52 + -50. Let -35*r**3 - 40*r + 35*r**t - 80 + 25*r**3 + 5*r**3 = 0. What is r?
-1, 4
Let b(j) = -j**3 + 5*j + 12. Let z be b(3). Factor 3*i + z + 3/4*i**2.
3*i*(i + 4)/4
Let y be (-69)/(-161) - (32/(-7) - 0). Let p be (-4)/((-11)/1 + y). Determine f so that -4*f**2 - 16/3 + 8*f + p*f**3 = 0.
2
Let p = -82 + 85. Factor p*i + 3*i + 5 + 0 + i**2 + 4.
(i + 3)**2
Let j(t) be the third derivative of t**9/47040 - t**8/4704 + t**7/3920 + t**5/20 + 15*t**2. Let w(b) be the third derivative of j(b). Factor w(f).
3*f*(f - 3)*(3*f - 1)/7
Factor -1/6*x**3 + 0*x - 1/3*x**2 + 0.
-x**2*(x + 2)/6
Let i be -9 + 7 + (-104)/(-39). Let m be (-2)/10 - 23/(-15). What is o in -i - m*o - 2/3*o**2 = 0?
-1
Suppose 4*x = 12, 3*z - 4*x + 15 = 4*z. Suppose -z = 4*d - 83. Determine w, given that 0*w**2 - 6*w**3 + d*w**4 - 18*w**4 + 4*w**2 = 0.
0, 1, 2
Let v(t) be the third derivative of -t**8/714 - t**7/1785 + 7*t**6/255 + 31*t**5/510 + t**4/34 + t**2 - 86*t. What is a in v(a) = 0?
-2, -1, -1/4, 0, 3
Let n(r) = -3*r**3 - 190*r**2 + 768*r - 752. Let b(a) = 2*a**3 + 192*a**2 - 768*a + 752. Let v(j) = -7*b(j) - 6*n(j). Suppose v(z) = 0. What is z?
2, 47
Let r(z) be the third derivative of -2*z**3 + 3/20*z**5 + 0*z + 1/70*z**7 + 1/2*z**4 - 1/10*z**6 - 8*z**2 + 0. Factor r(f).
3*(f - 2)**2*(f - 1)*(f + 1)
Let j(c) = 5*c - 2. Let o be j(1). Determine q so that 5 + 4*q**o - q**4 + 2224*q**2 + 11 - 16*q - 2224*q**2 = 0.
-2, 2
Let d(m) be the second derivative of 2*m**2 - 1/10*m**5 + m**3 + 0*m**4 - 4*m + 0. Factor d(l).
-2*(l - 2)*(l + 1)**2
Suppose 0 = -s - 115 + 504. Factor -2*x + 396 - 6*x + x**2 - s.
(x - 7)*(x - 1)
Let n(m) be the first derivative of -m**7/315 - m**6/90 + m**4/18 + m**3/9 - 9*m**2/2 - 2. Let b(w) be the second derivative of n(w). Factor b(p).
-2*(p - 1)*(p + 1)**3/3
Suppose -1 = j + h, 4 = -h - 0. Factor 0*c**4 + 1/3*c**5 + 2/3*c**2 - 4/3*c**j + c - 2/3.
(c - 1)**3*(c + 1)*(c + 2)/3
Factor -2 + 11/5*k - 1/5*k**2.
-(k - 10)*(k - 1)/5
Let m = -32697 - -32699. Factor 1/5*c**3 + c - 2/5 - 4/5*c**m.
(c - 2)*(c - 1)**2/5
Let y(n) = n**3 + 6*n**2 + 4*n - 2. Let z be y(-4). Let f = z - 10. What is l in -5*l**4 - l**4 + 2*l**3 + f*l**4 = 0?
0, 1
Let a(v) be the first derivative of 3*v**4/20 - 7*v**3/15 - 9*v**2/5 - 8*v/5 - 80. Suppose a(d) = 0. Calculate d.
-1, -2/3, 4
Let d be 23/46*(-168)/(-9) + 0 + -4. Factor -8/3*y + 4 + 4/3*y**4 - d*y**2 + 8/3*y**3.
4*(y - 1)**2*(y + 1)*(y + 3)/3
Let v(b) = b + 1. Let o(d) = -4*d - 4. Let x(u) = 4*o(u) + 14*v(u). Let g be x(-2). Factor -8*q**g + 6*q**3 - q**4 + 3*q**5 - 5*q**5 + 5*q**4 - 8*q.
-2*q*(q - 2)**2*(q + 1)**2
What is r in -9*r**3 - 14 + 4*r**2 - r**3 + 18*r**4 - 12*r**3 + 14 = 0?
0, 2/9, 1
Suppose 7/3 - 4/3*f**2 - f = 0. What is f?
-7/4, 1
Let d(f) be the second derivative of -f**6/50 - 9*f**5/100 + 7*f**4/20 + 27*f**3/10 + 27*f**2/5 + 13*f + 4. Suppose d(r) = 0. Calculate r.
-3, -2, -1, 3
Let p be ((-14)/(-35))/(12/40*2). Determine h so that -p - h - 1/3*h**2 = 0.
-2, -1
Let h(f) be the first derivative of -f**6/10 + 3*f**5/5 - 5*f**4/4 + f**3 - 3*f - 8. Let d(y) be the first derivative of h(y). Factor d(z).
-3*z*(z - 2)*(z - 1)**2
Fa