(z). Solve l(p) = 0 for p.
-1, 2
Suppose 6*n = -35*n + 164. Factor -3*d**3 + n*d**3 - 13*d**2 + 3*d**2 - 4*d + 7*d**2 + 0*d.
d*(d - 4)*(d + 1)
Let w(v) be the third derivative of 14*v**5/5 - 38*v**4/3 + 43*v**3/3 - 2*v**2 - 35. Let r(x) = 2*x**3 - 1. Let l(q) = 10*r(q) - w(q). Factor l(u).
4*(u - 6)*(u - 2)*(5*u - 2)
Let u be (0 - -3)*3/(-1 + 4). Suppose -5*z = 5*n - 115, 2*z - u*n + 8*n = 55. Factor 16*k + z*k + 10*k**2 - 41*k - 5*k**3.
-5*k*(k - 1)**2
Let t be ((-22396)/(-440) - 51)/(7/(-6) - -1). Solve 0*v + t*v**5 + 0 + 0*v**2 + 3/5*v**4 - 6/5*v**3 = 0.
-2, 0, 1
Let i(f) be the second derivative of -5*f**4/12 + 845*f**3/6 - 835*f**2 - 14*f + 75. Factor i(h).
-5*(h - 167)*(h - 2)
Let p = 313 + -64. Factor 5 - 250*i + 6*i**4 + p*i - i**4 - 10*i**2 - i**5 + 2*i**3.
-(i - 5)*(i - 1)**2*(i + 1)**2
Let j(m) be the third derivative of 0*m**3 - 23/72*m**4 - 51*m**2 + 0*m + 1/180*m**5 + 0. Suppose j(q) = 0. What is q?
0, 23
What is t in 57*t**3 + 0 + 182/3*t**2 + 13/3*t**4 + 8*t = 0?
-12, -1, -2/13, 0
Let u(d) be the third derivative of -d**7/945 - 13*d**6/90 + 53*d**5/90 - 20*d**4/27 + d**2 + 50. Factor u(b).
-2*b*(b - 1)**2*(b + 80)/9
Let v = 111135/472396 + 1/27788. What is t in 6/17*t + v + 2/17*t**2 = 0?
-2, -1
Factor 0 - 2/9*o**4 + 0*o + 20*o**2 + 86/9*o**3.
-2*o**2*(o - 45)*(o + 2)/9
Factor 28/3*t + 22 + 2/3*t**2.
2*(t + 3)*(t + 11)/3
Let c(z) be the first derivative of 0*z + 0*z**3 + 5/2*z**4 - 83 + 7*z**5 + 0*z**2 + 5/2*z**6. Let c(x) = 0. What is x?
-2, -1/3, 0
Let y(f) = -10 + 4 + 11 - 131*f. Let b be y(-1). Factor 3*p**3 - 11 - 7*p**2 - 2*p**3 - 1 + b*p - 120*p.
(p - 3)*(p - 2)**2
Let h(w) be the third derivative of w**8/168 + 2*w**7/35 + 3*w**6/16 + 11*w**5/120 - w**4 - 3*w**3 - 280*w**2. Let h(t) = 0. Calculate t.
-2, -3/2, 1
Let v(q) be the first derivative of 190*q**6/3 - 1028*q**5/5 + 197*q**4 + 4*q**3/3 - 80*q**2 + 16*q - 404. What is p in v(p) = 0?
-2/5, 2/19, 1
Let h(x) be the first derivative of 4 + 28/5*x + 27/10*x**2 - 1/15*x**3. Factor h(j).
-(j - 28)*(j + 1)/5
Suppose 0 = -a + 3*g - 31, 2*a + 7*g = 10*g - 29. What is m in -2/3*m**5 + 2*m**4 + 10/3*m**a + 0*m + 6*m**3 + 0 = 0?
-1, 0, 5
Let i(h) be the third derivative of h**7/490 + h**6/42 + h**5/30 - 13*h**4/42 + 5*h**3/14 - 10*h**2 - 2. What is g in i(g) = 0?
-5, -3, 1/3, 1
Let i be (-3)/36 + (-9)/54 + 5/20. Let m(l) be the first derivative of i*l - 10 - 4*l**2 + l**4 + 4/3*l**3. Factor m(o).
4*o*(o - 1)*(o + 2)
Suppose 366*l - c = 371*l + 8, -23 = c. Suppose 0 - 3/4*y**4 + 12*y - 3/4*y**5 + 9*y**l + 21*y**2 = 0. What is y?
-2, -1, 0, 4
Let k(i) = 9*i**3 + 156*i**2 + 715*i + 583. Let a(y) = 8*y**3 + 148*y**2 + 712*y + 584. Let f(n) = -5*a(n) + 4*k(n). Determine o so that f(o) = 0.
-21, -7, -1
Let a = -113014 + 113014. Factor 4/5*k**3 + 0*k**2 + 0*k**4 - 2/5*k + a - 2/5*k**5.
-2*k*(k - 1)**2*(k + 1)**2/5
Let q(u) = 3*u**3 - 8*u**2 + u - 10. Let w be q(3). Let c be 31/7 - ((-18)/(-21))/w. Factor 2/9 - 2/9*v**c + 4/9*v**3 + 0*v**2 - 4/9*v.
-2*(v - 1)**3*(v + 1)/9
Let k(n) be the third derivative of 0*n - 1/126*n**4 + 1/630*n**5 - 13 - n**2 + 1/63*n**3. Find x such that k(x) = 0.
1
Determine m, given that -96/7 - 36/7*m**2 - 120/7*m + 3/7*m**4 + 6/7*m**3 = 0.
-2, 4
Let r(p) be the first derivative of 2/3*p**3 + 0*p - 25*p**2 - 204. Let r(t) = 0. What is t?
0, 25
Let t(p) be the second derivative of 0 + 64*p + 10/7*p**2 - 4/21*p**3 - 1/84*p**4. Solve t(k) = 0.
-10, 2
Let k(d) be the third derivative of -d**5/20 + 881*d**4/2 - 1552322*d**3 + 3*d**2 + 2161*d. Factor k(o).
-3*(o - 1762)**2
Factor -44/7*d + 1/7*d**2 + 0.
d*(d - 44)/7
Let t = 374 - 353. Find d such that d**2 - 4*d + 4*d**2 + t + 89*d + 59 = 0.
-16, -1
Let r(b) be the third derivative of b**5/80 - b**4/32 - b**3/4 - 376*b**2. Factor r(c).
3*(c - 2)*(c + 1)/4
Let r be 5/(23/(391/170)). What is n in 1/4*n**3 + 0 - r*n**2 + 1/4*n = 0?
0, 1
Suppose 4*d = -0*h - 4*h - 12, 0 = 13*h + 78. Factor 0 + 3/2*k**5 + 27/2*k**d - 21/2*k**2 - 15/2*k**4 + 3*k.
3*k*(k - 2)*(k - 1)**3/2
Let l(f) = f**3 - 18*f**2 - 49*f + 33. Let u be l(21). Suppose 366 = 13*y + u. Factor -2/5*w - 2/5*w**4 - 6/5*w**2 + 0 - 6/5*w**y.
-2*w*(w + 1)**3/5
Let q = 2471/7422 + 1/2474. Factor 108 + q*s**2 - 12*s.
(s - 18)**2/3
Suppose 3*s - 2*b = 11, -8*s + 3*s = -4*b - 17. Factor 3*q**4 - 10*q**5 + 9*q**s - 6*q**3 + 4*q**5 + 27*q**5.
3*q**3*(2*q + 1)*(5*q - 2)
Factor 28/3*q**2 - 1/3*q**5 - q**4 + 8*q + 2*q**3 + 0.
-q*(q - 3)*(q + 2)**3/3
Suppose 87/2 + 3/2*w**2 + 45*w = 0. What is w?
-29, -1
Let b(o) = 9*o**2 + 23*o - 11. Let c(l) be the third derivative of l**5/15 + 11*l**4/24 - l**3 - 8*l**2 + 5. Let j(d) = 3*b(d) - 7*c(d). Factor j(a).
-(a - 1)*(a + 9)
Let l be (-18)/126 + (-3 - (-176)/56). Suppose -75*d**2 + l + 0*d + 45*d**3 - 9*d**4 + 3/5*d**5 = 0. Calculate d.
0, 5
Factor -652/11*d - 1/11*d**2 + 0.
-d*(d + 652)/11
Suppose 56*g + 7 = 57*g. Let i be (-30)/105*(-4)/20*g. Factor 2/5*z**2 + 6/5*z**3 + i*z**4 - 6/5*z - 4/5.
2*(z - 1)*(z + 1)**2*(z + 2)/5
Let y(m) be the third derivative of 1/16*m**4 + 0 - 1/16*m**3 + 28*m**2 + 0*m - 3/160*m**5. Solve y(u) = 0.
1/3, 1
Let t(x) be the third derivative of x**5/420 + 193*x**4/168 + 191*x**3/21 + 1405*x**2. Suppose t(w) = 0. Calculate w.
-191, -2
Let m(z) = -18*z - 305. Let t be m(-17). Let c(y) = 2*y**2 + 4*y - 4. Let b be c(t). Solve -2/7*a**b + 0*a + 0 = 0.
0
Let s(b) be the second derivative of b**6/105 + b**5/70 - b**4/42 - b**3/21 + b - 113. Find g such that s(g) = 0.
-1, 0, 1
Let o = 278296 - 2504632/9. Factor o*x + 10/3*x**2 - 2/9*x**3 + 0.
-2*x*(x - 16)*(x + 1)/9
Find t, given that -t**4 - 199 + 5418*t + 202*t**3 - 600*t**2 - 2438*t - 2382*t = 0.
1, 199
Let q = 228957 - 228954. Find i, given that 3*i**2 + 0 - 6*i - 3/4*i**4 + 3/2*i**q = 0.
-2, 0, 2
Let x(r) = r**3 + 180*r**2 + 252*r + 199. Let k(i) = 2*i**2 - i + 3. Let j(s) = -42*k(s) + 2*x(s). Factor j(n).
2*(n + 1)**2*(n + 136)
Factor -34019*s + 6499*s - 199*s**3 - 51*s**3 - 5*s**4 - 4080*s**2 - 37948 - 28612.
-5*(s + 8)**3*(s + 26)
Let x = 2497/10 - 1003/10. Let p = x - 149. Factor 0 - 14/5*t**3 + 32/5*t - 16/5*t**2 - p*t**4.
-2*t*(t - 1)*(t + 4)**2/5
Let q(w) be the second derivative of w**4/42 + 12*w**3/7 + 68*w**2/7 + 85*w - 2. Factor q(j).
2*(j + 2)*(j + 34)/7
Let h(y) = -y**4 - 391*y**3 - 8190*y**2 - 37182*y + 439402. Let r(b) = -2*b**4 + 13*b**3 + b - 1. Let p(x) = -h(x) - 2*r(x). Factor p(f).
5*(f - 5)*(f + 26)**3
Let y be ((-37479)/1053 + 35)*((-36)/(-32))/(-3). Factor 14/9*v + 8/3 + y*v**2.
2*(v + 3)*(v + 4)/9
Let v(c) be the first derivative of -12*c**2 + 13/6*c**3 - 20 - 1/8*c**4 + 18*c. What is r in v(r) = 0?
1, 6
Let h be (-4 + 1)/(30/5 - (-20 - -27)). Factor 0 + d**2 - 1/3*d**4 + 0*d**h + 2/3*d.
-d*(d - 2)*(d + 1)**2/3
Let y(c) be the first derivative of c**7/420 + c**6/20 + 3*c**5/8 + 25*c**4/24 - c**2 + 3*c + 109. Let i(z) be the second derivative of y(z). Factor i(x).
x*(x + 2)*(x + 5)**2/2
Let b(i) be the first derivative of -i**6/15 + 422*i**5/75 - 259*i**4/30 - 262*i**3/5 + 138*i**2/5 - 7584. Let b(t) = 0. What is t?
-2, 0, 1/3, 3, 69
Let s = -1332513/55 - -121143/5. Factor -s - 8/11*z**2 + 2/11*z**3 - 2*z.
2*(z - 6)*(z + 1)**2/11
Let h(j) be the third derivative of 0 - 5/2*j**3 + 0*j - 1/2520*j**6 + 0*j**4 - 11*j**2 - 3/280*j**5. Let v(g) be the first derivative of h(g). Factor v(k).
-k*(k + 9)/7
What is h in 27777*h - 2613645 + 7037*h - 80*h**2 - 5894*h = 0?
723/4
Let q(m) be the first derivative of m**5/40 - 41*m**4/16 + 1681*m**3/24 + 1085. Suppose q(a) = 0. What is a?
0, 41
Find c such that -672/5 - 716/5*c - 28/5*c**2 + 16/5*c**3 = 0.
-21/4, -1, 8
Let y be (2/(462/99))/(2/231). Suppose 2 + 21/4*n**5 + 59/2*n**4 + 17*n + y*n**2 + 235/4*n**3 = 0. Calculate n.
-2, -1, -1/3, -2/7
Let p(c) be the first derivative of -c**7/1050 + c**5/150 - 21*c**3 + 66. Let h(d) be the third derivative of p(d). Determine l so that h(l) = 0.
-1, 0, 1
Suppose -33*i**4 - 252*i + 192 - 54*i**4 - 54*i**4 + 249*i**3 + 3*i**5 + 156*i**4 - 78*i**4 - 129*i**2 = 0. Calculate i.
-1, 1, 4, 16
Let j(n) = -n**3 + 13*n**2 + 13*n + 16. Let m be j(14). Determine g, given that -37*g**m + 36*g**2 - 25*g + 7*g = 0.
-18, 0
Let s be (12/(-17))/(213/51 - 5). Suppose -15/7*y - 3/7*y**4 + 9/7 - 3/7*y**5 + 18/7*y**3 - s*y**2 = 0. Calculate y.
-3, -1, 1
Suppose 2*r - 2