 i(s) = 11*s**4 + 371*s**3 - 383*s**2 - 375*s + 382. Let m(k) = 3*k**4 - 2*k**3 + k**2 + 1. Let b(t) = i(t) - 2*m(t). What is d in b(d) = 0?
-76, -1, 1
Solve -4*w**4 + 0*w**2 + 0 + 2/3*w**5 + 0*w + 10/3*w**3 = 0.
0, 1, 5
Let r(l) be the second derivative of l**7/420 - l**6/90 - 31*l**3/3 + 4*l + 7. Let g(i) be the second derivative of r(i). Find w such that g(w) = 0.
0, 2
Let j(a) be the second derivative of 7*a**2 + 5/6*a**3 - a - 1/12*a**4 - 1. Factor j(y).
-(y - 7)*(y + 2)
Let m(x) be the second derivative of 5*x**4/36 - 2125*x**3/18 + 1060*x**2/3 - 10268*x. Factor m(q).
5*(q - 424)*(q - 1)/3
Let q be 60/9 + (-6)/36*4. Let x(m) be the second derivative of 2/7*m**7 + 23*m + 1/2*m**3 + 19/10*m**q + 93/20*m**5 + 19/4*m**4 + 0 - 3*m**2. Factor x(w).
3*(w + 1)**3*(w + 2)*(4*w - 1)
Let n(p) be the first derivative of 4*p**5/45 - 13*p**4/9 - 80*p**3/27 + 56*p**2/3 + 2834. Find z such that n(z) = 0.
-3, 0, 2, 14
Let a be 7 - (-9 + (-12)/3). Let d be a/(-12)*(-54)/30. Factor -4/3*k**5 + 0*k**2 + 8/3*k**d - 4/3*k + 0*k**4 + 0.
-4*k*(k - 1)**2*(k + 1)**2/3
Let v(m) be the second derivative of 108*m**7/7 - 33*m**6/5 - 208*m**5/5 + 29*m**4/2 + 92*m**3/3 + 12*m**2 - 555*m. Let v(j) = 0. What is j?
-1, -2/9, 3/4, 1
Suppose -51 = -2*n - c, 0*n = 4*n + c - 107. Suppose -4*q = -5*l - 41, 4*l + n = q + q. Factor v**2 + v**2 - 31*v**4 + v**5 + 29*v**q - v.
v*(v - 1)**3*(v + 1)
Let a(k) be the second derivative of 13/138*k**4 + 32*k - 3 + 15/23*k**2 + 1/230*k**5 - 29/69*k**3. Factor a(c).
2*(c - 1)**2*(c + 15)/23
Let i be (-28)/((-47880)/34295) - (-5)/(-9). Factor 0*h + 0 - 54*h**2 - i*h**4 - 72*h**3 - 3/2*h**5.
-3*h**2*(h + 1)*(h + 6)**2/2
Let t(d) be the second derivative of d**4/10 + 2888*d**3/5 + 6255408*d**2/5 - 111*d - 17. Solve t(k) = 0.
-1444
Let r = -1668959/120 - -13908. Let k(z) be the second derivative of r*z**5 + 1/36*z**4 + 0*z**3 + 0*z**2 + 0 + 25*z. Factor k(l).
l**2*(l + 2)/6
Let f(q) be the second derivative of q**6/135 - 4*q**5/15 + 19*q**4/27 + 520*q**3/9 - 175*q**2 - 7*q - 81. Find w, given that f(w) = 0.
-7, 1, 15
Suppose -2*w - 4*f = 54, -2*f = -3*w + 7*w + 108. Let u be (32/(-30))/(w/135). Suppose 80/3*i**2 - 100/3*i**3 - u*i + 0 = 0. Calculate i.
0, 2/5
Let z = -1349836 + 5399399/4. Factor z*u - 5/4*u**2 - 75/2.
-5*(u - 6)*(u - 5)/4
Let v be 2*7 - ((-20)/(-5) + -8). Suppose 10*s - v = 22. Determine m so that 24*m**2 + 8 - 25*m + 16*m**3 + 2*m**4 - 20*m**s + 12*m**5 - 3*m - 14*m**4 = 0.
-1, 2/3, 1
Let o be 2/(-16) + (-1967945)/(-1416). Let n = 1390 - o. Factor 0*a**3 - 8/3*a + 1 - n*a**4 + 2*a**2.
-(a - 1)**3*(a + 3)/3
Solve 92/11*y**2 - 2/11*y**4 + 0 + 0*y - 90/11*y**3 = 0 for y.
-46, 0, 1
Let w be (640/(-21))/((-3100)/27125). Let 688/3*x**2 - 480*x - 16/3*x**3 + w - 2/3*x**5 - 10*x**4 = 0. Calculate x.
-10, 1, 2
Solve -122*x**2 - 405*x**4 + 403*x**4 - 124*x**3 - 3 + 3 = 0 for x.
-61, -1, 0
What is p in 4/7*p**2 + 2/7*p**5 - 50/7*p + 24/7 - 4*p**4 + 48/7*p**3 = 0?
-1, 1, 12
Suppose 618 = -2*h + 658, -3*h + 52 = -4*n. Factor 47/7*r + 1/7*r**n + 46/7.
(r + 1)*(r + 46)/7
Let j(u) be the first derivative of -u**6/180 + u**4/12 + 21*u**3 + 147. Let r(d) be the third derivative of j(d). Factor r(b).
-2*(b - 1)*(b + 1)
Determine u, given that 537/8*u - 3/8*u**2 + 543/4 = 0.
-2, 181
Suppose 253*o - 246*o = 14. Let r(c) be the first derivative of -8 + 8/33*c**3 - 6/11*c - c**o. Solve r(k) = 0 for k.
-1/4, 3
Let s(c) = -6*c**3 - 161*c**2 - 165*c - 10. Let o(m) = -4*m**3 - 160*m**2 - 164*m - 8. Let b(q) = 5*o(q) - 4*s(q). Factor b(z).
4*z*(z - 40)*(z + 1)
Let c(t) be the third derivative of 5*t**7/42 + 61*t**6/24 - 64*t**5/15 + 13*t**4/6 + 296*t**2. Suppose c(a) = 0. Calculate a.
-13, 0, 2/5
Factor -66*x**3 + 157*x**2 - 353*x**2 - 5*x**4 + 357*x**3 - 131*x**3 - 2890*x - 909*x**2.
-5*x*(x - 17)**2*(x + 2)
Find t, given that -3/4 + 105/8*t**2 + 207/8*t = 0.
-2, 1/35
Suppose 5*d - 2*b - 2 = 0, -5*b = 31*d - 32*d - 18. Let k be d/(-14)*2800/(-160). Suppose -k*y + 3 - 1/2*y**2 = 0. Calculate y.
-6, 1
Let o(m) = 2*m**3 + 224*m**2 + 16*m + 27351. Let n be o(-113). Factor 0 + 148/3*x**3 - 152/3*x**2 - 1/3*x**n - 34/3*x**4 + 0*x.
-x**2*(x - 2)**2*(x + 38)/3
Let s(i) be the third derivative of -i + 0*i**3 - 19*i**2 - 1/10*i**6 + 0 + 0*i**5 + 8/105*i**7 + 0*i**4 - 1/84*i**8. Determine t, given that s(t) = 0.
0, 1, 3
Let k(z) be the second derivative of 2*z**6/15 + 136*z**5/5 + 264*z**4 + 3136*z**3/3 + 2080*z**2 + 6786*z. Factor k(i).
4*(i + 2)**3*(i + 130)
Let a(v) be the first derivative of -3/4*v - 9/8*v**2 - 66 - 1/2*v**3. What is y in a(y) = 0?
-1, -1/2
Let w(v) be the third derivative of v**8/48 - 104*v**7/105 + 101*v**6/8 + 15*v**5/2 + 1174*v**2. Let w(o) = 0. Calculate o.
-2/7, 0, 15
Let n be (-45)/(-2)*(-48)/(-40). Suppose 2 = -2*z - 2*c - 2, 3*c = 4*z - n. Factor -12*j**3 - 16*j**z - 219*j + 235*j + 12*j**4.
4*j*(j - 2)*(j - 1)*(3*j + 2)
Let s = 153 + -58. Let d be 38/s - 16/(-10). Factor -d*v**2 + 2*v**2 - 16*v**4 + 12*v**5 - 8*v**2 - 16*v**5 - 20*v**3.
-4*v**2*(v + 1)**2*(v + 2)
Factor 0 - 2/15*u**5 - 8/3*u**4 - 24*u**2 - 54/5*u - 236/15*u**3.
-2*u*(u + 1)**2*(u + 9)**2/15
Let o(w) be the first derivative of 24 + 17/12*w**2 - 5/3*w - 4/9*w**3 + 1/24*w**4. Find f, given that o(f) = 0.
1, 2, 5
Factor 815*p + 4*p**3 - 79169 - 472*p**2 - 30663 - 86881 + 16713 + 16385*p.
4*(p - 50)**2*(p - 18)
Let s(k) = 2*k**2 + 36*k + 36. Let g be s(-1). Let h(l) be the second derivative of 3/11*l**3 + 19*l - 1/22*l**4 - 6/11*l**g + 0. Factor h(d).
-6*(d - 2)*(d - 1)/11
Suppose -a - 7*a = 120. Let o be (24/36)/((-2)/a). Solve 7*c**3 - 10*c - 6*c**4 + c**4 + 3*c**3 + o = 0 for c.
-1, 1
Let b be (-3804)/(-10)*-1 + (-18)/(-45). Let g = -377 - b. Let -34/3*t**g + 2*t**4 + 10/3*t**5 + 8*t - 8/3 + 2/3*t**2 = 0. What is t?
-2, -1, 2/5, 1
Find f, given that 120*f + 606/5 - 6/5*f**2 = 0.
-1, 101
Factor 4/3*s**3 - 47*s**2 - 58 + 731/3*s.
(s - 29)*(s - 6)*(4*s - 1)/3
Let o be 716/1611 + 52/45. Factor 2/5*f**3 - 2/5*f - o + 8/5*f**2.
2*(f - 1)*(f + 1)*(f + 4)/5
Let y(n) be the second derivative of n**4/12 - 7*n**3/2 - 65*n**2 - 1146*n. Determine f, given that y(f) = 0.
-5, 26
Let r be -9 + 15 - (-36)/(-12)*2. Factor r + 68/7*h + 4/7*h**2.
4*h*(h + 17)/7
Determine o, given that -5832 + 272*o**3 - 45*o**2 + 272*o**3 - 71*o**2 + 278*o**3 - 820*o**3 + 1890*o = 0.
4, 27
Let m = 15748 + -15737. Let q(o) be the first derivative of m - 4*o**2 + 12*o - 20/3*o**3. Factor q(w).
-4*(w + 1)*(5*w - 3)
Let r = -1135235/4 + 283809. Solve 4*v + 0*v**3 + 3*v**2 - r*v**4 + 0 = 0.
-2, 0, 4
Let x = 116 - 184. Let p = x + 81. What is a in -12*a - 3*a**3 - 36*a**2 - 20*a - 4 + 8*a - p*a**3 = 0?
-1, -1/4
Suppose 0 = 5*t + 3*b + 105, 3*t - 5*b + 24 = -39. Let g be (-66)/(-21) + (-10 - 207/t). Determine p, given that -6/7 + 9/7*p - 3/7*p**g + 0*p**2 = 0.
-2, 1
Suppose -201 - 63*x - 15*x**2 + 14*x**2 - 35 = 0. What is x?
-59, -4
Let m be (-24)/(-56)*2 - (108/28 - 5). Let a(o) be the first derivative of -8/3*o + 4/9*o**3 - 12 - 2/3*o**m. Factor a(x).
4*(x - 2)*(x + 1)/3
Let l(o) = 2*o**2 - o. Let a(p) = -5*p - 19. Let j be a(-4). Let n(i) = -5*i**2 + 3. Let s(f) = j*n(f) + 2*l(f). Factor s(x).
-(x - 1)*(x + 3)
Let c(z) = 3*z - 34. Let s be c(12). Determine d so that -396*d**4 + d + 0*d**2 + d**s + 0*d**2 - d**3 + 395*d**4 = 0.
-1, 0, 1
Let u(c) = -106*c**2 + 2331*c + 22. Let n be u(22). Factor n*r + 0 + 24*r**2 + 3/2*r**3.
3*r**2*(r + 16)/2
Let h be (16 - ((-2907)/(-95) - 9))*4/(-14). Factor -2/5*v**3 + 0*v - 6/5*v**2 + h.
-2*(v - 1)*(v + 2)**2/5
Let z(m) be the first derivative of 5*m**6/6 + 34*m**5 + 765*m**4/2 + 3080*m**3/3 - 8575*m**2/2 - 10290*m - 165. Find w such that z(w) = 0.
-21, -7, -1, 2
Let j(o) = -13*o**2 + 127*o - 126. Let f(a) = 57*a**2 - 509*a + 504. Let y(n) = -6*f(n) - 26*j(n). Factor y(u).
-4*(u - 1)*(u + 63)
Factor 1065*l - 73 + 2023*l - 3011 - 4*l**2.
-4*(l - 771)*(l - 1)
Let m(w) be the third derivative of w**7/315 + 353*w**6/180 + 4981*w**5/15 - 6240*w**4 + 21600*w**3 - 1923*w**2 - w - 1. Solve m(z) = 0 for z.
-180, 1, 6
Let p = 261 + -142. Suppose p*i = 124*i - 10. Factor -31*x - 12*x - 25*x**2 + 21*x**i + 11.
-(x + 11)*(4*x - 1)
Let a(b) be the first derivative of -b**5/450 + b**4/60 + 4*b**3/45 + 19*b**2 + 105. Let g(m) be the second derivative of a(m). Factor g(r).
-2*(r - 4