t r(v) = -v**3 - 7*v**2 - v - 1. Let z be r(-7). Suppose 0 = 2*y - 4*f + 8 + 6, 4*y - 2*f = 2. Factor -y*i + 9 - 1 + i**2 - z.
(i - 2)*(i - 1)
Let k(n) be the second derivative of 6 - 3*n + 1/50*n**5 + 8/5*n**2 - 1/15*n**3 - 4/15*n**4. Factor k(o).
2*(o - 8)*(o - 1)*(o + 1)/5
Let c be (-1089 + 1108)/(76/8). Solve -15/8*k**3 + 0 + 3/8*k**4 - 9/8*k + 21/8*k**c = 0.
0, 1, 3
Let h(i) be the second derivative of i**5/5 - 229*i**4/3 + 2*i - 61. Find p, given that h(p) = 0.
0, 229
Let b(y) be the first derivative of y**4/2 + 8*y**3 - 61*y**2 + 96*y - 2981. Let b(n) = 0. What is n?
-16, 1, 3
Let g(f) be the first derivative of 4*f**3/3 - 480*f**2 - 9653. Factor g(u).
4*u*(u - 240)
Let w(m) be the second derivative of -3*m**4/8 + 8*m**3/3 + 33*m**2 + 5349*m. Suppose w(f) = 0. Calculate f.
-22/9, 6
Suppose 1/6*y**4 + 4/3*y - 1/6*y**2 + 0 - 4/3*y**3 = 0. Calculate y.
-1, 0, 1, 8
Let c(a) be the third derivative of a**5/300 + 241*a**4/30 + 116162*a**3/15 - 290*a**2. Let c(p) = 0. What is p?
-482
Let l be (9 + -32 + 23)/20. Let 72/7*p**2 + 0*p + 4/7*p**3 + l = 0. What is p?
-18, 0
Let g be 3/(243/(-54)*(-5)/7). Let t(j) be the first derivative of 33/5*j**2 + 16 - g*j**3 + 4*j. Suppose t(q) = 0. Calculate q.
-2/7, 5
Let h(m) be the first derivative of -1/4*m**4 + 0*m + 1/15*m**5 + 23 - 4/9*m**3 + 0*m**2. Factor h(a).
a**2*(a - 4)*(a + 1)/3
Let q be (-11)/(2 - 1) - ((-24050)/(-30))/(-65). Let -q*w**4 - 2/3*w**2 + 1/3*w**5 + 0*w + 0 + 5/3*w**3 = 0. What is w?
0, 1, 2
Let q(d) be the first derivative of -1/3*d**3 - 42*d - 21 + 43/2*d**2. Factor q(w).
-(w - 42)*(w - 1)
Let j(n) be the first derivative of 9/28*n**4 + 1/5*n**5 - 2/7*n**2 + 0*n - 37 - 4/7*n**3. Factor j(x).
x*(x - 1)*(x + 2)*(7*x + 2)/7
Factor -2/11*s**3 - 2513282/11*s + 0 - 4484/11*s**2.
-2*s*(s + 1121)**2/11
Let x = -641/4 - -161. Let z = 1250693/4 - 312673. Factor -x*q - z*q**3 + q**2 + 0.
-q*(q - 3)*(q - 1)/4
Suppose -26*m + 70 = -242. Let m*d**3 + 1142*d - 1148*d + 3*d**2 - 3*d**4 - 6*d**4 = 0. Calculate d.
-2/3, 0, 1
Let g(u) be the first derivative of -u**4/24 - 25*u**3/18 + 13*u**2/6 + 349. Factor g(c).
-c*(c - 1)*(c + 26)/6
Let u = -4526 - -4565. Let t(c) be the second derivative of -1/8*c**4 + 0 + 0*c**2 + 3/8*c**3 - u*c. Find o such that t(o) = 0.
0, 3/2
Let 3/2*a**2 + 759/2*a + 0 = 0. Calculate a.
-253, 0
Suppose -5 = -2*q - 1. Let g(t) = -7*t - 70. Let x be g(-11). Suppose -4 - 3*z + 1 + x - 3*z**q + 2 = 0. What is z?
-2, 1
Let o(g) be the second derivative of 0 - 115*g + 17/105*g**6 + 8/7*g**2 - 4/147*g**7 - 43/42*g**4 - 22/21*g**3 + 4/35*g**5. Solve o(c) = 0 for c.
-1, 1/4, 2, 4
Let h(o) be the first derivative of 5 + 0*o + 13/20*o**5 - 9/40*o**6 - 9/2*o**2 - 5/9*o**4 + 2/9*o**3. Let a(x) be the second derivative of h(x). Factor a(p).
-(p - 1)*(9*p - 2)**2/3
Let h = 2063629/9 - 229285. Factor -64/9 - 20/9*n**2 - 2/9*n**3 - h*n.
-2*(n + 2)*(n + 4)**2/9
Let m(i) = -i**3 + 11*i**2 - 21*i + 118. Let o be m(10). Suppose 34*k - 37*k - 5*t - 10 = 0, -3*k = 4*t + o. Solve 2/5*f**3 + k - 4/5*f + 2/5*f**2 = 0.
-2, 0, 1
Let s = 52 - 382. Let b = s - -673. Factor 2 + 9*t**4 - 33*t**2 + 3*t**3 + b*t**5 - 14 + 36*t - 346*t**5.
-3*(t - 2)*(t - 1)**3*(t + 2)
Let d(a) = 2*a**2 + 12*a + 20. Let g(z) = -4*z**2 - 24*z - 41. Let x(y) = 9*d(y) + 4*g(y). Factor x(t).
2*(t + 2)*(t + 4)
Let l(z) be the first derivative of -7*z**2 + 22 + 2/3*z**3 + 12*z. Find o, given that l(o) = 0.
1, 6
Let q(j) = -12*j**2 - 1. Let f(c) = -1940598*c**3 - 940632*c**2 - 152064*c - 8170. Let h(t) = 2*f(t) + 44*q(t). Factor h(r).
-4*(99*r + 16)**3
Suppose 161*x = 165*x + 32, 0 = u - x - 10. Suppose 5 - 3/2*d**5 + 0*d**3 + 3/2*d + 8*d**4 - 13*d**u = 0. Calculate d.
-1, -2/3, 1, 5
Let l(v) = -13*v**3 + 2*v**2 - 5*v - 6. Let b be l(-3). Let -66*u + 497*u + b + 550*u**2 + 184*u - 268 + 45*u**3 = 0. Calculate u.
-11, -1, -2/9
Let t(j) = 8*j**4 - 5*j**3 + 27*j - 8. Let h = 80 - 86. Let p(i) = -2*i**4 + i**3 - 7*i + 2. Let y(g) = h*t(g) - 22*p(g). Factor y(n).
-4*(n - 1)**3*(n + 1)
Let -1640/7*q**3 + 32/7*q**4 - 28*q + 2004/7*q**2 - 200/7 = 0. Calculate q.
-1/4, 1/2, 1, 50
Let w be -10 + 15 + (-55)/12. Let o(x) be the third derivative of 27*x**2 - w*x**4 + 0 + 0*x**3 + 0*x + 1/12*x**5. Factor o(c).
5*c*(c - 2)
Let l = -12137 - -12137. Let w(u) be the second derivative of 25*u + 0*u**3 + 0 - 3/100*u**5 + l*u**2 - 1/4*u**4. Let w(x) = 0. What is x?
-5, 0
Factor 2*r + 0 - 1/7*r**3 + 5/7*r**2.
-r*(r - 7)*(r + 2)/7
Let r(f) be the third derivative of -2*f**7/105 + 9*f**6/2 - 133*f**5/5 + 397*f**4/6 - 88*f**3 - 1848*f**2 + 1. Factor r(v).
-4*(v - 132)*(v - 1)**3
Let i(p) be the second derivative of p**7/28 - p**6/5 - 27*p**5/40 + 8*p**4 - 25*p**3 + 36*p**2 + 8*p + 62. Let i(x) = 0. What is x?
-4, 1, 2, 3
Let y(b) be the third derivative of b**9/37800 - b**8/5600 + b**7/3150 + b**4/24 + 17*b**3/2 - 37*b**2. Let r(h) be the second derivative of y(h). Factor r(o).
2*o**2*(o - 2)*(o - 1)/5
Let a = 661892 + -661888. Find t such that 8*t**a - 13*t - 127/3*t**3 + 16/3*t**5 + 4/3 + 122/3*t**2 = 0.
-4, 1/4, 1
Let d(s) = -38*s**2 - 37*s - 89. Let w be d(-7). Let n = 1696 + w. Let 0 + 1/7*q**n + 0*q + 0*q**3 - 1/7*q**2 = 0. What is q?
-1, 0, 1
Let m be ((-17208)/(-630) + -28)/(9/(-300))*10. Suppose -m - 4/7*b**2 + 160/7*b = 0. Calculate b.
20
Let c(s) be the first derivative of -3*s**4/4 - 37*s**3 - 1113*s**2/2 - 3381*s + 103. Factor c(r).
-3*(r + 7)**2*(r + 23)
Let c(v) be the second derivative of -v**3 - 11*v**2 - 17*v. Let n be c(-4). What is d in 2 - n - 2*d**2 + 20*d - 16*d = 0?
0, 2
Let k(v) be the third derivative of -v**7/630 + 3*v**5/10 - 5*v**4/24 - v**3/3 + 2*v**2 - 26. Let c(g) be the second derivative of k(g). Factor c(p).
-4*(p - 3)*(p + 3)
Suppose -39/7*x**3 - 48/7*x**2 + 0 - 9/7*x**4 - 12/7*x = 0. What is x?
-2, -1/3, 0
Let a(x) be the third derivative of x**5/15 - 271*x**4/3 - 362*x**3 + 6345*x**2. Factor a(w).
4*(w - 543)*(w + 1)
Let r(h) be the second derivative of h**5/40 + 3*h**4/8 + 23*h**3/12 + 15*h**2/4 - 5580*h. Factor r(v).
(v + 1)*(v + 3)*(v + 5)/2
Factor -13*q - 4406*q**4 - 15*q**2 - 67*q - 4409*q**4 + 8820*q**4 + 60 + 30*q**3.
5*(q - 1)**2*(q + 2)*(q + 6)
Let i(d) be the first derivative of 4*d**3/9 - 16*d**2 - 1540*d/3 + 2653. Suppose i(j) = 0. What is j?
-11, 35
Let g(b) be the third derivative of 0 + 24*b**3 - 5*b**4 + 161*b**2 + 11/20*b**5 + 0*b - 1/40*b**6. Find d, given that g(d) = 0.
3, 4
Let k(u) be the first derivative of -2*u**3/9 - 15*u**2 - 592*u/3 - 6254. Factor k(q).
-2*(q + 8)*(q + 37)/3
Factor 4135*p**2 - 4455*p**2 + 18*p**3 + 13*p**3 - 26*p**3 + 620*p.
5*p*(p - 62)*(p - 2)
Let o(a) be the third derivative of a**6/280 - 58*a**5/35 + 456*a**2 + 2. Find q, given that o(q) = 0.
0, 232
Let g be (50 - 12) + -10 - 32/(-4). Let h(f) be the second derivative of 0 + 1/462*f**7 + 1/66*f**3 + 0*f**2 - g*f + 0*f**4 - 1/110*f**5 + 0*f**6. Factor h(v).
v*(v - 1)**2*(v + 1)**2/11
Let a = -72 + 75. Suppose -a*z + 8 = -7*z. Let t(s) = -13*s**2 + 16*s + 59. Let c(h) = 6*h**2 - 8*h - 30. Let d(b) = z*t(b) - 5*c(b). Let d(i) = 0. Calculate i.
-2, 4
Let p be (-131)/(-1310)*(20 - (1 + 7)). Factor 6/5*n**3 - p*n**4 + 24/5 + 66/5*n + 54/5*n**2.
-6*(n - 4)*(n + 1)**3/5
Let t(n) = -18*n**4 + 100*n**3 - 110*n**2 + 4*n. Let v(p) = 32*p**4 - 197*p**3 + 219*p**2 - 6*p. Let u(l) = 5*t(l) + 2*v(l). Factor u(g).
-2*g*(g - 2)**2*(13*g - 1)
Let y(w) be the first derivative of -w**6/15 + 836*w**5/5 - 1094113*w**4/10 + 290928*w**3 - 1089936*w**2/5 - 12445. Determine q, given that y(q) = 0.
0, 1, 1044
Let b = 54199 + -54195. Factor 3645/2 + 1215*q + 65*q**3 - 540*q**2 - 5/2*q**b.
-5*(q - 9)**3*(q + 1)/2
Let t be (9*16/1008*21)/15. Determine f, given that 0 - t*f**3 + 13/5*f**2 + 0*f = 0.
0, 13
Let s(x) be the third derivative of -x**7/1540 - 3*x**6/220 - 29*x**3/3 + 14*x**2. Let j(f) be the first derivative of s(f). Factor j(k).
-6*k**2*(k + 9)/11
Let a(j) be the third derivative of j**5/30 - 179*j**4/36 + 118*j**3/9 - 319*j**2. Factor a(m).
2*(m - 59)*(3*m - 2)/3
Let n(p) be the second derivative of -p**5/5 - 59*p**4/3 - 218*p**3 - 954*p**2 - 2236*p. Let n(w) = 0. What is w?
-53, -3
Determine q, given that -952/13*q - 2/13*q**2 - 113288/13 = 0.
-238
Let i(w) = 3*w**2 - 45*w. Let u(s) = 9*s**2 - 130*s. Let k = -636 - -630. Let t(z) = k*u(z