0.
284
Let s(q) be the third derivative of -q**5/120 - 13*q**4/48 + 4*q**3 + 5509*q**2 + q. Factor s(i).
-(i - 3)*(i + 16)/2
Let r be (-47)/(-60) + (-3)/4. Let j(p) be the third derivative of 0*p + r*p**6 + 0*p**5 + 6*p**2 + 0 + 4/3*p**3 - 1/2*p**4. Factor j(u).
4*(u - 1)**2*(u + 2)
Let r(i) be the third derivative of i**5/15 - 8*i**4 - 1298*i**3/3 + 157*i**2 - 7. Factor r(m).
4*(m - 59)*(m + 11)
Let l(f) be the third derivative of 7*f**6/220 + 3*f**5/5 - 117*f**4/44 + 4*f**3 - 3*f**2 - 10. Find h such that l(h) = 0.
-11, 4/7, 1
Let v(h) = h**2 - 728*h + 8597. Let b be v(12). What is q in 8/3*q + 16/3 - 1/3*q**4 - b*q**2 - 8/3*q**3 = 0?
-4, -1, 1
Let g be (-357)/119 + (0 + 6)*1. Let n(z) be the second derivative of 1/6*z**g + 12*z + 5/36*z**4 + 0 - 1/3*z**2. Factor n(w).
(w + 1)*(5*w - 2)/3
Suppose -16 + 92 - 59 = -169*b + 17. Determine n so that b*n**2 - 3/4*n**4 + 0*n**3 + 0*n + 0 - 3/4*n**5 = 0.
-1, 0
Let n(p) be the first derivative of 2*p**3/3 + 28*p**2 - 760*p + 559. Factor n(m).
2*(m - 10)*(m + 38)
Let x(h) be the third derivative of h**8/10080 - 17*h**7/2520 - h**6/20 - 4*h**5/3 + 52*h**2. Let d(k) be the third derivative of x(k). Let d(y) = 0. What is y?
-1, 18
Let v(h) = 9*h - 42. Let z be v(5). Let -4*a**z - 30*a - 28*a + 18*a**2 - 2*a**2 + 77*a - 31*a = 0. Calculate a.
0, 1, 3
Let j = 159 + -155. Let a(y) = 5*y**3 - 19*y + 7. Let t(v) = -3*v**3 + v**2 + 10*v - 4. Let p(o) = j*a(o) + 7*t(o). Factor p(x).
-x*(x - 6)*(x - 1)
Factor 0*s - 32 + 2/9*s**2.
2*(s - 12)*(s + 12)/9
What is g in 2/7*g**2 - 40/7*g - 6 = 0?
-1, 21
Let d = -68902 - -68904. What is q in -2/5*q**3 + 3/5*q**4 + 2/5*q**5 + 0*q**d + 0*q + 0 = 0?
-2, 0, 1/2
Factor -125*a - 49*a**3 + 58*a**3 - 40*a**2 - 135*a**2 - 39*a**3.
-5*a*(a + 5)*(6*a + 5)
What is b in -32/7*b**2 + 2/7*b**3 + 204/7 - 46/7*b = 0?
-3, 2, 17
Let n(c) = 6*c - 9*c + 13*c**3 + 0*c**3 + 16*c**2 - 4 + 2*c. Let y(w) = -14*w**3 - 16*w**2 + 2*w + 4. Let h(s) = -4*n(s) - 3*y(s). Factor h(o).
-2*(o + 1)**2*(5*o - 2)
Let u be ((-10)/(-150))/(32/9). Let j(k) be the second derivative of -1/16*k**4 + 1/16*k**3 + u*k**5 - 5*k + 0*k**2 + 0. Suppose j(p) = 0. What is p?
0, 1
Solve 599*x - 80 + 21*x**2 - 663*x + 15*x**2 + 16*x**3 - 4*x**4 = 0.
-2, -1, 2, 5
Suppose -2*c - 1 = -w, 2*c = 2*w + 6*c - 26. Let a be w/7 + 1 + -2. Determine l so that 1/4*l + a + 1/4*l**2 = 0.
-1, 0
Let t(k) be the second derivative of -k**5/5 + 10*k**4 - 38*k**3 + 56*k**2 + 241*k. Solve t(f) = 0.
1, 28
Let x(f) = -794*f + 3180. Let s be x(4). Let c(m) be the first derivative of -75*m**2 + 5*m**3 - 3 + 500*m - 1/8*m**s. Let c(t) = 0. Calculate t.
10
Let k(q) = 8*q**2 - 52*q + 100. Let o(r) = -30*r + 9*r**2 + 100 + 15*r - 40*r. Let y(f) = -5*k(f) + 4*o(f). Factor y(g).
-4*(g - 5)**2
Suppose 2/11*x**3 - 162/11*x**2 - 30*x - 166/11 = 0. Calculate x.
-1, 83
Let h(y) be the third derivative of y**6/3780 - y**5/105 + y**4/7 + 15*y**3/2 - 32*y**2 - 1. Let o(z) be the first derivative of h(z). Factor o(j).
2*(j - 6)**2/21
Let z(f) = 4*f - 11. Suppose -h = -4*h + 12. Let b be z(h). Suppose 15*r**2 - 6*r**4 - 32*r - 12 + b*r - 15*r**4 + 27*r**3 + 18 = 0. What is r?
-1, 2/7, 1
Let k(c) be the second derivative of c**4/12 - 24*c**3 - 54*c + 19. Determine n so that k(n) = 0.
0, 144
Let m = 67 - 47. Factor 1616*p - 216 + 3*p**3 + 10*p**2 + m*p**2 - 1580*p.
3*(p - 2)*(p + 6)**2
Let w(s) be the second derivative of s**6/195 + s**5/13 + 4*s**4/13 + 22*s**3/39 + 7*s**2/13 - 15*s + 1. Factor w(j).
2*(j + 1)**3*(j + 7)/13
Let t = -14669/3 + 4890. Let w(h) be the second derivative of t*h**3 + 1/10*h**5 + 0 + 14*h + 1/3*h**4 + 0*h**2. Factor w(b).
2*b*(b + 1)**2
Let m(z) be the second derivative of z**4/6 + 148*z**3 + 49284*z**2 - 473*z. What is o in m(o) = 0?
-222
Let o(t) = t**4 - t**3 + 2*t**2 + t. Let g(v) = 4*v**4 + 19*v**3 - 338*v**2 - 99*v. Let d(c) = g(c) + 3*o(c). Determine k, given that d(k) = 0.
-8, -2/7, 0, 6
Suppose 5*p + 2176 = 2191. Let y(v) be the third derivative of 0*v**3 - 1/135*v**5 + p*v**2 + 0*v + 1/540*v**6 + 0 + 1/108*v**4. Let y(d) = 0. What is d?
0, 1
Let s be 7 + 279/(-2835)*-5. Let u = s - 16/9. Factor -u*c**4 + 18/7*c**5 + 0 + 26/7*c**3 + 0*c - 4/7*c**2.
2*c**2*(c - 1)**2*(9*c - 2)/7
Let a = 1601616/7 - 228792. Factor 0*d**2 - 96/7 + a*d - 6/7*d**3.
-6*(d - 2)**2*(d + 4)/7
Let l(c) be the second derivative of c**7/294 - 25*c**6/42 + 369*c**5/10 - 819*c**4 - 1764*c**3 - 5522*c. Factor l(q).
q*(q - 42)**3*(q + 1)/7
Factor -7374/7*c + 3/7*c**2 + 4531323/7.
3*(c - 1229)**2/7
Let x(p) be the second derivative of p**5/100 + 52*p**4/15 - 7841*p. Suppose x(u) = 0. Calculate u.
-208, 0
Factor -828/5 + 2/15*c**2 - 38/15*c.
2*(c - 46)*(c + 27)/15
Factor 8*b + 56/3 - 2/3*b**2.
-2*(b - 14)*(b + 2)/3
Let o(g) = g**3 - 3*g + 2. Let w be o(2). Let m = -694907 - -694907. Factor -1/4*k**2 + m*k + 0 - 3/2*k**3 - k**5 - 9/4*k**w.
-k**2*(k + 1)**2*(4*k + 1)/4
Suppose -75*r + 76*r = -5*l + 592, -112 = -l + 3*r. Let c = l + -103. Factor 27/5*t**4 - c*t**3 - 9/5*t + 63/5*t**2 - 6/5.
3*(t - 1)**3*(9*t + 2)/5
Let j be 148/(-259)*(-18)/(-9)*(-28)/24. Let 2/3*d**2 - j*d - 2 = 0. What is d?
-1, 3
Factor 91981*y - 37431*y**2 + 133*y**3 + 4*y**4 + 174327*y**2 + 43443*y + 1343*y**3.
4*y*(y + 1)*(y + 184)**2
Suppose 56*j - 304 = 54*j. Solve 2941 + j*l**3 + 3658 - 1686 + 13872*l - 2550*l**2 - 3*l**4 = 0.
-1/3, 17
Let d(t) be the third derivative of t**6/1080 - t**5/360 + 29*t**3/6 - 11*t**2 - 2. Let c(a) be the first derivative of d(a). What is j in c(j) = 0?
0, 1
Let m be 1296/(-416) - -6 - (-9)/2. What is y in -m*y - 2/13*y**3 - 72/13 - 2*y**2 = 0?
-6, -1
Let l(a) = -1 - a**3 + 3*a**3 - 24*a + 18*a**2 - 37 - 6. Let k(c) = -4*c**3 - 36*c**2 + 48*c + 90. Let z(u) = -2*k(u) - 5*l(u). What is w in z(w) = 0?
-10, -1, 2
Let g(p) = -11*p**3 - 828*p**2 + 2465*p - 1674. Let n(o) = -45*o**3 - 3315*o**2 + 9860*o - 6700. Let z(c) = 25*g(c) - 6*n(c). Solve z(q) = 0 for q.
-165, 1, 2
Let q(r) be the first derivative of -1/70*r**5 + 5/7*r**2 + 14 + 3/7*r**3 + 8*r + 1/14*r**4. Let x(j) be the first derivative of q(j). What is l in x(l) = 0?
-1, 5
Let c(i) be the second derivative of 0*i**6 - 2/9*i**3 + 0*i**4 + 1/12*i**5 + 0*i**2 + 0 - 65*i - 1/126*i**7. Let c(j) = 0. What is j?
-2, -1, 0, 1, 2
Let s = -177174 - -177176. Factor 3/4*d**s - 9 + 3/4*d.
3*(d - 3)*(d + 4)/4
Let h(r) be the first derivative of 1/8*r**3 + 0*r**2 - 4 + 0*r**4 - 3/80*r**5 + 8*r. Let n(l) be the first derivative of h(l). Let n(p) = 0. Calculate p.
-1, 0, 1
Find s, given that 144*s + 3/8*s**5 - 9/4*s**4 - 111/8*s**3 + 267/4*s**2 - 420 = 0.
-4, 2, 5, 7
Let m(n) be the third derivative of n**8/504 + 37*n**7/315 + 35*n**6/36 - 685*n**5/18 - 44*n**4/9 + 3388*n**3/9 + 40*n**2 - 62*n. What is d in m(d) = 0?
-22, -1, 1, 7
Suppose 2*w = l, -889 = 4*w + 8*l - 929. Factor -63*m - 1323/2 - 3/2*m**w.
-3*(m + 21)**2/2
Let j be 30/1500*-5 + 0 + 3/5. Factor -5*z - j*z**2 - 8.
-(z + 2)*(z + 8)/2
Let d be -17*258/731 - (-43)/7. Let -7*x + 0 - d*x**3 - 2*x**2 = 0. What is x?
-7, 0
Let j(s) be the third derivative of s**7/420 + s**6/90 - 28*s**3/3 - 17*s**2. Let h(g) be the first derivative of j(g). Factor h(r).
2*r**2*(r + 2)
Factor -11 - 9*k**2 - 103/2*k.
-(2*k + 11)*(9*k + 2)/2
Let o be (-45)/(-3816)*-4 + 2/3. Let d = o + 5/106. Factor 0*n - 4/9*n**2 + 0*n**4 - 2/9*n**5 + d*n**3 + 0.
-2*n**2*(n - 1)**2*(n + 2)/9
Let x(t) = -24*t**4 - 54*t**3 - 56*t**2 - 28*t - 14. Let s(o) = -25*o**4 - 53*o**3 - 53*o**2 - 26*o - 15. Let w(l) = -6*s(l) + 7*x(l). Factor w(j).
-2*(j + 1)**2*(3*j + 2)**2
Let q(f) = -f**3 + 12*f**2 - 19*f - 16. Let s be q(10). Let x be ((3 + -2)*-1)/(33/s). Factor 10/11 + 8/11*h - x*h**2.
-2*(h - 5)*(h + 1)/11
Let g(n) = 15*n**2 + 89*n - 248. Let o be g(-8). Factor -3/2*d**2 + o + 1/6*d**3 + 10/3*d.
d*(d - 5)*(d - 4)/6
Let p(w) be the second derivative of -35/27*w**3 - 21*w - 4/135*w**6 + 16/27*w**4 - 1/15*w**5 + 1/189*w**7 + 4/3*w**2 + 0. Factor p(y).
2*(y - 4)*(y - 1)**3*(y + 3)/9
Let i(a) = 2564*a - 243578. Let n be i(95). What is c in 343/4 - 49/4*c - 7/4*c**n + 1/4*c**3 = 0?
-7, 7
Let k(p) be the second derivative of 60/7*p**2 + 22/21*p**3 - 206*p + 1/21*p**4 + 1. What is d in k(d) = 0?
-6, -5
Let v(w) = -26*w**4 - 652*w**3 - 4*w**2 + 640*w + 12. Let t(u) = -5*u**4 - 2*u**3 + 2. Let o(d) = -6*t(d) + v(d).