*t - 2)
Find h, given that -7675720*h + 2705*h**3 + 6748758*h - 488700*h**2 - 48951211 + 21440623*h + 9132339*h - 5*h**4 + 19791211 = 0.
1, 180
Let d = 673 + -673. Let c(h) be the first derivative of d*h + 5 - 1/4*h**3 - 1/16*h**4 - 1/4*h**2. What is a in c(a) = 0?
-2, -1, 0
Let k(j) be the second derivative of j**4/16 - 31*j**3/2 + 369*j**2/8 - 6*j - 348. Factor k(q).
3*(q - 123)*(q - 1)/4
Factor -45/4*y + 13/4*y**2 - 25/2 + 9/4*y**3 + 1/4*y**4.
(y - 2)*(y + 1)*(y + 5)**2/4
Factor 2*t + 58*t + 7*t + 69*t - 3469*t**2 + 3545*t**2 - 32.
4*(t + 2)*(19*t - 4)
Let x(s) be the second derivative of s**4/3 - 44*s**3 - 560*s**2 + 2246*s. Find n, given that x(n) = 0.
-4, 70
Let o(t) = -308*t**3 + 11220*t**2 - 170716*t - 34564. Let w(p) = -68*p**3 + 2493*p**2 - 37937*p - 7681. Let l(j) = -7*o(j) + 32*w(j). Factor l(v).
-4*(v - 31)**2*(5*v + 1)
Determine m so that 2652/5*m - 36/5*m**4 + 101*m**3 - 72/5 - 2174/5*m**2 = 0.
1/36, 2, 6
Let v = 398/29 - 10300/87. Let m = -103 - v. Solve 5/3*u - m*u**3 + 0*u**2 - 5/6 + 5/6*u**4 = 0 for u.
-1, 1
Let k(j) be the first derivative of -4/3*j**2 - 1/9*j**3 + 20/3*j - 29. What is m in k(m) = 0?
-10, 2
Let m(x) = x**4 + 56*x**3 - 48*x**2 - 51*x + 52. Let r(c) = -c**4 - 55*c**3 + 49*c**2 + 51*c - 52. Let y(b) = -4*m(b) - 5*r(b). Factor y(v).
(v - 1)**2*(v + 1)*(v + 52)
Let o be 7 - (3 + 10/(-4))/((-2)/(-16)). Suppose 0 + 8/3*r**o - 2/3*r + 4/3*r**2 - 4/3*r**4 - 2*r**5 = 0. Calculate r.
-1, 0, 1/3, 1
Let l(f) = -6*f**2 + 96*f - 50. Let p(v) = -3*v**2 + 48*v - 21. Let i(r) = 3*l(r) - 5*p(r). Let i(y) = 0. Calculate y.
1, 15
Let i(t) = -t + 8. Let z be i(8). Let b = -190533 + 190535. Factor z*v + 5/4*v**b + 0.
5*v**2/4
Let h(g) = -37*g**2 + 75*g + 383. Let d(t) = 34*t**2 - 74*t - 384. Let n(o) = 13*d(o) + 12*h(o). Determine p, given that n(p) = 0.
-22, -9
Let t(x) be the first derivative of 1/15*x**5 + 4/3*x**4 + 0*x + 32/3*x**3 - 5 - 11*x**2. Let w(f) be the second derivative of t(f). Factor w(i).
4*(i + 4)**2
Let w be 0/(2 + -2 - 1). Suppose -2*c - 3*c + 230 = w. Factor c + 5*i**2 - 43 + 16*i + 3*i**4 + 16*i**3 + 16*i**2 + 5*i**2.
(i + 1)**2*(i + 3)*(3*i + 1)
Suppose 52*x + 5*q = 50*x + 10, q - 2 = 3*x. Let b(d) be the third derivative of 0 + 11*d**2 + x*d**3 - 1/210*d**5 - 1/42*d**4 + 0*d + 1/420*d**6. Factor b(n).
2*n*(n - 2)*(n + 1)/7
Let b(t) = -t**3 - 93*t**2 - 365*t + 450. Let y(v) = -3*v**3 - 371*v**2 - 1463*v + 1798. Let h(x) = -13*b(x) + 3*y(x). Find o such that h(o) = 0.
-19, -6, 1
Let x(y) be the third derivative of -5/2*y**4 + 0*y + 1/84*y**8 - 121*y**2 - 1/3*y**6 + 8/3*y**3 + 0 + 4/3*y**5 + 0*y**7. Factor x(v).
4*(v - 1)**4*(v + 4)
Let a(x) be the third derivative of -x**8/144 - 13*x**7/189 - 25*x**6/216 + 13*x**5/27 + 4*x**4/9 - 3606*x**2. What is y in a(y) = 0?
-4, -3, -1/3, 0, 8/7
Let m(f) be the second derivative of -f**4/4 + 251*f**3/2 - 375*f**2 + 1312*f. Factor m(b).
-3*(b - 250)*(b - 1)
Let o(t) be the third derivative of 0*t + 0*t**3 - 1/68*t**4 - 1/102*t**5 - 1/1020*t**6 + 1/1785*t**7 - 2*t**2 + 6. Let o(f) = 0. Calculate f.
-1, 0, 3
Suppose -1138*m**2 + 1150*m**2 + 412*m + 331 + 421 + 724*m - 376*m**3 - 4*m**4 = 0. What is m?
-94, -1, 2
Let t(j) be the second derivative of 1/15*j**4 + 0 + 67/10*j**3 + 5*j**2 - 64*j. Suppose t(c) = 0. What is c?
-50, -1/4
Suppose 6*i - 120 + 36 = 0. Suppose i*m - 10 = 12*m. Factor -2*b**m + 0*b**3 - 8*b**3 - 8*b**4 + 0*b**4 + 0*b**3.
-2*b**3*(b + 2)**2
Factor 950 + 565/3*f - 1/3*f**2.
-(f - 570)*(f + 5)/3
Let g = 532 - 920. Let m = -1154/3 - g. Suppose -m - v**2 - 17/3*v = 0. What is v?
-5, -2/3
Let q(w) be the first derivative of -12*w**5/5 + 2*w**4 + 112*w**3 + 176*w**2 - 384*w - 614. Determine i, given that q(i) = 0.
-4, -2, 2/3, 6
Let o = -113 + 119. Suppose -3*h**3 + o*h**3 - 2*h**2 - 88*h**5 + 87*h**5 = 0. Calculate h.
-2, 0, 1
Let f be 18/(-24)*(-1168)/24 - (23 + -9). Find z such that 135/4*z - 15/2*z**4 + 25/2 - 25/4*z**3 + f*z**2 = 0.
-1, -5/6, 2
Let a = -16 - 201. Let l = 221 + a. Factor 2/3*k**2 + 1/3*k**5 - k**3 + 0 + 0*k**l + 0*k.
k**2*(k - 1)**2*(k + 2)/3
Let h(y) be the second derivative of -y**5/10 - 2*y**4 - 13*y**3 - 28*y**2 + 274*y. Factor h(i).
-2*(i + 1)*(i + 4)*(i + 7)
Let l = 2510/337 - 4683/674. Factor 19/2*d - 6 - 4*d**2 + l*d**3.
(d - 4)*(d - 3)*(d - 1)/2
Let a(j) be the second derivative of -j**7/630 + 7*j**6/180 - j**5/5 + 13*j**4/12 + 32*j. Let k(s) be the third derivative of a(s). Solve k(m) = 0.
1, 6
Factor 3*y**4 + 84*y**3 + y**4 + 256*y + 559931*y**2 - 559595*y**2.
4*y*(y + 1)*(y + 4)*(y + 16)
Solve 2460*c - 570 - 1629 - 5*c**2 + 215*c - 471 = 0.
1, 534
Let o(g) be the third derivative of g**8/112 - g**7/14 + 7*g**6/40 + g**5/20 - g**4 + 2*g**3 + 412*g**2 + 3*g. Determine c so that o(c) = 0.
-1, 1, 2
Let u(a) be the second derivative of a**5/14 - 103*a**4/42 + 274*a**3/21 - 176*a**2/7 - 7791*a. Determine i so that u(i) = 0.
1, 2, 88/5
Let q = 10/22577 + 22517/135462. Factor -1/2*b + q*b**2 + 0.
b*(b - 3)/6
Let z(l) = -15*l**3 - 20*l**2 + 26*l + 3. Let r(p) = -2*p**3 + p**2 - 2*p + 1. Let j(b) = 3*r(b) - z(b). Let j(t) = 0. What is t?
-32/9, 0, 1
Let i = 969 - 966. Let w(o) be the second derivative of 0*o**2 + 6*o - 3/40*o**5 + 0 - 1/4*o**4 + 3/4*o**i. Factor w(s).
-3*s*(s - 1)*(s + 3)/2
Suppose -115/3*h + 70/3*h**4 - 40/3*h**2 - 10 - 5*h**5 + 130/3*h**3 = 0. Calculate h.
-1, -1/3, 1, 6
Suppose 12399 = 361*w + 317*w - 15399. Let i(x) be the first derivative of 0*x + w + x**2 - 1/3*x**3. What is h in i(h) = 0?
0, 2
Let f be ((-50)/(-500))/((-3)/(-6)). Let -2/5*t**2 - f*t**3 + 13/5*t - 2 = 0. What is t?
-5, 1, 2
Let c(h) be the second derivative of 22*h + 19/10*h**3 - 1/20*h**4 + 6*h**2 + 0. Factor c(j).
-3*(j - 20)*(j + 1)/5
Factor -5/4*p**2 - 23/2*p + 1/4*p**3 - 10.
(p - 10)*(p + 1)*(p + 4)/4
Let w(s) be the first derivative of s**5/10 + 383*s**4/16 - 289*s**3/6 + 193*s**2/8 + 801. Let w(n) = 0. Calculate n.
-193, 0, 1/2, 1
Let r(y) be the third derivative of 1/15*y**5 - 2*y**4 + 22/3*y**3 + 11*y**2 + 0 + 0*y. Factor r(g).
4*(g - 11)*(g - 1)
Let p(s) = -28*s**3 - 6*s**2 - s + 2. Let w be p(-2). Determine i so that w*i**3 - 35*i**2 - 219*i**3 + 20 + 5*i**4 + 10*i**2 + 15*i = 0.
-1, 1, 4
Let y be (-100)/(-36) - (1560/(-90) + 80/4). Determine r, given that 19/3*r - 14/9*r**2 - 8 + y*r**3 = 0.
3, 8
Suppose 0 = 6*k - 18*k + 36. Factor 32*i**3 - 3*i**4 - 4*i**k - 192*i**2 + 20*i**3.
-3*i**2*(i - 8)**2
Let y(h) = 18*h**3 + 266*h**2 + 308*h + 10. Let o(k) = 5*k**3 + 89*k**2 + 102*k + 3. Let a(w) = -10*o(w) + 3*y(w). Factor a(j).
4*j*(j - 24)*(j + 1)
Let j(s) = s**3 + 28*s**2 - 380*s. Let m be j(-38). Let n(t) be the first derivative of m*t + 8/5*t**5 + t**4 + 1 - 20/3*t**3 + 4*t**2. Solve n(z) = 0 for z.
-2, 0, 1/2, 1
Let k(s) be the second derivative of 1/21*s**7 + 1/3*s**4 + 20*s - 3/5*s**5 + 1/15*s**6 + 0 - 3*s**2 + 5/3*s**3. Suppose k(n) = 0. What is n?
-3, -1, 1
Let u = -322646 + 968096/3. Find x, given that 44/3 + 14/3*x**2 - u*x = 0.
2/7, 11
Let m = 429041 - 428977. Solve 0 - 40*p**2 - m*p - 25/4*p**3 = 0.
-16/5, 0
Let r be ((-72)/(-192))/(18/(-8)) - 280/(-96). Solve -r*x**2 + 31/4*x + 3/2 = 0 for x.
-2/11, 3
Let s(n) be the first derivative of n**4 + 167 - 104/3*n**3 + 184*n**2 - 352*n. Determine w so that s(w) = 0.
2, 22
Let r(p) be the second derivative of 0*p**2 + 6*p - 1/3*p**4 + 0*p**3 + 2/15*p**6 + 0*p**5 + 4. Factor r(b).
4*b**2*(b - 1)*(b + 1)
Let l(x) be the third derivative of -3/4*x**6 + 0*x + 17/70*x**7 - 11*x**2 + x**4 + 0*x**3 + 3/5*x**5 - 3/112*x**8 + 1. Let l(f) = 0. What is f?
-1/3, 0, 2
Let k = 113302 - 453191/4. Solve k*g + 4 + 1/4*g**2 = 0 for g.
-16, -1
Let m(n) be the first derivative of -n**4 + 220*n**3/3 - 1886*n**2 + 19044*n - 32. Find d, given that m(d) = 0.
9, 23
Let t(r) = -r**2 - 9*r - 18. Let b be t(-5). Suppose 11*l**2 + l**3 - 31*l**2 + 21*l**b - 2*l = 0. What is l?
-2, 0, 1
Let x = 16 - 6. Let k = x + -8. Solve -k + 6*h - 8*h + h**3 - h = 0.
-1, 2
Let r(p) be the second derivative of p**7/210 - 11*p**6/30 + 259*p**5/100 - 457*p**4/60 + 176*p**3/15 - 10*p**2 + 64*p. Factor r(l).
(l - 50)*(l - 2)*(l - 1)**3/5
Let 185018*g**5 + 28*g**4 - 3 + 3 - 184998*g**5 + 0 - 32*g**3 - 16*g**2 = 0. Calculate g.
-2, -2/5, 0, 1
Let m be -37 - (-33 + (-164)/41). Let 3*y**2 + 9/4*y**4 - 5*y**3 - 1/4*y**5 + 0 + m*y =