 3
Let b = 1790 - 1788. Let x(k) be the first derivative of -1/16*k**4 + 0*k - 18 - 1/8*k**b - 1/6*k**3. Find p such that x(p) = 0.
-1, 0
Let c(h) be the third derivative of -h**8/168 - 59*h**7/105 - 29*h**6/30 + 55*h**2. Factor c(o).
-2*o**3*(o + 1)*(o + 58)
Let r be (98/(-10) - -10)/(4/40). Let i be r + -3 - (-112)/21 - 3. What is b in 0*b**2 + 0 + 12*b - i*b**3 = 0?
-3, 0, 3
Suppose 32 = 2*j - 4. Find v, given that -j*v**4 + 14*v**4 - 3*v**2 - 8*v**3 - v**2 = 0.
-1, 0
Let k be 24/180 - 1/(-160)*-18. Let f(q) be the second derivative of -25/2*q**2 - 32*q + 0 - 5/6*q**3 - k*q**4. Factor f(j).
-(j + 10)**2/4
Let u(y) = -11*y + 46. Let p be u(3). Find l such that -15*l**3 - 4*l**5 - 51*l**2 - p*l**2 - 17*l**3 + 28*l**4 = 0.
-1, 0, 4
Let v(l) be the first derivative of -19*l**4/16 - 2077*l**3/2 - 255348*l**2 + 53792*l + 4397. Factor v(w).
-(w + 328)**2*(19*w - 2)/4
Let r be (-98)/(-28) - (-1)/(-2). Factor -37*d**5 + r*d**3 - 13*d**3 - 19*d**4 + 4*d**4 + 32*d**5.
-5*d**3*(d + 1)*(d + 2)
Let n(r) = -4*r**2 + 68*r + 48. Let q(a) = -5*a**2 + 70*a + 43. Let c(x) = -4*n(x) + 3*q(x). Factor c(u).
(u - 63)*(u + 1)
Let v(l) be the third derivative of -l**7/70 - 3*l**6/40 + 13*l**5/20 + 15*l**4/8 - 8900*l**2. Find j, given that v(j) = 0.
-5, -1, 0, 3
Let z(s) = 3*s**2 + 24*s - 123. Let m(d) = -5*d**2 - 49*d + 244. Let y(r) = 4*m(r) + 7*z(r). Solve y(u) = 0 for u.
5, 23
Let q(h) be the second derivative of -29*h**4/8 + 12*h**3 + 15*h**2 + 5*h - 89. Determine c so that q(c) = 0.
-10/29, 2
Let p(y) be the second derivative of -y**6/45 - 5*y**5/6 - 21*y**4/2 - 515*y**3/9 - 350*y**2/3 + 1708*y. Suppose p(q) = 0. Calculate q.
-14, -5, -1
Let s = 159421/60 + -2657. Let x(n) be the second derivative of 0 - 11/36*n**4 + 35/18*n**3 + 10*n - 25/6*n**2 + s*n**5. What is j in x(j) = 0?
1, 5
Find h such that h**3 + 9*h + 9*h**3 - 525*h - 180 - 227*h**2 + 0*h**3 - 17*h**3 = 0.
-30, -2, -3/7
Let k be 2 - -9*3/(-243)*-6. Let f(t) be the first derivative of 0*t + t**4 + 0*t**2 + k*t**3 - 4/5*t**5 + 19. Factor f(h).
-4*h**2*(h - 2)*(h + 1)
Let m(g) be the second derivative of 1634661*g**5/80 - 81747*g**4/8 + 565*g**3/2 - 3*g**2 + 1097*g. Factor m(p).
3*(7*p - 2)*(279*p - 2)**2/4
Let u(a) = -4*a - 12. Let w be u(-4). Suppose -w*g + 18 = -g. Let n(j) = 11*j**2 + 19*j. Let h(k) = k**2 - k. Let f(y) = g*h(y) - n(y). Factor f(d).
-5*d*(d + 5)
Suppose -106 = -33*x + 533 + 219. Let s(t) be the first derivative of x + 0*t**2 + 0*t + 18/55*t**5 - 6/11*t**4 + 8/33*t**3. Factor s(w).
2*w**2*(3*w - 2)**2/11
Find i, given that -5/6*i**3 + 14 + 2/3*i + 1/6*i**5 - 35/2*i**2 + 7/2*i**4 = 0.
-21, -2, -1, 1, 2
Let q(v) = -12*v**3 - 124*v**2 + 1168*v - 2465. Let z(k) = 5*k**3 + 63*k**2 - 584*k + 1226. Let u(x) = -2*q(x) - 5*z(x). Factor u(p).
-(p - 4)**2*(p + 75)
Let s(a) be the first derivative of -a**7/6300 + a**6/675 - a**5/300 - 21*a**3 - 69. Let w(b) be the third derivative of s(b). Solve w(v) = 0.
0, 1, 3
Suppose -4*b - 8*y + 116 = 0, -3*b - 3016*y = -3014*y - 35. Factor 354/5*s**2 + 410758/5 + 2/5*s**b + 20886/5*s.
2*(s + 59)**3/5
Let v(i) be the third derivative of -i**6/540 + i**5/10 - 95*i**4/108 + 23*i**3/9 - 3*i**2 + 2309. Suppose v(c) = 0. Calculate c.
1, 3, 23
Find m, given that 0 - 8*m**4 - 54*m + 24*m**2 + 10/9*m**5 + 12*m**3 = 0.
-9/5, 0, 3
Let r(n) be the second derivative of n**4/14 + 53*n**3/21 - 18*n**2/7 - 4*n - 48. Factor r(g).
2*(g + 18)*(3*g - 1)/7
Let c(g) be the first derivative of 5*g**3/3 - 4095*g**2 + 3353805*g - 2147. Factor c(z).
5*(z - 819)**2
Let o be (-51)/(-136) - 441265/(-40). Let i be o/308 + 1/(-11)*-2. Suppose 0 + i*u**4 - 8/3*u**2 - 112/3*u**5 + 4*u**3 + 0*u = 0. What is u?
-2/7, 0, 1/4, 1
Solve -304182/11*p**2 - 13479210/11*p - 25760268/11 - 2334/11*p**3 - 6/11*p**4 = 0 for p.
-129, -2
Suppose 5*l = -15, -5*x = -5*l - 1 - 34. Let c(i) be the first derivative of 16 - 4*i - x*i**2 - 4/3*i**3. Factor c(h).
-4*(h + 1)**2
Let k be 1/12 - (-119)/(-1428). Let q(t) be the second derivative of 1/60*t**4 + 0 + 0*t**3 + k*t**2 + 16*t - 1/50*t**5 + 1/150*t**6. Factor q(g).
g**2*(g - 1)**2/5
Suppose -62272*f + 428*f**4 - 12*f**5 - 37632 - 81988/3*f**2 - 6748/3*f**3 = 0. Calculate f.
-8/3, -1, 21
Let l = 5924/3 + -29614/15. Let o(y) be the second derivative of 0*y**3 + 1/20*y**4 - l*y**2 + 10*y + 0 - 1/100*y**5. Find h such that o(h) = 0.
-1, 2
Suppose -178 + 546 = 16*s. Let d(q) be the first derivative of 0*q + 2*q**2 - s + 2/3*q**3. Solve d(x) = 0 for x.
-2, 0
Let q(b) be the second derivative of -5*b**7/63 - 43*b**6/90 - 13*b**5/15 - b**4/3 + 836*b + 2. Find o such that q(o) = 0.
-2, -3/10, 0
Let q(a) be the second derivative of 0 + 1/2*a**4 - 123*a - 2/5*a**5 + 0*a**3 + 0*a**2. Factor q(f).
-2*f**2*(4*f - 3)
What is m in -1/2*m**2 - 149*m + 0 = 0?
-298, 0
Let d = -47245/6 - -7875. Let g(f) be the third derivative of 0*f + 0 + 21*f**2 - 5/12*f**4 - d*f**3 - 1/12*f**5. Factor g(y).
-5*(y + 1)**2
Let v = 321 + -211. Factor -8*t + 111*t**5 - 8*t**2 + 8*t**4 - 219*t**5 + 6*t**3 + v*t**5.
2*t*(t - 1)*(t + 1)*(t + 2)**2
Suppose 2/3*i**2 + 1592*i - 4778/3 = 0. What is i?
-2389, 1
Let x(r) be the first derivative of -r**6/3 - 104*r**5/5 - 119*r**4 - 88*r**3 + 423*r**2 - 1680. Determine y so that x(y) = 0.
-47, -3, 0, 1
Let n(p) be the second derivative of -p**7/105 + 16*p**6/75 - 7*p**5/5 + 4*p**4/3 + 71*p**3/15 - 56*p**2/5 + 10*p - 6. Solve n(m) = 0 for m.
-1, 1, 7, 8
Let f = -12442 - -37451/3. Let s(v) be the second derivative of 1/30*v**5 + 0 + 31*v + 25/3*v**3 + 5/6*v**4 + f*v**2. Factor s(r).
2*(r + 5)**3/3
Let q(a) be the third derivative of 2*a**7/15 + 58*a**6/5 - 1199*a**5/15 + 176*a**4 - 424*a**3/3 - 860*a**2. Let q(g) = 0. What is g?
-53, 2/7, 1, 2
Let i be (-71 + (-2364)/(-84))*14/(-5). Solve -75/2*p**4 + 3/2*p**2 - 66*p + i*p**3 - 18 = 0 for p.
-2/5, 1, 3
Let a(x) = -2770*x - 19388. Let z be a(-7). Let 0 - 2/11*t**3 + 8/11*t + 6/11*t**z = 0. Calculate t.
-1, 0, 4
Let p be (2 - 0) + 18/18. Suppose -819 = -3*b - 813. Find s such that 7/4*s + 1/2*s**b + 1 - 1/4*s**p = 0.
-1, 4
Solve -266/5*v**2 - 8712/5 + 2/5*v**3 + 8976/5*v = 0 for v.
1, 66
Let z(o) be the first derivative of -o**6/420 + o**5/210 - 15*o**2 - 19. Let f(w) be the second derivative of z(w). Factor f(k).
-2*k**2*(k - 1)/7
Let y = 133071/380 + -1401/4. Let z = 82/95 + y. Factor -2*b**3 - 2/5*b + z - 16/5*b**2.
-2*(b + 1)**2*(5*b - 2)/5
Let a(d) be the first derivative of -4*d**5/15 - 52*d**4/3 - 448*d**3 - 17248*d**2/3 - 109760*d/3 + 2816. Factor a(s).
-4*(s + 10)*(s + 14)**3/3
Let r(s) be the third derivative of s**7/1260 - s**6/80 - 11*s**5/36 + 25*s**4/4 + 250*s**3/9 + 161*s**2 + 2*s. Let r(k) = 0. What is k?
-10, -1, 10
Let c(p) be the second derivative of -67*p**3/6 + p**2/2 - 8*p. Let r be c(-3). Solve -25*b**3 - 20*b**2 - 5*b**4 + r*b - 202*b = 0 for b.
-4, -1, 0
Let i(w) = 26*w**2 - 4*w. Let y(m) = -53*m**2 + 2484*m - 1532644. Let x(f) = -6*i(f) - 3*y(f). Factor x(u).
3*(u - 1238)**2
Let q(b) = 7*b**4 - 327*b**3 + 1046*b**2 + 1344*b - 3. Let x(j) = -11*j**4 + 655*j**3 - 2082*j**2 - 2688*j + 5. Let v(h) = -5*q(h) - 3*x(h). Factor v(d).
-2*d*(d - 4)*(d + 1)*(d + 168)
Let a(x) be the second derivative of x**4/6 + 17*x**3/6 + 16*x**2 - 16*x. Let z(o) = o**2 - 2. Let l(h) = 2*a(h) - 6*z(h). Factor l(f).
-2*(f - 19)*(f + 2)
Let r be 33/(-44)*(-36 + 1704/54). Factor 4/3*y + 1/6*y**2 - r.
(y - 2)*(y + 10)/6
Let k be -8 - -7 - (-57 - 1)/2. Suppose 2*a - 4*v - 44 = 0, 4*v = -7*a + 3*a + k. Factor -24*m**3 + 8*m**3 + a*m**3 - 8*m**2.
-4*m**2*(m + 2)
Factor 312633*y + 187*y**2 - 1285*y**2 - 1008*y**2 + 4159022 + 180171*y - 42597734 + 3*y**3.
3*(y - 234)**3
Let j(z) be the third derivative of z**6/40 + z**5 - 13*z**2 + 22*z. Factor j(v).
3*v**2*(v + 20)
Factor -43330245*x - 1874551362 - 257094*x**2 + 7851273*x - x**4 + 38514561 - 828*x**3.
-(x + 207)**4
Factor 239/4*a - 1/4*a**2 - 235.
-(a - 235)*(a - 4)/4
Let d(p) be the second derivative of p**6/1260 + p**5/90 + 5*p**4/126 - p**2 - 175*p. Let b(s) be the first derivative of d(s). Factor b(u).
2*u*(u + 2)*(u + 5)/21
Let w(a) = -6*a**2 - 464*a + 47517. Let u(n) = -n**2 - 4*n - 1. Let c(g) = -7*u(g) + w(g). Factor c(s).
(s - 218)**2
Let r = 62/809 + 132099310/8899. Let p = -14832 + r. What is u in 8/11 + 578/11*u**2 - p*u = 0?
2/17
Suppose 13*x - 3*