is n?
-1, 4
Factor -133/3*f - 1/3*f**2 + 230.
-(f - 5)*(f + 138)/3
Suppose 5*g + 8 + 17 = -2*k, 0 = g + 5. Let o(n) be the third derivative of k - 2*n**3 - 1/20*n**5 - 14*n**2 + 0*n + 1/2*n**4. What is u in o(u) = 0?
2
Let b(f) be the third derivative of 1/300*f**5 + 4/15*f**3 + 1/600*f**6 + 0 + 4*f - 1/12*f**4 - 5*f**2. Determine s, given that b(s) = 0.
-4, 1, 2
Let w(s) be the second derivative of -s**6/6 + 9*s**5/2 - 295*s**4/12 + 35*s**3 - 4442*s. Factor w(h).
-5*h*(h - 14)*(h - 3)*(h - 1)
Let t = 985337/218964 - -1/218964. Solve -3/2*q**5 + 15/2 + 15*q**3 - 3*q**2 - 27/2*q - t*q**4 = 0.
-5, -1, 1
Let h(i) = -10*i**2 - 118*i - 967. Let s(u) = -11*u**2 - 117*u - 968. Let z(r) = -7*h(r) + 6*s(r). Factor z(m).
(2*m + 31)**2
Factor 0 - 8*c + 7/2*c**3 - 1/2*c**4 - 4*c**2.
-c*(c - 4)**2*(c + 1)/2
Let i(p) be the first derivative of 4/3*p**3 - 21/2*p**4 + 0*p - 17/5*p**5 - 139 - 1/6*p**6 + 28*p**2. Factor i(r).
-r*(r - 1)*(r + 2)**2*(r + 14)
Let a = 24735 + -24733. Solve 578/5 + 68/5*d + 2/5*d**a = 0 for d.
-17
Let k(p) be the first derivative of -5*p**4/4 - 25*p**3/3 + 85*p**2 + 400*p + 3394. Factor k(w).
-5*(w - 5)*(w + 2)*(w + 8)
Let m(s) = 8*s + 28. Let c be m(-16). Let g = -61 - c. Factor 14*w**3 + 64 + 22*w + g*w - 13*w + 144*w - 108*w**2.
2*(w - 4)**2*(7*w + 2)
Let q(g) be the third derivative of g**7/70 + 67*g**6/10 - 81*g**5/2 + 203*g**4/2 - 271*g**3/2 + 136*g**2. Factor q(i).
3*(i - 1)**3*(i + 271)
Let b(f) be the first derivative of 0*f**4 + 44 + 0*f - 26/15*f**3 + 12/5*f**2 + 2/25*f**5. Factor b(m).
2*m*(m - 3)*(m - 1)*(m + 4)/5
Let r(q) = q**3 + 296*q**2 - 1459*q - 77695. Let z be r(-300). Let 1/2*h**4 + h + 2 - 5/4*h**3 - 5/2*h**2 + 1/4*h**z = 0. What is h?
-2, -1, 1, 2
Let t be 111/(-185) - (-56)/10. Let q be (-247)/(-95) - 1/t*-2. Solve 12/7 - q*v**3 - 3/7*v**5 - 15/7*v**4 + 24/7*v + 3/7*v**2 = 0 for v.
-2, -1, 1
Let d = 20852/59 - 18896984/53867. Let m = d + -36/83. Solve -24/11*u + m + 6/11*u**2 = 0.
2
Let c be 8 - 328/(-84)*(-4 - -2). Let d(t) be the first derivative of 1/42*t**4 + c*t**2 - 10/63*t**3 + 0*t + 17. Determine g, given that d(g) = 0.
0, 1, 4
Let i(d) be the second derivative of 37*d + d**2 + 1/6*d**4 - 3/2*d**3 - 1 + 9/20*d**5 - 2/15*d**6. Suppose i(f) = 0. Calculate f.
-1, 1/4, 1, 2
Suppose -19*n = 107*n + 28 - 532. Let s(m) be the first derivative of -1/4*m**n - 1/2*m**2 - 14/27*m**3 + 11 - 2/9*m - 2/45*m**5. Find c such that s(c) = 0.
-2, -1, -1/2
Determine n so that 1/3*n**4 - 404/3*n + 140 - 31/3*n**2 + 14/3*n**3 = 0.
-14, -6, 1, 5
Let v(l) be the third derivative of l**6/480 + 37*l**5/8 + 34225*l**4/8 + 6331625*l**3/3 - 610*l**2. Factor v(z).
(z + 370)**3/4
Let p(d) be the first derivative of 9 - 8*d**3 - 21 + 23*d**2 - 44 - 5*d**2 + d**4. Suppose p(j) = 0. What is j?
0, 3
Let r(n) be the second derivative of -n**4/30 + 26*n**3 + 784*n**2/5 + 7595*n. Let r(s) = 0. What is s?
-2, 392
Let f = -8649 - -8653. Let t(c) be the first derivative of 3/4*c**f - 6*c**2 + 15 - 12*c + c**3. Factor t(r).
3*(r - 2)*(r + 1)*(r + 2)
Let m = 1081 + -1355. Let k = 278 + m. Suppose 2/17*s**k - 2/17*s**2 - 6/17*s**3 + 6/17*s + 0 = 0. What is s?
-1, 0, 1, 3
Let c(h) = -3*h**2 - 1011*h - 1089. Let j(x) = 9. Let k(f) = -c(f) - 9*j(f). Factor k(r).
3*(r + 1)*(r + 336)
Let l(c) = -2*c**2 - 4*c + 5. Let k(h) = 2*h + 3 + 3 - 3*h**2 + h**2 - 7*h. Let f(u) = 5*k(u) - 6*l(u). Factor f(x).
x*(2*x - 1)
Let b(m) be the first derivative of m**3 - 82 - 5/4*m**2 - 1/8*m**4 + 0*m. Factor b(a).
-a*(a - 5)*(a - 1)/2
Let l(r) be the second derivative of r**6/6 + 15*r**5/2 + 35*r**4 + 205*r**3/3 + 135*r**2/2 - 2*r - 2336. Factor l(z).
5*(z + 1)**3*(z + 27)
Suppose -15*x - 18 = -63. Suppose 0 = -3*z - 2*a + 5, -a = -x*z - 30 + 32. Factor -1/4*d**4 + z - 2*d + 1/2*d**3 + 3/4*d**2.
-(d - 2)*(d - 1)**2*(d + 2)/4
Let u(b) be the first derivative of 2/3*b**3 + 1/10*b**5 + 75 + 0*b + 0*b**2 + 1/2*b**4. Factor u(x).
x**2*(x + 2)**2/2
Let j be (-455706)/(-3492) + 1/(3/45). Solve -216*d - j*d**2 - 3/2*d**4 - 27*d**3 - 96 = 0 for d.
-8, -1
Let h(c) be the first derivative of -c**4/16 + 127*c**3/12 - 125*c**2/4 - 6250. Solve h(x) = 0 for x.
0, 2, 125
Let z(p) = -p**3 - 29*p**2 + 32*p + 66. Suppose 110 + 4 = -4*y - 3*n, 5*n = 4*y + 130. Let x be z(y). Find q, given that -22/5*q**3 - x*q - 48/5*q**2 - 4/5 = 0.
-1, -2/11
Let r be (28 - 30)/((-4)/6). Factor 15*y**2 - 18*y**3 + 13*y**3 + 5*y**3 + 5*y**r.
5*y**2*(y + 3)
Let o(g) be the second derivative of g**5/570 - 7*g**4/76 + 113*g**2 + 92*g - 1. Let l(h) be the first derivative of o(h). Factor l(b).
2*b*(b - 21)/19
Let m(r) be the first derivative of 2*r**5/45 - 8*r**4/9 - 50*r**3/9 - 98*r**2/9 - 80*r/9 - 5198. What is f in m(f) = 0?
-2, -1, 20
Find h such that -6295/3*h**3 + 1985/3*h**2 + 15*h**5 + 0 + 3475/3*h**4 + 790/3*h = 0.
-79, -2/9, 0, 1
Let y(s) = -s - 37. Let x be y(-18). Let z be (-21 - x)/(4/(-18)). Factor 3 + 12*k - z*k**4 - 6*k**3 - 3*k**5 + 15*k**5 + 6*k**2 - 3*k - 15*k**5.
-3*(k - 1)*(k + 1)**4
Let f be 1/2 + 3120/2400. Factor -f + 3/5*h + h**2 + 1/5*h**3.
(h - 1)*(h + 3)**2/5
Let j(h) be the second derivative of h**4/42 + 5*h**3/21 - 50*h**2/7 + h - 123. Factor j(v).
2*(v - 5)*(v + 10)/7
Suppose 0 = 625*t + 874*t - 3544 + 546. Factor 0 - 1/2*x**4 - x**3 + 0*x + 4*x**t.
-x**2*(x - 2)*(x + 4)/2
Let u(a) be the first derivative of 7*a**5/30 + 19*a**4/12 - 2*a**3 - 67*a**2/2 + 107. Let o(k) be the second derivative of u(k). Solve o(i) = 0.
-3, 2/7
Factor -50*b**2 + 2/3*b**3 + 1122*b - 6534.
2*(b - 33)**2*(b - 9)/3
Let c be ((-4)/(-6)*1)/((-2)/(-9)). Factor -179685*q**2 + 5 - 495*q**4 - 5*q**5 - 1 - 17445*q**c + 1110*q**3 - 4.
-5*q**2*(q + 33)**3
Let w(s) be the second derivative of -s**5/80 - 3*s**4/32 - 123*s**2/2 + s + 1. Let b(p) be the first derivative of w(p). Find z such that b(z) = 0.
-3, 0
Let z(r) be the third derivative of 1/180*r**5 - 10/3*r**3 - 1/54*r**4 + 0 + 0*r - 1/1620*r**6 + 9*r**2. Let c(f) be the first derivative of z(f). Factor c(l).
-2*(l - 2)*(l - 1)/9
Let j be -2*1/(-7) + 141/21. Suppose -j*d - 51 + 149 = 0. Factor 0*c**4 + 32 + d*c + 72*c**2 - 28*c**3 - 94*c + 4*c**4.
4*(c - 2)**3*(c - 1)
Suppose -14*v + 46 = -12*v + 2*q, 3*q = -v + 33. What is k in 6*k**2 - 50 - 45*k - v*k**2 + 176*k**3 - 177*k**3 = 0?
-5, -2
Let a(p) = 7*p**5 - 135*p**4 - 27*p**3 + 17*p**2 + 17*p. Let s(n) = n**4 + n**3 + n**2 + n. Let r(v) = -3*a(v) + 51*s(v). Factor r(q).
-3*q**3*(q - 22)*(7*q + 2)
Let t = 1985 + -1980. Let r(i) be the first derivative of i**4 + 2/5*i**t - 2*i + 0*i**3 + 4 - 2*i**2. Factor r(c).
2*(c - 1)*(c + 1)**3
Let o(h) = 5*h**2 + 3022*h - 456014. Let a(y) = 90*y**2 + 51375*y - 7752235. Let l(r) = -2*a(r) + 35*o(r). Find x, given that l(x) = 0.
302
Let b(y) be the second derivative of -y**6/360 + 53*y**5/120 - 13*y**4/6 - 5*y**3/6 + 4*y**2 - 84*y. Let k(x) be the second derivative of b(x). Factor k(j).
-(j - 52)*(j - 1)
Let b(v) = -v**2 - 6*v - 29. Let y(l) = 2*l**2 + 11*l + 59. Let t = 106 - 110. Let n(o) = t*y(o) - 9*b(o). Factor n(a).
(a + 5)**2
Let z = -687 - -689. Factor -12*d**z - 307*d + 12*d**4 + 157*d + 147*d + 3*d**3.
3*d*(d - 1)*(d + 1)*(4*d + 1)
Suppose 41 - 73 = -8*z. Let s(v) = -5*v**2 + 245*v + 266. Let r(g) = 30*g**2 - 1465*g - 1595. Let f(o) = z*r(o) + 25*s(o). Solve f(i) = 0 for i.
-1, 54
Let h(f) be the first derivative of -3*f**4/4 + 17*f**3 - 141*f**2 + 504*f - 3015. Factor h(p).
-3*(p - 7)*(p - 6)*(p - 4)
Let l(s) be the first derivative of -20*s**3/3 - 4055*s**2/2 + 1015*s - 2457. Factor l(d).
-5*(d + 203)*(4*d - 1)
Factor -1542/7*u - 220 - 2/7*u**2.
-2*(u + 1)*(u + 770)/7
Let h(t) be the third derivative of -t**6/150 + 4*t**5/25 + 24*t**4/5 + 128*t**3/3 - 190*t**2 - 6. Let h(v) = 0. Calculate v.
-4, 20
Let v(j) be the second derivative of 2*j**7/21 - 4*j**6/15 - 3*j**5 + 10334*j. Determine l, given that v(l) = 0.
-3, 0, 5
Let r(b) be the third derivative of -11*b**6/360 - 109*b**5/180 - 83*b**4/36 + 8*b**3/9 - 1752*b**2 - 2. Factor r(l).
-(l + 2)*(l + 8)*(11*l - 1)/3
Let n(t) be the second derivative of -t**6/15 + 51*t**5/5 + 52*t**4 + 314*t**3/3 + 105*t**2 - 625*t. Factor n(u).
-2*(u - 105)*(u + 1)**3
Let v(y) be the first derivative of -y**3 + 639*y**2/2 - 636*y + 1812. Solve v(a) = 0 for a.
1, 212
Let x be 6 + -5*(-112)/40. Factor -74*z - 378*z - 88*z -