3*p**4 - 1/3*p**5 - 74/3*p + 25*p**3 = 0. Calculate p.
-16, -1, 1, 2, 3
Let c(g) = g**3 - 42*g**2 + 422*g + 53. Let p be c(17). Let v(w) be the first derivative of -3/8*w**p - 1/12*w**3 + 6 - 1/2*w. Determine u, given that v(u) = 0.
-2, -1
Factor -38/17*y + 2/17*y**2 + 120/17.
2*(y - 15)*(y - 4)/17
Let y(a) = -3*a**2 + 19*a - 18. Let r(s) = 2*s**2 - s - 3. Let p(n) = r(n) - y(n). Let p(u) = 0. Calculate u.
1, 3
Suppose -2*k = 5*t - 15, -11*k = -6*k + 5*t - 30. Factor 36*f**3 + 16*f**4 - 3*f**k - 16*f**3 + f**5 - 16*f**3 - 18*f**3.
-2*f**3*(f - 7)*(f - 1)
Suppose -2*f - 11 = -s, -3*s = 4*f + f. What is t in 0*t**2 + 8*t**3 - 4*t + 8*t**2 - 12*t**4 - 4*t**s - 4 + 8*t**4 = 0?
-1, 1
Let c = -34 - -16. Let p(a) = a + 21. Let t be p(c). Solve 2*k**t + 2*k**2 - 4*k - k**3 - 2*k**4 - 5*k**3 + 8*k**3 = 0 for k.
-1, 0, 1, 2
Suppose 3*a - 13*a + 520 = 0. What is f in -20*f**3 - 7*f**4 + 10*f**4 - 28*f - 10*f**4 + 11*f**4 - a*f**2 = 0?
-1, 0, 7
Let h(n) = n**2 + 22*n + 103. Let l(r) be the first derivative of -r**3/3 - 5*r**2 - 52*r - 323. Let u(m) = -4*h(m) - 7*l(m). Factor u(k).
3*(k - 8)*(k + 2)
Let y = 67396246 + -214117853963/3177. Let g = 21/353 + y. Factor -g*z**3 - 4/9*z**4 - 80/3*z**2 - 200/9*z + 500/9.
-4*(z - 1)*(z + 5)**3/9
Factor -2*h**3 + 26*h**2 + 21 - 33*h + 263 + 413*h + 68.
-2*(h - 22)*(h + 1)*(h + 8)
Suppose 0 = -4*b + 9*b + 5*w + 50, 0 = -5*w - 70. What is z in 0 + z**2 - 1/3*z**b + 0*z**3 + 2/3*z = 0?
-1, 0, 2
Let r(q) be the second derivative of 1/30*q**6 + 12*q - 1/5*q**5 + 2/3*q**3 - 2 - 3/2*q**2 + 1/6*q**4. Factor r(j).
(j - 3)*(j - 1)**2*(j + 1)
Let f(j) be the second derivative of 2460375*j**4/4 + 4050*j**3 + 10*j**2 - j - 42. What is p in f(p) = 0?
-2/1215
Suppose -1039625*x**3 - 3562513*x - 2833560*x - 4580*x**4 - 5*x**5 + 4209010*x**2 + 889238*x + 2116000 + 226035*x = 0. Calculate x.
-460, 1, 2
Let m = -22 - -5. Let r be (m + 2 + -3)*20/(-8). Solve r*y**2 + 4*y - 2*y - 6*y - 8*y + 12*y**3 = 0 for y.
-4, 0, 1/4
Let n(f) be the second derivative of 0*f**2 + 26*f**4 - 6*f**3 + 208/15*f**6 - 193/5*f**5 + 119*f + 0 - 32/21*f**7. What is y in n(y) = 0?
0, 1/4, 3
Let v(u) be the second derivative of -3/80*u**5 + 1/120*u**6 + 0*u**2 + 3*u - 13 + 0*u**3 + 1/24*u**4. Factor v(d).
d**2*(d - 2)*(d - 1)/4
Let a(w) be the first derivative of w**4/16 - 683*w**3/12 - 171*w**2/2 + 1992. Find i such that a(i) = 0.
-1, 0, 684
Factor -2/7*i**2 + 44/7 - 6*i.
-2*(i - 1)*(i + 22)/7
Let b(u) be the second derivative of 3*u**7/14 - 32*u**6/5 + 849*u**5/20 + 37*u**4/2 - 318*u**3 - 540*u**2 + 316*u - 2. Let b(w) = 0. Calculate w.
-1, -2/3, 2, 6, 15
Suppose -462 + 2286 = -57*l. Let q be ((-1053)/(-156))/((-60)/l). Solve 34/5*j**4 - 26/5*j**3 - q + 9/5*j**5 + 21*j - 104/5*j**2 = 0.
-3, 2/9, 1
Let y(m) = -6*m - 154. Let n be y(-26). Suppose -209 - 21*g - g**n + 4*g**2 + 29 - 24*g + 2*g**2 = 0. What is g?
-3, 12
Let w(z) be the first derivative of -2*z**3/27 + 5*z**2/3 - 52*z/9 + 110. Solve w(r) = 0 for r.
2, 13
Let x(y) = -y**2 + 11 - 14*y + 0*y**2 + 2*y - 5*y. Let o(v) = -8*v + 5. Let m = 7 + 0. Let f(h) = m*o(h) - 3*x(h). Let f(g) = 0. What is g?
2/3, 1
Let j(s) = -5*s**3 + 4*s**2 - 43*s + 2. Let c(n) = 28*n**3 - 20*n**2 + 214*n - 11. Let f(h) = -2*c(h) - 11*j(h). Factor f(d).
-d*(d - 5)*(d + 9)
Let c(z) be the second derivative of 3*z**5/100 + 43*z**4/20 + 271*z**3/10 - 189*z**2/2 + 1824*z. Factor c(d).
3*(d - 1)*(d + 9)*(d + 35)/5
Let x = 170867 + -170865. What is m in -2/3*m**3 + x*m + 0*m**2 - 4/3 = 0?
-2, 1
Factor -29/2 - 3/4*z**2 + 89/4*z.
-(z - 29)*(3*z - 2)/4
Let w = -40/3183 + 8528/3183. Solve -19/3*r**3 + 0 + w*r**2 + 0*r - 5/6*r**4 = 0 for r.
-8, 0, 2/5
Suppose -2*a - 5*c = 7, 0 = 4*a - 155*c + 158*c - 7. Let i(w) be the second derivative of 0*w**3 + 0*w**2 - 1/96*w**a - 11*w - 1/160*w**5 + 0. Factor i(b).
-b**2*(b + 1)/8
Suppose -4363*h + 25180 = -65085 + 7368. Suppose 43/2*s - 31*s**2 - 7/2*s**4 - 11/2 - 1/2*s**5 + h*s**3 = 0. Calculate s.
-11, 1
Let b = 60547 - 423827/7. Suppose -6/7*j**4 + 0*j + 0*j**2 + b*j**5 - 8/7*j**3 + 0 = 0. Calculate j.
-1, 0, 4
Suppose l = -3 + 8, n = -4*l + 153. Let p = n - 131. Factor -36*s + s**p - 66 + 2*s**2 + 174.
3*(s - 6)**2
Suppose 7*r + 100 = -201. Let i = r - -64. Let h(a) = -2*a**2 + 8*a + 5. Let p(j) = -9*j**2 + 33*j + 21. Let q(v) = i*h(v) - 5*p(v). Factor q(x).
3*x*(x + 1)
Suppose -5*l + 0 - 5 = 0, 0 = -3*g + 5*l + 17. What is r in -3*r**3 + 3*r**2 + 132*r**g - 263*r**4 + 122*r**4 + 3*r**2 = 0?
-1, 0, 2/3
Let t(n) be the first derivative of -2/7*n**2 + 24 - 2/7*n - 2/21*n**3. Factor t(y).
-2*(y + 1)**2/7
Let v be 22/2 + (53 - 16) + -44. Factor -v*s**2 - 24/5 + 46/5*s - 2/5*s**3.
-2*(s - 1)**2*(s + 12)/5
Let u be (-171)/(-12) - 3/12. Suppose -i = 4, -5*i - u - 8 = -a. Find d, given that -15*d**2 - 2*d**2 - 3*d**a + d + 5*d**3 + 19*d = 0.
0, 2
Let d = 183196/9 - 20380. Let p = -212/9 - d. What is r in 4/3*r - p*r**2 + 8/3 = 0?
-1, 2
Let u be ((-5)/(-25))/((-2)/(-370)). Factor 405*f + 14 + 82 - u*f + 406*f**2 + 98*f**3.
2*(f + 3)*(7*f + 4)**2
Let z(w) = w**4 + 1057*w**3 + 7*w**2. Let l(n) = 352*n**3 + 2*n**2. Let j(r) = 7*l(r) - 2*z(r). Factor j(k).
-2*k**3*(k - 175)
Let u(a) be the first derivative of -a**4/2 - 182*a**3/3 + 92*a**2 - 4656. Solve u(c) = 0.
-92, 0, 1
Suppose -11*l = -2 - 75. Let j(r) be the second derivative of 1/105*r**l + 0*r**2 + 0*r**4 + 2/25*r**5 + 0*r**3 + 8*r + 4/75*r**6 + 0. What is a in j(a) = 0?
-2, 0
Factor 1/7*o**2 + 3/7*o - 4.
(o - 4)*(o + 7)/7
Let p(r) = 11*r**5 - r**4 + 23*r**3 + r**2 + 17*r - 17. Let m(v) = 2*v**5 + 4*v**3 + 3*v - 3. Let n = 1028 - 994. Let g(w) = n*m(w) - 6*p(w). Factor g(q).
2*q**2*(q - 1)*(q + 1)*(q + 3)
Factor -1/7*y**2 + 4672/7*y - 5456896/7.
-(y - 2336)**2/7
Factor 2/17*v**2 + 28/17*v - 480/17.
2*(v - 10)*(v + 24)/17
Suppose -350 = 11*v - 4*v. Let t = v + 62. Find j, given that -21*j + t - 22 - 6*j**2 + 2*j**3 + 3*j = 0.
-1, 5
Let a(i) = -3*i**3 + 5*i**2 - 6*i - 4. Let f = 91 - 96. Let c(w) = w**3 - 2*w**2 + 3*w + 2. Let n(y) = f*c(y) - 2*a(y). What is h in n(h) = 0?
-1, 2
Let b(y) be the first derivative of -y**6/120 - y**5/6 - 17*y**4/24 - 4*y**3/3 + 91*y**2/2 + 86. Let q(c) be the second derivative of b(c). Factor q(z).
-(z + 1)**2*(z + 8)
Let l = 3671 + -3669. Let r(j) be the first derivative of 0*j - 35 - 2/65*j**5 + 2/39*j**3 + 1/26*j**4 - 1/13*j**l. Factor r(v).
-2*v*(v - 1)**2*(v + 1)/13
Let k be 2/(3*(-68)/(-24)). Let c = -26952 + 458186/17. Factor 4/17*n**2 - 2/17*n**4 - k*n**3 - 2/17 + c*n + 2/17*n**5.
2*(n - 1)**3*(n + 1)**2/17
Factor -2821 - 3401 + 5466 + 102*s - 42*s + 4*s**2 + 12*s**2.
4*(s + 9)*(4*s - 21)
Suppose -2*p + 1 + 5 = 0. Let g(v) = v - 4. Let w be g(6). Factor -3*j**w + 12 + 118*j**3 - 58*j + 63*j**2 - 132*j**p.
-2*(j - 3)*(j - 1)*(7*j - 2)
Let a = 22981 + -22978. Let u(p) be the first derivative of 0*p + 1 + 5/9*p**a - 1/12*p**4 + 0*p**2. Solve u(o) = 0 for o.
0, 5
Let q = 14783878/3880779 + 2/184799. Determine j so that -26/7*j**2 - 8/7 + 22/21*j**3 + q*j = 0.
6/11, 1, 2
Let g(j) be the first derivative of -49/5*j**5 - 10*j**2 - 48*j**3 - 273/4*j**4 + 0*j + 30. Let g(q) = 0. What is q?
-5, -2/7, 0
Let i = -13049/3 - -4350. Let z(k) be the second derivative of 0 + 3/4*k**5 + 39*k + 25/2*k**3 - 10*k**2 - 20/3*k**4 + i*k**6. Factor z(u).
5*(u - 1)**2*(u + 4)*(2*u - 1)
Let o(t) be the second derivative of t**4/24 + 43*t**3/6 + 42*t**2 - 243*t. Factor o(j).
(j + 2)*(j + 84)/2
Factor -34/3 + 34/3*w**2 - 1/3*w**3 + 1/3*w.
-(w - 34)*(w - 1)*(w + 1)/3
Let w(n) = -n**2 - 2*n + 6. Let m be w(-4). Let b be (7/m)/(1/(-2)) - 2. Factor -5 + 181*k**2 - 15*k**3 - 5*k + b*k**4 - 166*k**2 + 5.
5*k*(k - 1)**3
Suppose 2/9*a**4 - 9046/9*a**2 + 0 + 4520/9*a**3 + 1508/3*a = 0. What is a?
-2262, 0, 1
Let n be (-15 + 10070/665)/((-6)/(-14)). Factor n*f**3 - 13*f - 6*f**2 - 20/3.
(f - 20)*(f + 1)**2/3
Let a(i) be the first derivative of 4*i**3/3 + 56*i**2 + 208*i - 6852. Find l such that a(l) = 0.
-26, -2
Let y = 1586 - 986. Let k be (-2)/7 - y/(-875). Find h such that 0 + 1/5*h**5 - 2/5*h**4 + k*h**2 + 0*h - 1/5*h**3 = 0.
-1, 0, 1, 2
Let g = -585 + 597. Let v(z) be the first derivative of -g*z**2 + 10*z**3 - 3/5*z**5 - 20 - 3/4*z**4 + 0*z. Solve v(y) = 0 for y.
-4, 0, 1, 2
Let l = 680 - 182. What is p in -10*p**3 + 504*p**4 - l*p**4 + 2*p**5