. Let r(p) be the third derivative of d(p). Let r(y) = 0. What is y?
-1, 0, 1
Let r(h) = 47*h**2 + 738*h + 757. Let z(v) = 195*v**2 + 2950*v + 3030. Let q(k) = 25*r(k) - 6*z(k). Find s such that q(s) = 0.
-149, -1
Let z be -4 + 2/(-4)*334. Let a be (-14)/(-77) + z/33. Let x(w) = -2*w**2. Let h(r) = 2*r**2. Let c(q) = a*x(q) - 6*h(q). Factor c(s).
-2*s**2
Suppose 4*r + 56 = 4*u, 21*u - 4*r = 26*u - 88. Suppose -4*l = -5*a - u + 4, 4*a = l - 3. Factor -l + 3/4*k**3 + 3/4*k**2 - 3*k.
3*(k - 2)*(k + 1)*(k + 2)/4
Let a(h) be the first derivative of 0*h - 3/4*h**4 + 3/25*h**5 + 7/5*h**3 + 141 - 9/10*h**2. Factor a(d).
3*d*(d - 3)*(d - 1)**2/5
Factor -2/5*v**2 + 3028/5*v - 1146098/5.
-2*(v - 757)**2/5
Factor -368/5 - 2/5*j**2 + 62/5*j.
-2*(j - 23)*(j - 8)/5
Let x(h) be the first derivative of 0*h + 1/5*h**2 + 1 + 2/15*h**3. Factor x(q).
2*q*(q + 1)/5
Let t(v) be the third derivative of v**6/40 + 137*v**5/10 - 1671*v**4/8 + 1260*v**3 + 741*v**2 + 2*v. What is o in t(o) = 0?
-280, 3
Let 5067*u**2 + 5064*u**2 - 290 - 285*u - 10126*u**2 = 0. What is u?
-1, 58
Let r(w) be the second derivative of -3*w**5/20 + 245*w**4/4 - 121*w**3 - 732*w**2 + 112*w + 9. Solve r(s) = 0.
-1, 2, 244
Let o(g) be the second derivative of -g**5/60 + 7*g**4/24 + 5*g**3 - 7*g**2 + 4*g - 2. Let j(v) be the first derivative of o(v). Let j(n) = 0. Calculate n.
-3, 10
Let x(b) be the third derivative of 34*b**6/5 - 161*b**5/15 - 15*b**4/2 + 4*b**3/3 - 2859*b**2. Solve x(p) = 0 for p.
-1/4, 2/51, 1
Let w(u) = 13*u**2 + 35*u. Suppose 0 = t + 13 - 0. Let p(l) = -28*l**2 - 70*l. Let v(x) = t*w(x) - 6*p(x). Determine o so that v(o) = 0.
-35, 0
Let o(y) be the third derivative of -1/630*y**7 - 1/240*y**6 + 38*y**2 + 0*y**5 + 0*y + 0*y**4 + 0 + 1/2016*y**8 + 0*y**3. Factor o(a).
a**3*(a - 3)*(a + 1)/6
Let x(o) be the third derivative of o**5/90 + 22*o**4/9 - 368*o**3/9 - 11*o**2 + 71. Solve x(k) = 0 for k.
-92, 4
Solve 0 + 0*x - 4/5*x**3 - 3/5*x**2 - 1/5*x**4 = 0.
-3, -1, 0
Let h(k) be the first derivative of -2*k**3/3 - 222*k**2 - 437. Determine v so that h(v) = 0.
-222, 0
Suppose 0*d + 152/5*d**2 - 2/15*d**4 + 0 - 224/15*d**3 = 0. What is d?
-114, 0, 2
Factor 0 + 2/11*k**4 - 8/11*k**3 - 56/11*k**2 - 64/11*k.
2*k*(k - 8)*(k + 2)**2/11
Let h(c) be the third derivative of -c**6/280 - c**5/4 - 67*c**4/56 - 33*c**3/14 + 15*c**2 + 8*c. What is o in h(o) = 0?
-33, -1
What is q in 0*q + 0 - 4/5*q**4 + 36/5*q**2 + 18/5*q**3 - 2/5*q**5 = 0?
-3, -2, 0, 3
Let d(v) = v**3 + 7*v**2 + 2*v - 4. Let h(b) be the first derivative of 1/3*b**3 + 3 + 1/2*b**2 + 0*b. Let u(k) = d(k) - 6*h(k). Factor u(n).
(n - 2)*(n + 1)*(n + 2)
Let j be 2*((-426)/639)/(2/(-3)). Determine h so that -5/2*h**3 + 10*h + 15*h**j - 15/4*h**4 + 0 = 0.
-2, -2/3, 0, 2
Let b(z) be the third derivative of 15*z**2 + 0*z - 4/15*z**5 + 5/3*z**3 + 1/12*z**4 + 4/15*z**6 + 0. Let k(s) be the first derivative of b(s). Factor k(p).
2*(4*p - 1)*(12*p - 1)
Let b be (-26)/(1*(-4)/4). Solve 25*t**2 + 29*t - 46*t**2 + b*t + 26*t**2 = 0.
-11, 0
Let n(v) = v**4 + v**3 + 2*v. Let q(k) = -4*k**4 + 33*k**3 - 123*k**2 - 6*k + 164. Let u(h) = 5*n(h) + q(h). Factor u(b).
(b - 2)**2*(b + 1)*(b + 41)
Solve 2420 + 1980*n - 475*n**3 + 158*n**4 - 44*n**5 - 1025*n**2 + 39*n**5 - 53*n**4 = 0 for n.
-2, -1, 2, 11
Let m be 3 + (-15)/(-18)*-2. Let g be (-16)/36 - (-11)/((-693)/(-70)). Suppose -m*x + g*x**2 + 2/3 = 0. Calculate x.
1
Let j be (-34 + 22 + 14)/(((-80)/12)/(-2)). What is a in 3/5*a**2 + 6*a**3 - j - 6*a = 0?
-1, -1/10, 1
Let y(m) be the first derivative of 5*m**3/3 - 535*m**2/2 + 1560*m + 11049. Factor y(t).
5*(t - 104)*(t - 3)
Find a, given that -2/7*a**3 + 16/7*a**2 - 396/7 + 382/7*a = 0.
-11, 1, 18
Let i(x) = -17*x**2 + 8764*x - 2499830. Let c(y) = -4*y**2 + 2196*y - 624958. Let j(g) = 9*c(g) - 2*i(g). Let j(z) = 0. What is z?
559
Suppose -13 - 2 = -4*n + 1. Let j(i) be the third derivative of -1/4*i**5 + 1/4*i**n + 16*i**2 - 7/40*i**6 + 0 + 0*i**3 + 0*i. Factor j(l).
-3*l*(l + 1)*(7*l - 2)
Factor 0 + 2/3*t**2 + 460/3*t.
2*t*(t + 230)/3
Let z(t) = 2*t - 6. Let u(d) = -d + 18. Let n be u(14). Let w be z(n). Factor 2*y**2 - 7*y**w + 0*y**2.
-5*y**2
Let t(z) be the second derivative of -14*z**3 - 2/21*z**7 + 6/5*z**6 - 138*z + 10*z**2 + 0 - 26/5*z**5 + 34/3*z**4. Let t(b) = 0. Calculate b.
1, 5
Factor 259 - r**2 + 558 + 2*r - 193.
-(r - 26)*(r + 24)
Let l(u) = 2*u**3 + 34*u**2 + 130*u - 19. Let p be l(-11). Suppose -10/11*v + 24/11*v**5 + 106/11*v**p + 0 + 2*v**2 - 142/11*v**4 = 0. What is v?
-1/3, 0, 1/4, 1, 5
Let q(o) = 2*o**2 + o - 3. Let n be q(-2). Suppose n*w - 7*w = -20. Determine x so that 14*x - 8*x**2 + 0 - 1 - w = 0.
3/4, 1
Suppose 18 = 1048*c - 1091*c + 104. Let b(k) be the third derivative of 23*k**c - 16/3*k**3 + 0*k - 1/30*k**5 - 2/3*k**4 + 0. Factor b(i).
-2*(i + 4)**2
Let h(t) be the first derivative of t**6/10 + 3*t**5/4 + t**4/2 - 10*t**3 - 36*t**2 + 14*t - 63. Let a(b) be the first derivative of h(b). Solve a(u) = 0.
-3, -2, 2
Determine j, given that 0 - 244*j**3 - 140/3*j**4 + 0*j - 4/3*j**5 - 348*j**2 = 0.
-29, -3, 0
Let v(p) be the first derivative of -2*p**3/9 + 187*p**2/3 - 124*p - 914. Let v(a) = 0. Calculate a.
1, 186
Let o(d) = 17*d**2 - 3096*d + 6014. Let s(z) = -9*z**2 + 1551*z - 3006. Let f(j) = 6*o(j) + 11*s(j). Suppose f(x) = 0. What is x?
2, 503
Let s = -112462/11 + 787267/77. Factor 18/7*p - 15/7 - s*p**2.
-3*(p - 5)*(p - 1)/7
Suppose 130*a - 1260 = -85*a - 100*a. Let v(t) be the first derivative of 0*t + 4/27*t**3 - 1/9*t**2 - 1/18*t**a + 41. Find s such that v(s) = 0.
0, 1
Let r(w) be the second derivative of -1/112*w**7 - 7/80*w**6 - 9/32*w**5 - 5/32*w**4 + w**3 + 0 - 115*w + 9/4*w**2. Determine c, given that r(c) = 0.
-3, -2, -1, 1
Let r(w) = -256*w**3 - 86*w**2 - 1745*w - 4563. Let b(s) = -51*s**3 - s**2 + 2*s. Let p(c) = 15*b(c) - 3*r(c). Factor p(d).
3*(d + 3)*(d + 39)**2
Let v(u) be the first derivative of 4/3*u**6 + 62/7*u**5 + 0*u**2 + 11/2*u**4 + 112 + 20/21*u**3 + 0*u. Determine y so that v(y) = 0.
-5, -2/7, -1/4, 0
Suppose 9 = -3*v, 3851 = -3*w + 4*v - 412. Let r = w + 1425. Suppose -5/2*g**5 + 5/2*g**2 + 5/2*g**3 + r*g - 5/2*g**4 + 0 = 0. Calculate g.
-1, 0, 1
Let a(z) be the first derivative of z**5/45 - 13*z**4/18 + 8*z**3/3 + 45*z**2 - 84. Let f(q) be the second derivative of a(q). Factor f(v).
4*(v - 12)*(v - 1)/3
Let z be 6/(-6 - (-21)/3). Let d be z/35 + 64/160. Suppose 0*q**3 - 2/7*q**4 + 6/7*q**2 + d*q + 0 = 0. Calculate q.
-1, 0, 2
Let k = -55858/17 - -3286. Let j be 16/(-152) - 8/(-76). Factor 6/17*u + j - k*u**2.
-2*u*(2*u - 3)/17
Factor 0 - 206/9*m + 2/9*m**3 - 68/3*m**2.
2*m*(m - 103)*(m + 1)/9
Let t(r) be the first derivative of -18*r**2 - 2/15*r**6 + 26*r + 16*r**3 + 8/5*r**5 - 15 - 22/3*r**4. Let n(w) be the first derivative of t(w). Factor n(g).
-4*(g - 3)**2*(g - 1)**2
Let x(a) = -2*a**2 + 12*a - 16. Let r be x(7). Let i = 44 + r. Factor 6*u**2 - 12 - 24*u - 5*u**2 + i*u**2.
3*(u - 2)*(5*u + 2)
Factor -1/4*x**4 - 23*x**3 + 91/4 + 23*x - 45/2*x**2.
-(x - 1)*(x + 1)**2*(x + 91)/4
Let j be 12/27 + (-36623)/(-2385) + 19. Suppose -j*t - 1/5*t**2 - 7569/5 = 0. What is t?
-87
Suppose 0 = -0*o + 5*o - 135. Let x = o - 25. What is i in -77*i**x - 32*i - 10 + 81*i**2 + 74 = 0?
4
Suppose 2*m = -4*p + 416, -307 = -9*p + 6*p - 4*m. Let 22*b**3 + 71*b**3 + 27*b**3 + 7*b**2 - 245*b**5 + p*b**4 + 13*b**2 = 0. What is b?
-2/7, 0, 1
Let f be -1 - -2 - 3 - (-83 - 3666/(-47)). Factor 6/5*d**f - 2/5*d**5 + 8/5*d**2 - 4/5*d**4 + 0 - 8/5*d.
-2*d*(d - 1)**2*(d + 2)**2/5
What is t in -76*t + 151/2 + 1/2*t**2 = 0?
1, 151
Suppose 13*t - 371 = 12*t. Let a be (-1 - 0)*(-530)/t. Suppose a*v - 8/7 - 2/7*v**2 = 0. Calculate v.
1, 4
Let d(n) be the first derivative of 3*n**5/20 + 81*n**4/8 + 549*n**3/4 - 3645*n**2/2 + 6075*n + 1242. Determine l, given that d(l) = 0.
-30, 3
Let y(f) be the first derivative of -f**5/90 - 29*f**4/18 - 841*f**3/9 - 185*f**2/2 - 235. Let b(i) be the second derivative of y(i). Factor b(m).
-2*(m + 29)**2/3
Let w be 3/9 - 110/6. Let k = -21 - w. Let i(q) = -3*q**4 + 2*q**3 - q**2 + q + 1. Let z(p) = -p**4 - p**3 + p + 1. Let h(m) = k*i(m) + 3*z(m). Factor h(j).
3*j**2*(j - 1)*(2*j - 1)
Let p = -54885 + 6147039/112. Let d = 87/16 + p. Solve 18/7 - 1/7*y**2 + 3/7*y**4 - d*y + 13/7*y**3 = 0.
-