 1
Let j(p) be the second derivative of 0*p**2 + 0 + 90*p + 23/6*p**3 + 1/12*p**4. Solve j(d) = 0 for d.
-23, 0
Let f(j) = 85*j**2 - 388005*j + 443027495. Let z(r) = -5*r**2 + 22824*r - 26060441. Let g(p) = -2*f(p) - 35*z(p). Solve g(c) = 0.
2283
Suppose -c = 4*k - 2*k + 40, -4 = -k. Let f = 51 + c. Determine i, given that -8*i + i**2 - 8 + 2*i**f - 3*i**2 + 4*i**2 = 0.
-2, -1, 2
Let u(k) be the second derivative of -13/18*k**3 + 1/36*k**4 - 7/3*k**2 - 33*k - 1. Let u(h) = 0. Calculate h.
-1, 14
Let c(y) be the second derivative of -y**6/15 - 7*y**5/2 + 6*y**4 - 4817*y. Determine o, given that c(o) = 0.
-36, 0, 1
Let z = -97751/6 - -16292. Let x(l) be the third derivative of 0*l + 8*l**2 - 2/105*l**7 + 0 + 1/10*l**6 + 0*l**3 + z*l**4 - 1/5*l**5. Factor x(a).
-4*a*(a - 1)**3
Let f(n) = -5*n + 4*n**2 - 3*n**2 - 45*n - 30*n - 3*n**2 - 798. Let a(c) = 1. Let r(h) = 2*a(h) - f(h). Factor r(p).
2*(p + 20)**2
Let g(v) be the third derivative of v**4 - 31*v**2 - 7/30*v**5 + 4/3*v**3 + 0*v + 0. Solve g(l) = 0 for l.
-2/7, 2
Factor -2020/9 + 2/9*j**2 - 1006/9*j.
2*(j - 505)*(j + 2)/9
Let l = -51/58 - -429/290. Let v = 2/111 - -656/555. Suppose -3/5 - v*w + l*w**4 + 6/5*w**3 + 0*w**2 = 0. What is w?
-1, 1
Let d(x) = -x**4 + 30*x**3 + 31*x**2 - 9*x - 3. Let v(w) = -29*w**3 - 32*w**2 + 9*w + 4. Let l(q) = -4*d(q) - 3*v(q). Factor l(y).
y*(y - 9)*(y + 1)*(4*y - 1)
Let w(u) be the third derivative of u**6/900 - 44*u**5/225 + 484*u**4/45 + 911*u**2. Factor w(i).
2*i*(i - 44)**2/15
Let -20808/7*i - 412/7*i**4 + 0 - 2/7*i**5 - 42024/7*i**2 - 21626/7*i**3 = 0. Calculate i.
-102, -1, 0
Let l(a) = 20*a - 31. Suppose 0 = 2*t - 3*s - 8, 0*s + 15 = 3*t - 3*s. Let i be l(t). Factor -h**4 + 12*h**2 - 12*h**3 + 105*h + 5*h**4 - i*h.
4*h*(h - 1)**3
Suppose 21*n + n**2 - 63 - 90 - 29 + 20 = 0. What is n?
-27, 6
Let y(r) be the first derivative of 3*r**4 - 76*r**3/3 + 40*r**2 - 371. Factor y(b).
4*b*(b - 5)*(3*b - 4)
Let -8/15*i**5 + 266/15*i**2 - 352/15*i**4 + 88/15*i + 2/5*i**3 + 0 = 0. Calculate i.
-44, -1/2, 0, 1
Suppose -4*l - 2*r - 1930 = 0, -1441 = 3*l - 3*r - 2*r. Let q = l + 482. Factor 1/5*y**4 - 1/5*y - 1/5*y**2 + q + 1/5*y**3.
y*(y - 1)*(y + 1)**2/5
Suppose -43*w + 116*w - 61 = 158. Factor -6/5*c**2 + 0 + 2/5*c**w + 4/5*c.
2*c*(c - 2)*(c - 1)/5
Suppose 0 = 952*v - 951*v. Let p(a) be the third derivative of 2/27*a**3 + 0 + v*a + 26*a**2 + 5/108*a**4 - 1/90*a**5. Factor p(j).
-2*(j - 2)*(3*j + 1)/9
Suppose 2*t + 326 = -3*o + 329, -2*t + 13*o + 19 = 0. Factor 3/4*n**3 - 15/4*n**2 + 0 + t*n.
3*n*(n - 4)*(n - 1)/4
Factor -3/5*o**3 + 351/5*o + 1512/5 - 12*o**2.
-3*(o - 7)*(o + 3)*(o + 24)/5
Let j = -12422 + 62111/5. Let a(w) be the third derivative of w**4 + 0*w + j*w**5 + 0 + 1/60*w**6 + 8/3*w**3 + 15*w**2. Determine b so that a(b) = 0.
-2
Let c(w) = -w**5 + w**4 + w**3 + w. Let o = 230 - 226. Let a(b) = 6*b**5 + 8*b**4 + 16*b**3 - 26*b - 12. Let k(h) = o*c(h) + a(h). Determine x so that k(x) = 0.
-3, -2, -1, 1
Let f(y) be the third derivative of -89*y**2 + 2/3*y**5 + 1/10*y**6 + 0*y - 16/3*y**3 + 0 + 2/3*y**4. Suppose f(l) = 0. What is l?
-2, 2/3
Factor 2954*c**3 + 906*c**4 - 1804*c**4 + 1033704*c**2 + 671*c**3 - 101648736 + 100611504*c + 902*c**4 - 101*c**3.
4*(c - 1)*(c + 294)**3
Let s = 85064 + -48060914/565. Let t = s - 4/113. Factor 0*q + 0 - 2/5*q**3 + t*q**2.
-2*q**2*(q - 1)/5
Let q be 12*(2/(-4) - -1). Suppose -j = u - 2, -10 = q*u - 11*u - 4*j. Factor -3/7*a**u + 18/7 + 15/7*a.
-3*(a - 6)*(a + 1)/7
Let o(f) be the third derivative of 1/8*f**4 - 93*f**2 - 11/9*f**3 + 0*f + 1/15*f**5 + 1/360*f**6 + 0. Factor o(n).
(n - 1)*(n + 2)*(n + 11)/3
Factor 158*t**3 - 45*t - 670*t**3 + 138*t**3 + 5*t**4 + 147*t**3 + 95*t**2 + 172*t**3.
5*t*(t - 9)*(t - 1)**2
Let d(j) be the third derivative of j**5/5 - 571*j**4/8 - 143*j**3/2 + 791*j**2 - 1. Factor d(h).
3*(h - 143)*(4*h + 1)
Let a(z) be the first derivative of 2*z**5/5 - 79*z**4/8 + 52*z**3 + 499*z**2/4 + 52*z - 7104. Suppose a(x) = 0. Calculate x.
-1, -1/4, 8, 13
Let p = -2402 + 9178. Factor -x**3 + p*x + 2*x**3 + 38*x**2 - 185193 + 2971*x - 209*x**2 + 0*x**2.
(x - 57)**3
Let i(t) be the first derivative of -1/48*t**4 + 0*t**3 + 15*t + 1/8*t**2 + 3. Let h(p) be the first derivative of i(p). Suppose h(s) = 0. What is s?
-1, 1
Let x(o) be the third derivative of 7/90*o**5 + 126*o**2 + 0*o**4 - 23/360*o**6 + 0 + 0*o + 0*o**3 + 1/210*o**7. Determine g so that x(g) = 0.
0, 2/3, 7
Let w = -323616 + 323616. Find k such that 22/3*k**3 + 32/3*k**4 + w + 14/3*k**5 + 4/3*k**2 + 0*k = 0.
-1, -2/7, 0
Let q(n) = 10*n**3 + 20*n**2 - 540. Let z(p) = p**3 - 5*p**2. Let v(u) = q(u) - 5*z(u). Determine s, given that v(s) = 0.
-6, 3
Let w = 2030993/7 - 290139. Solve -w - 6/7*f + 2/7*f**2 = 0 for f.
-2, 5
Let l(q) be the first derivative of -1 - 1/2*q**4 - 6*q**3 - 8*q**2 + 0*q. Let l(r) = 0. Calculate r.
-8, -1, 0
Suppose 3*k + 45 = 0, -598*w + 601*w - 3 = -k - 18. Factor w - 10/13*a**3 - 6/13*a - 14/13*a**2 - 2/13*a**4.
-2*a*(a + 1)**2*(a + 3)/13
Let -431319*j + 324723 - 4982*j**3 + 505*j**3 - 6518*j**3 - 3*j**5 - 51*j**3 + 117318*j**2 + 327*j**4 = 0. Calculate j.
1, 7, 47
Let y(b) = -6*b - 15. Let u be y(-3). Find x such that 40 + 14008*x**2 - 5*x + 5*x**u + 0*x**3 - 14048*x**2 = 0.
-1, 1, 8
Let a be (-3)/(80 - -1) + 60706/12906. Suppose -i + s - 4 = 0, 8 = 2*s - 0. Suppose a*c**2 - 4/3*c - 10/3*c**3 + i = 0. Calculate c.
0, 2/5, 1
Factor -338633*l**2 + 22556880*l - l**4 - 2*l**4 - 7*l**4 - 22180932 + 6*l**4 - 39439*l**2 + 2128*l**3.
-4*(l - 177)**3*(l - 1)
Suppose -5*b + 10 = 0, 11*c - 5*b - 14 = 7*c. Let o(f) be the first derivative of -c + 1/7*f**3 + 1/14*f**2 - 3/7*f - 1/28*f**4. Let o(v) = 0. What is v?
-1, 1, 3
Let d(l) be the first derivative of -l**4/20 - 11*l**3/30 - 3*l**2/5 - 40*l - 64. Let j(o) be the first derivative of d(o). Find y, given that j(y) = 0.
-3, -2/3
Suppose 107 - 107 = -8*d. Let w be 380/(-1216)*(-6)/5. Factor d*o + w - 3/8*o**2.
-3*(o - 1)*(o + 1)/8
Let r(d) be the first derivative of 2*d**6/9 - 226*d**5/3 + 234*d**4 - 2242*d**3/9 + 280*d**2/3 + 754. Find i, given that r(i) = 0.
0, 1/2, 1, 280
Let f(u) = -u**2 - 5*u. Let j(b) = 3*b**2 + 22*b + 32. Let r(z) = -2*f(z) - j(z). Determine c so that r(c) = 0.
-8, -4
Let o = -585 + 817. Suppose o*u = 223*u + 36. Find s such that 0*s**3 + 0 + 0*s - 2/7*s**u + 0*s**2 = 0.
0
Let g(v) = 12*v**3 - 2*v**2 - 15*v + 8. Let b be g(4). Let m be b/152 - 1/2. Solve -3/5*w**5 + 6/5*w**m + 21/5*w - 6/5 - 24/5*w**2 + 6/5*w**3 = 0.
-2, 1
Let m(h) be the first derivative of -9*h**4/4 + 28*h**3 + 59*h**2/2 + 10*h - 6699. Determine n, given that m(n) = 0.
-1/3, 10
Determine c, given that 0 - 2178*c**5 - 504/5*c**2 + 16/5*c + 3524/5*c**3 + 7854/5*c**4 = 0.
-2/5, 0, 2/33, 1
Suppose -m - 5*i = 5, 3 = -6*m + 10*m - 3*i. Suppose 5*b - 9 = 3*u, -2*b + 4*u = -m*u + 2. What is r in -3/5*r**b + 0*r + 12/5 - 9/5*r**2 = 0?
-2, 1
Factor 592/3*k - 294*k**2 - 8/9.
-2*(3*k - 2)*(441*k - 2)/9
Let 194*w**3 - 10 - 609*w**5 + 10 - 46*w**4 - 258*w**2 + 1233*w**5 + 108*w - 622*w**5 = 0. Calculate w.
0, 1, 3, 18
Let u(d) be the second derivative of d**4/20 - 133*d**3 + 265335*d**2/2 - 717*d. Suppose u(g) = 0. Calculate g.
665
Let d be 1/(-7) - (-54 - 34466/(-798)). Factor -5/3*f**4 - d*f**3 + 0 - 19*f**2 - 6*f.
-f*(f + 3)**2*(5*f + 2)/3
Let 0*f**4 + 0*f - 1/3*f**5 - 2*f**2 + 7/3*f**3 + 0 = 0. What is f?
-3, 0, 1, 2
Let m(k) be the second derivative of -4913/2*k**2 + k + 10 + 1/20*k**5 + 289/2*k**3 - 17/4*k**4. Suppose m(n) = 0. What is n?
17
Let a(v) be the second derivative of -1/4*v**2 - 2*v - 1/80*v**5 + 1/24*v**4 - 14 + 1/24*v**3. Factor a(j).
-(j - 2)*(j - 1)*(j + 1)/4
Suppose -32901*i + 32880*i + 63 = 0. Let n(m) be the first derivative of 0*m + 3/2*m**4 - 18 + 8/3*m**i - 14/15*m**5 - 4/3*m**2. Let n(l) = 0. What is l?
-1, 0, 2/7, 2
Let 88*k**3 - 890/3*k**2 - 290/3 - 364*k - 8/3*k**4 = 0. What is k?
-1/2, 5, 29
Let u(i) be the third derivative of -2*i**2 + 0*i - 1/600*i**6 + 0*i**5 - 3 + 0*i**3 + 1/30*i**4. Factor u(a).
-a*(a - 2)*(a + 2)/5
Let i(y) be the second derivative of 7*y**5/2 + 195*y**4/8 + 190*y**3/3 + 75*y**2 + 4*y - 742. Determine b, given that i(b) = 0.
-2, -10/7, -3/4
Suppose 3*f + 21 = 2*h + 13, 0 = 3*f + 5*h - 20. Let d be (4 - f - (-195)/135) + -5. Factor -2/9 + d*t - 2/9*t*