- 92*t**2 + 48*t + 4*t**5 + 28*t**2.
4*t*(t - 1)**2*(t + 2)*(t + 6)
Let x(m) be the first derivative of -3*m**5/20 - 513*m**4/4 - 29581*m**3 - 174420*m**2 - 346800*m + 3781. Let x(j) = 0. Calculate j.
-340, -2
Let g(z) = z**4 - 2*z**3 + z**2 + 1. Let c(v) = -20*v**4 + 164*v**3 + 52*v**2 - 1044*v - 1032. Let r(t) = c(t) + 24*g(t). Find l, given that r(l) = 0.
-28, -3, -1, 3
What is s in -507*s**4 + 64*s**2 + 180*s**3 - 239*s**2 + 502*s**4 = 0?
0, 1, 35
Let k = -771 + 769. Let r be 435/4640*(1 + k/(-6)). Let 0 - 1/4*d**2 - 1/8*d - r*d**3 = 0. Calculate d.
-1, 0
Suppose -5*c = -7*g + 76 - 121, 0 = -5*c - 4*g - 10. Let n(k) = k**2 + 5. Let a be n(0). Solve 2*r**c + 1/2*r - r**4 - r**3 + 1/2*r**a - 1 = 0.
-1, 1, 2
Let g be (-520)/143*37/(-148). Factor 0 - 2/11*n**3 - 8/11*n - g*n**2.
-2*n*(n + 1)*(n + 4)/11
Let n = -881 - -2618/3. Let x = 29/3 + n. Factor 8/3*t**2 + 1/6 + x*t.
(4*t + 1)**2/6
Let 3/4*h**5 - 1881/2*h**2 + 1881/2*h**4 + 0*h + 0 - 3/4*h**3 = 0. What is h?
-1254, -1, 0, 1
Let m(o) be the second derivative of o**6/330 - 7*o**5/110 + 13*o**4/132 - o + 474. Let m(k) = 0. What is k?
0, 1, 13
Let h(p) = p - 14. Let k be h(12). Let j be 3/(-15) + k/(340/(-54)). Factor 2/17*q + 0 + j*q**2.
2*q*(q + 1)/17
Let z(d) = 7*d**3 + 31*d**2 + 44*d + 17. Let p(b) = -36*b**3 - 156*b**2 - 220*b - 84. Suppose 90 - 105 = 5*l. Let w(g) = l*p(g) - 16*z(g). Solve w(f) = 0.
-5, -1
Let y(l) be the first derivative of -3*l**3 + 1/5*l**5 + 12*l + 0*l**4 - 2*l**2 + 120. Factor y(d).
(d - 3)*(d - 1)*(d + 2)**2
Let o(r) be the second derivative of r**7/294 - 11*r**6/840 + r**5/210 - r**2/2 + r - 12. Let y(t) be the first derivative of o(t). Factor y(b).
b**2*(b - 2)*(5*b - 1)/7
Suppose 24 = -4*o + 3*w + 27, 3*o = 2*w + 4. Let d(q) be the first derivative of -2/27*q**3 + 0*q - o + 2/9*q**2. Factor d(z).
-2*z*(z - 2)/9
Let c(k) = -2*k**3 + 17*k**2 - 68*k + 85. Let v(i) = 7650*i**2 - 3*i**3 - 7625*i**2 + 127 - 101*i + 0*i**3. Let r(d) = 8*c(d) - 5*v(d). Factor r(n).
-(n - 5)*(n - 3)**2
Let i(h) = -20*h**2 + 499*h + 29. Let r be i(25). Let d(k) be the first derivative of 0*k**2 - 1/6*k**3 + 1/8*k**r + 0*k + 18. Factor d(p).
p**2*(p - 1)/2
Let x = -4 - -7. Let b(s) = -s**2 - 16*s - 43. Let u be b(-11). Determine r, given that 2*r**2 - 12*r**2 + u*r**2 - 2*r**x - 2*r**3 + 2*r**4 = 0.
0, 1
Let m(v) be the first derivative of -3*v**4/4 - 392*v**3 - 114063*v**2/2 + 232854*v + 96. Factor m(r).
-3*(r - 2)*(r + 197)**2
Suppose -5*t = -2*l - 327, -31*l - 3*t = -29*l + 287. Let a = l - -759/5. Determine r so that -4/5*r**3 + 2/5*r**2 + 0 - 2/5*r**4 + a*r = 0.
-2, -1, 0, 1
Let p(i) be the second derivative of 4*i**6/5 - 39*i**5/5 + 129*i**4/8 - 45*i**3/4 + 3283*i. Factor p(x).
3*x*(x - 5)*(4*x - 3)**2/2
Let g(r) = 5*r**2 - 608*r + 4311. Let s be g(7). Let -s*t**4 + 0 - 30*t - 1175/2*t**3 - 250*t**2 + 135/2*t**5 = 0. What is t?
-1, -1/3, -2/9, 0, 6
Let t(y) = 17*y**2 - 46*y + 29. Let p(h) = 13*h**2 - 41*h + 28. Let s(v) = 4*p(v) - 3*t(v). Solve s(n) = 0.
1, 25
Let c(y) = -8*y**3 - 106*y**2 - 468*y - 537. Let q(j) = 7*j**3 + 109*j**2 + 472*j + 538. Let i(g) = 2*c(g) + 3*q(g). Determine p so that i(p) = 0.
-18, -3, -2
Let j = 86369/4 - 43183/2. Find s such that -j*s - 3/2 + 3/4*s**2 = 0.
-1, 2
Let h(x) be the first derivative of 0*x**4 - 3/5*x**5 + 3*x**3 + 3*x**2 - 66 + 0*x. Factor h(o).
-3*o*(o - 2)*(o + 1)**2
Suppose 3*m - 2*n = -669, 26*n = -2*m + 25*n - 453. Let c be (90/m)/((-2)/10). Suppose y + 0 - 7/3*y**c = 0. What is y?
0, 3/7
Let x(g) be the third derivative of g**5/60 - 3*g**4/4 - g**3/3 + 23*g**2. Let n be x(19). Suppose 0*z**2 + z**2 + n*z - 30*z + 14*z = 0. Calculate z.
-1, 0
Let h(r) be the third derivative of -r**6/24 - 2*r**5/3 + 15*r**4/8 + 2*r**2 - 2*r - 539. Suppose h(k) = 0. What is k?
-9, 0, 1
Let a(j) be the first derivative of 0*j + 0*j**2 + 1/120*j**4 + 2/3*j**3 + 1/3600*j**6 - 7 + 1/400*j**5. Let p(d) be the third derivative of a(d). Factor p(r).
(r + 1)*(r + 2)/10
Let t(q) = -26*q**3 - 54*q**2 + 8*q + 8. Let z(p) = -28*p**3 - 59*p**2 + 10*p + 10. Let u(m) = 5*t(m) - 4*z(m). Solve u(a) = 0 for a.
-17/9, 0
Let w(f) be the second derivative of -f**4/42 - 31*f**3/3 - 642*f**2/7 + 6266*f. Factor w(y).
-2*(y + 3)*(y + 214)/7
Let v(f) = -f**3 + 4*f**2 + 17*f - 14. Let l be v(8). Let p = 676/5 + l. What is i in -p + 21/5*i - 6/5*i**2 - 9/5*i**3 = 0?
-2, 1/3, 1
Let l be (-12 - (-896)/72)/(-22*10/(-2805)). Factor 16/3*u**2 + l*u**4 - 65/6*u**3 + 0 + 0*u - 1/6*u**5.
-u**2*(u - 32)*(u - 1)**2/6
Let z(q) be the second derivative of -2*q + 0*q**3 - 11*q**2 + 1/30*q**5 + 0 - 1/4*q**4. Let i(r) be the first derivative of z(r). Factor i(o).
2*o*(o - 3)
Suppose -2*w = -0*w + 5*v - 288, 4*w = 2*v + 576. Factor -295*p**2 - 95*p - 76 + w*p**2 + 146*p**2 - 14.
-5*(p + 1)*(p + 18)
Let f(g) be the second derivative of g**7/420 - g**6/180 - g**5/10 - 5*g**3 + 3*g**2/2 - 56*g. Let v(o) be the second derivative of f(o). Solve v(t) = 0.
-2, 0, 3
Let j(i) be the second derivative of i**5/110 - i**4/66 - 4*i**3/33 + 4*i**2/11 - 2603*i. Let j(s) = 0. What is s?
-2, 1, 2
Let t(a) be the third derivative of a**8/336 + a**7/84 + 11*a**3/3 - 61*a**2. Let k(h) be the first derivative of t(h). Factor k(l).
5*l**3*(l + 2)
Let o be ((-108)/10)/((-57)/((-10545)/(-148))) + -11. Find d, given that -11/4 + o*d + 1/4*d**2 = 0.
-11, 1
Let t = -577 - -580. Let x(h) = h - 2. Let n be x(4). Factor -3*z**3 - 6*z**n + 6*z - t*z + 4*z**4 + 2*z**4.
3*z*(z - 1)*(z + 1)*(2*z - 1)
Suppose 0*g + 180 = 5*g. Factor 14 + 22 + 38*b**2 - 22*b - g*b**2.
2*(b - 9)*(b - 2)
Let k(s) be the third derivative of -s**5/60 + 11*s**4/24 - 7*s**3/2 + 10*s**2. Let u be k(8). Find d, given that d + 3*d - d**3 + 6 + u*d = 0.
-2, -1, 3
Let w(z) be the second derivative of z**4/18 + 16*z**3/3 - 51*z**2 - 2148*z. Factor w(y).
2*(y - 3)*(y + 51)/3
Let d(n) = 3*n**2 - n + 2. Let h be d(1). Suppose 2*z - 19 = -v + 12, -4*z - 3*v + 65 = 0. Let 4*s**3 - 10*s**4 - 2*s**2 - 6*s**4 + z*s**h = 0. Calculate s.
0, 1
Let k(w) = -5*w**3 - 314*w**2 + 8190*w + 8450. Let f(l) = 3*l**3 + 161*l**2 - 4095*l - 4225. Let y(c) = 7*f(c) + 4*k(c). Factor y(q).
(q - 65)**2*(q + 1)
Let n(z) be the second derivative of -z**6/420 + 2*z**5/105 + z**4/84 - 4*z**3/21 - 35*z**2 + z + 21. Let x(a) be the first derivative of n(a). Factor x(q).
-2*(q - 4)*(q - 1)*(q + 1)/7
Solve 1274*q - 1938*q**5 + 17565*q**2 + 1933*q**5 + 295*q**4 + 1063*q**3 - 6048*q**3 - 36424 + 12496*q - 51056 = 0 for q.
-2, 3, 4, 27
Let y be (-3)/13 - (-4 + -6 + (-7100)/(-780)). Solve 2/3*z**3 - y*z**5 + 0 + 2/3*z**4 - 2/3*z**2 + 0*z = 0.
-1, 0, 1
Let b = 72 - 56. Let x(f) = f**3 - 14*f**2 - 28*f - 61. Let w be x(b). Find i such that 4/13 - 24/13*i**2 - 14/13*i**w - 6/13*i = 0.
-1, 2/7
Let w(o) be the second derivative of o**7/105 - 7*o**6/25 + 12*o**5/5 - 10*o**4/3 + 154*o - 3. Factor w(p).
2*p**2*(p - 10)**2*(p - 1)/5
Let z(r) be the third derivative of 16*r**2 + 5/12*r**4 + 0*r + 7/12*r**6 + 5/168*r**8 + 3/14*r**7 + 0 + 3/4*r**5 + 0*r**3. Suppose z(v) = 0. Calculate v.
-2, -1, -1/2, 0
Let o(m) be the third derivative of 1/30*m**5 + 1/12*m**4 - 1/105*m**7 - m**2 - 1/60*m**6 + 0*m**3 + 3*m + 0. Factor o(z).
-2*z*(z - 1)*(z + 1)**2
Let p(i) be the second derivative of i**6/15 - 247*i**5/40 + 109*i**4/4 - 293*i**3/12 - 59*i**2/2 - 1636*i. Determine b, given that p(b) = 0.
-1/4, 1, 2, 59
Let m(u) be the third derivative of -u**8/1680 + u**7/210 + u**6/20 + u**5/6 + 233*u**4/24 + 158*u**2. Let f(g) be the second derivative of m(g). Factor f(a).
-4*(a - 5)*(a + 1)**2
Factor 1/3*y**2 - 382/3 + 63*y.
(y - 2)*(y + 191)/3
Let z(a) be the third derivative of 19*a**6/40 - 9*a**5/20 - 7*a**4/2 - 3*a**2 - 43*a - 23. Factor z(u).
3*u*(u + 1)*(19*u - 28)
Suppose 0 = -2*r + 3*d + 29, -4*r + 55 = 13*d - 16*d. What is o in 22*o**3 + 20*o - 4*o**3 + 20*o**2 - r*o**3 = 0?
-2, 0
Suppose 2*b - 24 = 20*g - 24*g, -5*b - g = -6. Suppose 2*s = -2*s + 4*i - 4, -3*s - 4*i = -25. Solve -4*t**s - 16/3*t**2 + b - 4/3*t = 0.
-1, -1/3, 0
Let f(p) be the third derivative of p**5/60 - 5*p**4/24 - 34*p**3 + 150*p**2. Find m such that f(m) = 0.
-12, 17
Let f be 17 + -15 + (14286/(-22))/3. Let i = f + 215. Suppose i - 8/11*q**3 - 26/11*q + 32/11*q**2 = 0. Calculate q.
1/2, 3
Suppose k + r = -4, 8 = -3*k - 0*k - r. Let w be 9/(