l**4.
2*(l - 1)**2*(l + 1)**2
Let h be 44/(-16) + 3 + 75/84. Let t(f) be the first derivative of 3/14*f**4 - 11 + h*f**2 + 22/21*f**3 - 8/7*f. Factor t(q).
2*(q + 2)**2*(3*q - 1)/7
Let n(o) be the third derivative of o**11/166320 - o**10/75600 + 83*o**5/60 - 2*o**2 - 16. Let h(k) be the third derivative of n(k). Factor h(p).
2*p**4*(p - 1)
Let d = 1543/16951 + -3/737. Determine q, given that -14/23*q - d*q**2 - 12/23 = 0.
-6, -1
Let u be ((-724)/(-11765) + 8/(-30))*(-27)/6. Factor 12/13*l + u*l**3 + 2/13*l**4 + 22/13*l**2 + 0.
2*l*(l + 1)*(l + 2)*(l + 3)/13
Let y(c) = -2*c - 18. Let l be y(-10). Suppose -x + 2 - 5 = -s, -5*s + 3*x + 15 = 0. Let -l*u**3 - 5*u + 7*u**3 - s - 2 + 5*u**2 + 0 = 0. Calculate u.
-1, 1
Let t be (-9)/(-24)*2*1120/84. Let v be (23 + -11 - t) + 21/2. Let -5*h - v - 1/2*h**2 = 0. What is h?
-5
Let n = -86 - -89. Suppose -4*s + 72 = -4*i + 4, -85 = -5*s + n*i. Factor 109*b**2 - 100*b**5 + b - 120*b**4 - 61*b**2 - s*b + 44*b**3.
-4*b*(b + 1)**2*(5*b - 2)**2
Factor 29/6*z**2 + 47/3*z - 1/6*z**3 + 32/3.
-(z - 32)*(z + 1)*(z + 2)/6
Let j(h) = 11*h**4 - 253*h**3 - 264*h**2. Let y(b) = -21*b**4 + 508*b**3 + 529*b**2. Let t(a) = -11*j(a) - 6*y(a). Factor t(n).
5*n**2*(n - 54)*(n + 1)
Let r(u) be the first derivative of u**8/7560 - u**6/540 + u**5/270 - u**3/3 - 17*u**2/2 - 55. Let w(d) be the third derivative of r(d). Solve w(h) = 0 for h.
-2, 0, 1
Let l(i) = -i**5 - i**3 + i - 1. Let z(c) = -686*c**4 + c**5 - c**2 + 687*c**4 - 7*c**3 + 1 - 3 + 4*c. Let p(k) = 2*l(k) - z(k). Determine s so that p(s) = 0.
-1, 0, 2/3, 1
Let j = -1787806 - -1787806. Factor 0 + j*r - 52/3*r**2 + 2/3*r**3.
2*r**2*(r - 26)/3
Determine r so that 0*r**2 - 9/4*r**3 + 0*r + 1/4*r**5 + 2*r**4 + 0 = 0.
-9, 0, 1
Let u(s) be the second derivative of s**5/90 + 13*s**4/18 + 23*s**3/3 + 33*s**2 + 1707*s - 3. Factor u(z).
2*(z + 3)**2*(z + 33)/9
Factor -12*m - 59 - 400*m**3 + 205*m**3 + 196*m**3 + 7*m**2 - 85 + m**2.
(m - 4)*(m + 6)**2
Let i = 10394/195 + -41381/780. Suppose i*n**4 + 0 - 1/2*n**3 + 1/2*n - 1/4*n**2 = 0. Calculate n.
-1, 0, 1, 2
Let b = -140 + 147. Solve -43*u**3 - 50*u**3 + b*u**4 + 95*u**3 = 0.
-2/7, 0
Let u(h) = -2*h**2 - h + 1. Let a(r) = -9*r**2 + 14*r - 15*r - 2*r - 3. Let o(l) = a(l) - 5*u(l). Factor o(q).
(q - 2)*(q + 4)
Let h(m) be the first derivative of -m**6/10 - 3*m**5/4 + 7*m**4/2 - 76*m - 168. Let k(l) be the first derivative of h(l). Factor k(t).
-3*t**2*(t - 2)*(t + 7)
Let j be (-27014)/(-15585)*(-12)/(-26). Factor 2/5*d - j*d**2 + 2/5.
-2*(d - 1)*(2*d + 1)/5
Let t(w) be the second derivative of w**6/10 + 69*w**5/20 - 26*w**4 + 54*w**3 + 2*w - 1535. Suppose t(q) = 0. Calculate q.
-27, 0, 2
Find d, given that 3/5*d**2 + 1764/5 - 453/5*d = 0.
4, 147
Let c = 382 - 378. Determine o, given that 2 - o**4 + 7*o**c - 124*o - 44 - 78*o**2 - 6 + 4*o**3 = 0.
-3, -1, -2/3, 4
Suppose -162*i**4 - 150*i**4 - 48*i - 156*i**4 + 12*i**3 + 460*i**4 + 32*i**2 = 0. Calculate i.
-2, 0, 3/2, 2
Let a(w) = -w**4 - 56*w**3 - 111*w**2 + 17*w + 137. Let u(r) = r**4 + 28*r**3 + 55*r**2 - 9*r - 69. Let i(y) = -3*a(y) - 7*u(y). Suppose i(z) = 0. Calculate z.
-3, -2, 1
Let t be 4/26 - 693/(-143). Factor -u**t + 1204*u + 8*u**2 + 4*u**3 - 1204*u - 2*u**4.
-u**2*(u - 2)*(u + 2)**2
Let u = 51088/17675 - 84/2525. Let s be ((-5)/(-15))/((-14)/(-36)). Determine c so that -s*c**2 - 6/7 - u*c = 0.
-3, -1/3
Let c(d) be the third derivative of d**7/42 + 19*d**6/12 + 6*d**5 + 424*d**2 - d. Factor c(m).
5*m**2*(m + 2)*(m + 36)
Let f(w) = -7*w + 51. Let o be f(6). Factor 3*k + 3*k**2 + o - 4*k + 13*k.
3*(k + 1)*(k + 3)
Let t(w) = 7*w**4 - 19*w**3 + 84*w**2 + 137*w - 200. Let p(d) = -2*d**4 - 2*d**2 + d. Let x(a) = -3*p(a) - t(a). Factor x(v).
-(v - 10)**2*(v - 1)*(v + 2)
Let q be (-258)/(-6) - (-12)/(-15)*5. Suppose -q*s = -38*s - 3. Let -6/5*j**s + 3/5 + 3/5*j**4 + 3/5*j**5 + 3/5*j - 6/5*j**2 = 0. What is j?
-1, 1
Let f(x) be the second derivative of -1/8*x**3 - 1/48*x**4 + 36*x - 1/4*x**2 + 0. Factor f(i).
-(i + 1)*(i + 2)/4
Let d = 1755 + -1188. Let b = d + -205. Factor -4*u**4 - 4*u**5 + b*u**2 - 362*u**2.
-4*u**4*(u + 1)
Let x = -2016 + 2019. Suppose 0 = -3*c - 3*l - 9, l = 2*c - 3 - 6. Determine h, given that 13*h**5 - 11*h**4 + 11*h**x - 4*h**5 - 7*h**4 - c*h**2 = 0.
0, 1/3, 2/3, 1
Let l = 3750 + -74511/20. Let m(w) be the second derivative of l*w**5 + 12*w**2 + 0 + 9/2*w**6 + 34*w**3 + 2*w + 89/2*w**4. Solve m(y) = 0.
-2, -1, -2/5, -2/9
Solve 19/2*z**3 + 0*z**2 + 0*z - 1/2*z**5 + 9*z**4 + 0 = 0 for z.
-1, 0, 19
Let u(b) = -b**3 - 9*b**2 + 10*b - 11. Let w be u(4). Let a = w - -359/2. Factor 2 + 3*r**3 + 6*r + a*r**4 + 13/2*r**2.
(r + 1)**2*(r + 2)**2/2
Let y be 1/(-4)*152/(-38). Let o be y - (6 + (-1 - 6)). Factor -64/3 + 32/3*p - 4/3*p**o.
-4*(p - 4)**2/3
Suppose 6*u - 27 = -9. Factor -4*x - 39751*x**4 - 3*x**u - 2*x**5 + 39761*x**4 - 15*x**3 + 14*x**2.
-2*x*(x - 2)*(x - 1)**3
Suppose -87044 + 86938 = -53*v. Suppose -14/3*q**v - 10/3*q**3 - 2*q + 0 - 2/3*q**4 = 0. Calculate q.
-3, -1, 0
Let k = 88 - 41. Let u be (11/33)/(k/(-24) + 2). Factor -35*z**3 + 0*z**5 + 47*z**3 + 0*z**2 - u*z**2 - 4*z**5.
-4*z**2*(z - 1)**2*(z + 2)
Factor -1672/3*k**2 - 272/3*k**4 - 280/3 - 2/3*k**5 + 1108/3*k**3 + 1118/3*k.
-2*(k - 1)**4*(k + 140)/3
Let c(d) be the third derivative of -d**6/24 - 17*d**5/12 - 275*d**4/24 - 65*d**3/2 - 3*d**2 - 69. Find k such that c(k) = 0.
-13, -3, -1
Let y(f) = f**3 + 359*f**2 + 1048*f - 12. Let o be y(-3). Factor -o*k**2 - 306/5*k - 32/5*k**3 - 108/5.
-2*(k + 6)*(4*k + 3)**2/5
Let c = -282436 - -1977067/7. Solve -c*w - w**2 - 9/7 - 1/7*w**3 = 0 for w.
-3, -1
Let z(l) be the first derivative of 14*l**6/15 + 23*l**5/5 + 9*l**4 + 26*l**3/3 + 4*l**2 + 77*l + 96. Let t(n) be the first derivative of z(n). Solve t(g) = 0.
-1, -2/7
Let w(i) = i**2 + i. Let p(c) = 2*c**3 - 2*c**2 + 44*c. Suppose -27*z = -21*z - 264. Let n(f) = z*w(f) - 2*p(f). Factor n(o).
-4*o*(o - 11)*(o - 1)
Let x = 93 - 21. Let p = x - 70. Factor -3*n**2 + 9 - n**2 + 12*n - 6*n + n**p.
-3*(n - 3)*(n + 1)
Factor -1/8*k**4 + 33/8*k + 35/8*k**2 - 33/8*k**3 - 17/4.
-(k - 1)**2*(k + 1)*(k + 34)/8
Let t = -319 - -1597/5. Let a = -206 + 208. Let 0 - t*w + 2/5*w**a = 0. What is w?
0, 1
Let b = -294 + 326. Suppose -2*o - b = -10*o. Suppose 0 + 1/3*f**5 + 0*f + 0*f**2 + 0*f**o + 0*f**3 = 0. Calculate f.
0
Suppose 2*v + 2*d = 2, 4*v + 2*d - 3 = -3*d. Let o be (3 + (-136)/42)/((20/200)/(54/(-75))). Factor -2/7*c**2 + v*c - o.
-2*(c - 6)*(c - 1)/7
Let k(l) be the third derivative of l**8/4032 + l**7/63 + l**5/4 + l**4/12 + 210*l**2. Let w(s) be the third derivative of k(s). Factor w(h).
5*h*(h + 16)
Let o be (-2 - -7)*-3*(-6 - -5). Let q(t) be the third derivative of 0*t**3 + 1/160*t**6 - o*t**2 + 1/40*t**5 + 0 + 0*t**4 + 0*t. Factor q(u).
3*u**2*(u + 2)/4
Let q(l) be the second derivative of l**4/132 + 40*l**3/3 + 8800*l**2 - 160*l - 1. Let q(g) = 0. What is g?
-440
Let n(u) be the first derivative of 3*u**4/4 + 168*u**3 + 15903*u**2/2 - 467046*u - 4699. Factor n(j).
3*(j - 18)*(j + 93)**2
Factor -1/4*w**2 - 36 - 51/4*w.
-(w + 3)*(w + 48)/4
Let t(z) be the first derivative of 265 + 5/7*z**2 - 100/7*z + 11/14*z**4 + 22/7*z**3 + 2/35*z**5. What is d in t(d) = 0?
-5, -2, 1
Let h(v) be the first derivative of 3*v**4/8 + 10*v**3 + 111*v**2/4 + 27*v + 4609. Find a, given that h(a) = 0.
-18, -1
Let a be -46 + 61 - -1*(-9 - 4). Find v such that 1/4*v - 3/4 + 3/4*v**a - 1/4*v**3 = 0.
-1, 1, 3
Let x be 460/(-13) + (-1478 - -1514). Find u such that 6/13*u**2 - x - 8/13*u = 0.
-2/3, 2
Let t(b) be the first derivative of b**3/6 + 429*b**2/4 + 214*b + 5594. Factor t(h).
(h + 1)*(h + 428)/2
Let y = 5765/6 + -1919/2. Let -4 + y*d - 4/3*d**3 + 4*d**2 = 0. Calculate d.
-1, 1, 3
Suppose o + 18 = -4*p, 5*p + 38 = 13. Factor 0 - 4/7*l - 2/7*l**o.
-2*l*(l + 2)/7
Let l(p) = -32*p**2 + 210*p - 212. Let n(z) = -11*z**2 + 70*z - 71. Let j be (-1 + 18)*(26 - 27). Let x(d) = j*n(d) + 6*l(d). Let x(y) = 0. Calculate y.
1, 13
Let f(x) = -x**3 - 7*x**2 - 635*x - 2490. Let b be f(-4). Factor -2*s**4 - 9/2*s**3 + 0 - 1/4*s**5 - 4*s**b - 5/4*s.
-s*(s + 1)**3*(s + 5)/4
Let r(f) = 63*f**2 - 84*f - 48. Let g(u) be the third derivative of -13*u**5/60 + 17*u**4/24 + 5*u**3/3 + 22*u**2. Let o(y) = 24*g(y) + 5*r(y). Factor o(q).
3*q*(q - 4)
