te n.
-1/4, 0
Let u(r) = -2*r + 5. Let d be u(1). Suppose c - 8 = 4*q, 5*c - d*q = 3*c + 11. Factor -62*l**2 + l**3 - 3*l**4 - c*l**3 + 3*l**5 + 65*l**2.
3*l**2*(l - 1)**2*(l + 1)
Factor -5900 + 196*q + 3007 + 4*q**2 - 3731.
4*(q - 23)*(q + 72)
Let s(g) be the third derivative of g**6/120 + 7*g**5/60 - g**4/2 + 28*g**3/3 - 258*g**2. Let r be s(-9). Factor -6*n**r + 16/3*n + 8/3*n**3 - 5/3 - 1/3*n**4.
-(n - 5)*(n - 1)**3/3
Let j(s) = 5*s**2 - 3*s + 3. Let a(p) be the third derivative of -7*p**5/12 + 5*p**4/6 - 10*p**3/3 - 4*p**2 + 11. Let n(z) = -3*a(z) - 20*j(z). Factor n(u).
5*u**2
Let f(r) be the first derivative of r**5 + 285*r**4 + 59030*r**3/3 - 339150*r**2 + 1770125*r - 3876. Find p, given that f(p) = 0.
-119, 5
Let g(y) be the first derivative of 6*y**6 - 192*y**5/5 - 260*y**4 - 424*y**3 - 266*y**2 - 72*y - 4150. Solve g(x) = 0 for x.
-2, -1, -1/3, 9
Let x(c) = -25. Let t(b) = -14*b**4 + 88*b**3 + 74*b**2 - 28*b - 350. Let f(j) = -2*t(j) + 28*x(j). Suppose f(m) = 0. What is m?
-1, 0, 2/7, 7
Let k(m) be the third derivative of -m**5/120 - 101*m**4/48 + 26*m**3 + 6*m**2 - 117*m. Solve k(p) = 0 for p.
-104, 3
Let r be 19/(-323)*11/((-242)/187). Solve -15/2 + r*j**2 + j = 0 for j.
-5, 3
Let r(l) be the second derivative of -10*l**3 - 10*l**2 + 2 - 3/2*l**5 - 65/12*l**4 - 1/6*l**6 + 11*l. What is u in r(u) = 0?
-2, -1
Let d = -4140779/5 + 828185. Factor -20*j**2 - 4 - d*j + 26/5*j**3.
2*(j - 5)*(j + 1)*(13*j + 2)/5
Let r(d) be the first derivative of d**4/8 - 5*d**3 + 53*d**2/4 + 42*d - 4118. Factor r(y).
(y - 28)*(y - 3)*(y + 1)/2
Let c(l) = -79*l**2 - 31*l + 16. Let u(m) = -72*m**2 - 29*m + 15. Let g(r) = -10*c(r) + 11*u(r). Let g(k) = 0. What is k?
-5, 1/2
Let a(l) = -l**2 + l + 2. Let h(i) = -2*i**4 - 82*i**2 - 50*i**3 + 202*i - 8 - 250*i**2 - 494*i. Let j(d) = -4*a(d) - h(d). Factor j(s).
2*s*(s + 1)*(s + 12)**2
Let c(a) = -16*a**2 - 781*a - 621. Let u be c(-48). Factor 0 - 1/12*h**u - 5/6*h**2 + 0*h.
-h**2*(h + 10)/12
Let b(c) be the third derivative of -3/4*c**5 + 0 - 6*c**2 + 1/8*c**6 + 2/21*c**7 + 0*c**3 + 5/12*c**4 + 0*c. Solve b(n) = 0.
-2, 0, 1/4, 1
Let z = -3188/33 + 8215/66. Let a = -55/2 + z. Determine u so that -12/11*u**2 - 8/11*u**3 - 6/11*u**5 + 14/11*u - a + 16/11*u**4 = 0.
-1, 2/3, 1
Let r(x) = -30*x**2 - 16415*x - 16385. Let y(u) = -u**2 - 608*u - 607. Let t(o) = -2*r(o) + 55*y(o). Solve t(l) = 0.
-1, 123
Let t(m) be the second derivative of -m**7/10080 + m**6/360 + 3*m**5/160 - 37*m**4/6 - 98*m. Let k(p) be the third derivative of t(p). Factor k(f).
-(f - 9)*(f + 1)/4
Suppose 52974*n - 53073*n = -990. Find l such that 1/5*l**2 + 49/5 + n*l = 0.
-49, -1
Factor -1/4*h**4 + 39/2*h - 7*h**3 + 0 - 49/4*h**2.
-h*(h - 1)*(h + 3)*(h + 26)/4
Let k(n) be the second derivative of -n**4/48 + 244*n**3/3 - 119072*n**2 - 17*n - 4. What is r in k(r) = 0?
976
Let d(y) be the third derivative of y**6/40 + 989*y**5/12 + 2471*y**4/9 + 366*y**3 - 219*y**2 + 4. Solve d(k) = 0.
-1647, -2/3
Let z = -128 - -125. Let i(l) = -5*l**2 + 38*l + 8*l**2 + 160 + 32 + 7*l. Let f(p) = 3*p**2 + 46*p + 192. Let d(q) = z*f(q) + 2*i(q). Solve d(u) = 0 for u.
-8
Let s(c) = c**3 - 12*c**2 + 4*c - 12. Let v be s(12). Let w be ((-225)/v)/((-1)/12). Factor 625 - 5*o**3 - 94*o - 181*o + 73*o + w*o**2 - 173*o.
-5*(o - 5)**3
Let b(z) = 4*z**2 + 7*z + 91. Let k(h) = 2*h**2 + 4*h + 50. Let c(q) = -6*b(q) + 11*k(q). Factor c(v).
-2*(v - 2)*(v + 1)
Let z(o) be the third derivative of -2*o**7/189 + 67*o**6/270 - 121*o**5/135 - 127*o**4/54 + 44*o**3/9 - 5*o**2 - 33. Solve z(a) = 0.
-1, 2/5, 3, 11
Let p(l) be the third derivative of 1/15*l**5 + 1/84*l**8 + 0*l**4 - 30*l**2 - 2/105*l**7 + 0 + 0*l**3 + 2*l - 1/30*l**6. Factor p(c).
4*c**2*(c - 1)**2*(c + 1)
Let s = 809 - -363. Let c = s + -1172. Factor c - 3/2*b + 3/4*b**2.
3*b*(b - 2)/4
Let m(s) be the first derivative of -4*s**5/5 - 163*s**4 + 3344*s**3/3 - 1344*s**2 - 55. Factor m(b).
-4*b*(b - 4)*(b - 1)*(b + 168)
Let w(p) = -7*p**3 - p**2 + 536*p - 1102. Let v(u) = -u**3 - 8*u**2 - 2*u - 1. Let i(o) = 2*v(o) - w(o). Factor i(d).
5*(d - 11)*(d - 2)*(d + 10)
Let o = 6 - 4. Let c = -107 - -117. Factor 2*w**o - 3*w**4 + w**5 + 2*w**2 + c*w**2 - 2*w**2 - 8*w - 2*w**3.
w*(w - 2)**2*(w - 1)*(w + 2)
Let k(l) be the third derivative of 12*l**2 - l - 1/100*l**5 + 3/10*l**3 + 1/20*l**4 + 0. Suppose k(a) = 0. What is a?
-1, 3
Let y(m) = 324*m**2 + 3*m - 36. Let x(i) = -325*i**2 - 3*i + 30. Let a(k) = -6*x(k) - 5*y(k). Factor a(p).
3*p*(110*p + 1)
Let v(q) be the third derivative of 0*q**4 + 0*q + 19*q**2 - 1/20*q**5 - 2 + 2*q**3. Factor v(a).
-3*(a - 2)*(a + 2)
Solve -91*u + 37/3*u**3 - 50/3 - 4/3*u**5 + 33*u**4 - 289/3*u**2 = 0.
-1, -1/4, 2, 25
Let f(u) = 30*u**2 + 134*u - 667. Let x be f(3). Find t, given that 11/3*t**3 + 0*t + 2*t**4 + 1/3*t**x + 2*t**2 + 0 = 0.
-3, -2, -1, 0
Let c = 321005 + -321003. Factor 80*v**c + 98/5*v**4 + 742/5*v**3 + 0 + 56/5*v.
2*v*(v + 7)*(7*v + 2)**2/5
Suppose 5*n - u = 6 + 17, 4*u + 20 = 2*n. Solve 18*c**n - 278*c - 696*c**3 - 270*c**2 + 98 - 422 - 289*c + 684*c**3 + 3*c**5 = 0 for c.
-3, -1, 4
Suppose -17*y + 488 + 464 = 0. Factor y*i + 90 - 36*i**2 + 16 + 4*i**3 - 18 + 8.
4*(i - 6)*(i - 4)*(i + 1)
Let g(i) be the first derivative of -74/7*i**2 + 24/7*i - 115 + 8/7*i**3. Solve g(z) = 0 for z.
1/6, 6
Let f(q) = q**3 + 7*q**2 + 5*q - 4. Let d be f(-6). Let y = 108825 - 544074/5. Suppose -9/5*p**3 - y*p - 18/5 + 3/5*p**4 - 9*p**d = 0. What is p?
-1, 6
Solve 1087*b**2 - 82*b + 1183*b**2 - 38*b**3 - 121*b**3 - 2473*b**2 + b**5 - 37*b**4 = 0 for b.
-2, -1, 0, 41
Let p(l) be the first derivative of -180 - 50/27*l**3 - 14/3*l**2 + 1/2*l**4 - 16/9*l. Determine j, given that p(j) = 0.
-1, -2/9, 4
Suppose -1443/8*f**2 + 315*f + 63/4*f**3 - 3/8*f**4 - 150 = 0. Calculate f.
1, 20
Suppose -30*j + 58 = -j. Factor -2*i + i - 7*i + 0*i**2 + i**j - 5*i**2.
-4*i*(i + 2)
Determine y so that 24*y**2 + 22*y**4 + 5*y**5 - 560*y - 6*y**3 + 560*y - 85*y**4 + 40*y**3 = 0.
-2/5, 0, 1, 12
Let v = -261/980 + 31/98. Let q(i) be the second derivative of 12*i + 1/3*i**4 + 0*i**2 + 0 + v*i**5 + 1/2*i**3. Factor q(c).
c*(c + 1)*(c + 3)
Suppose -15501 = -4*h + z, -h + 1549 = -2*z - 2321. Factor -118*x**2 - 231 + 1215*x + x**3 + 4*x**3 + h + 253*x**2.
5*(x + 9)**3
Let j = -29068 + 261224/9. Let u = -3853/90 - j. Suppose 7/5*f**4 - 2/5*f + 2/5*f**2 + 0 + 19/10*f**3 + u*f**5 = 0. What is f?
-2, -1, 0, 1/3
Let g(w) be the first derivative of -w**6/18 + 17*w**5/15 - 37*w**4/6 + 82*w**3/9 + 25*w**2/2 - 33*w - 4. Let g(d) = 0. What is d?
-1, 1, 3, 11
Factor 75/2*h**2 - 1125/2*h + 25/2*h**3 + 1/2*h**4 + 0.
h*(h - 5)*(h + 15)**2/2
Factor 2304/7 - 2307/7*j + 3/7*j**2.
3*(j - 768)*(j - 1)/7
Let v(j) be the second derivative of -j**4/66 - 512*j**3/11 - 2520*j. Determine s so that v(s) = 0.
-1536, 0
Let y = 37 - 35. Solve 361*t**3 - 380*t**4 + 59*t**y + 293*t**2 + 100*t**5 - 320*t + 64 - 105*t**3 = 0.
-1, 2/5, 2
Let g(p) be the first derivative of 0*p**3 - 30 + 0*p + 4/5*p**5 - 1/3*p**6 + 0*p**2 - 1/2*p**4. Let g(f) = 0. Calculate f.
0, 1
Suppose 48/5 + 134/5*z**2 + 556/15*z + 92/15*z**3 + 2/5*z**4 = 0. Calculate z.
-9, -4, -2, -1/3
Let l(r) be the first derivative of r**3 - 186*r**2 + 369*r - 1378. Factor l(a).
3*(a - 123)*(a - 1)
Determine t so that 150975/2*t + 225*t**4 + 50625 - 674*t**2 - 25311*t**3 - 1/2*t**5 = 0.
-1, 2, 225
Let v(k) = -3*k**2 + 360*k - 1069. Let s(j) = -21*j**2 + 2520*j - 7479. Let q(r) = -4*s(r) + 27*v(r). Let q(t) = 0. What is t?
3, 117
Let l(w) = 4*w - 41. Let y be l(11). Factor -62*d - y*d**2 + 92*d + 10 - 85.
-3*(d - 5)**2
Let m(t) be the second derivative of 32/21*t**7 - 36*t**2 + 5/6*t**4 - 65*t + 489/20*t**5 - 56/5*t**6 - 46*t**3 + 0. Factor m(s).
(s - 2)**3*(8*s + 3)**2
Let v be -17*((-24)/20 + 2/10). Factor 5*m - 253*m**2 - v*m**3 + 153*m**2 + 12*m**3 + 89 + 11.
-5*(m - 1)*(m + 1)*(m + 20)
Let r(n) be the first derivative of -2/15*n**5 - 5/6*n**4 - 30 - 8/9*n**3 + 0*n + 0*n**2. Factor r(u).
-2*u**2*(u + 1)*(u + 4)/3
Let a(i) = -123*i + 12918. Let h be a(105). Factor -1/5*w**2 - 1/10*w + 0 + 3/10*w**h.
w*(w - 1)*(3*w + 1)/10
Let z = 12092 + -12087. Let u(w) be the second derivative of 11*w - 17/15*w**4 + 0 + 3/25*w**z + 2*w**2 + 6/5*w**3. Factor u(j).
4*(j - 5)*(j - 1)*(3*j + 1)/5
Let d be 7854/935*(1 - 12/