. Factor 0 + g*u + 1/8*u**2.
u*(u + 1)/8
Let p(i) = -1. Let g(m) = -5*m**2 + 6*m + 5. Let z(x) = -g(x) + p(x). Let h(r) = 11*r**2 - 13*r - 13. Let a(f) = -4*h(f) + 10*z(f). Factor a(t).
2*(t - 2)*(3*t + 2)
Suppose 2*a = -12*a - 5*a. Let t = -30/7 - -552/119. Factor 4/17*d**2 - t*d**3 + a*d + 2/17*d**4 + 0.
2*d**2*(d - 2)*(d - 1)/17
Let h be (-4)/1 + 659 + 16 + -18. Let r = h + -653. Solve 2/13*t**4 + 0*t + r + 6/13*t**3 + 4/13*t**2 = 0.
-2, -1, 0
Let s = -186633/4 - -46659. Find b such that -189/4*b + 45/4*b**2 - s*b**3 + 147/4 = 0.
1, 7
Determine i so that 101/2*i - 297 - 1/6*i**2 = 0.
6, 297
Let r be 4/(-12)*-2*3/2. Let t be (-3*r - (-12 + 9))/(-2). Find s, given that t*s + 4/5*s**3 + 0*s**2 + 0 = 0.
0
Let j(m) be the third derivative of -1/42*m**8 + 2/21*m**7 + 91*m**2 - 1/3*m**5 + 0*m + 1/3*m**4 + 0*m**6 + 0*m**3 + 0. Determine f so that j(f) = 0.
-1, 0, 1/2, 1, 2
Let b = 27/3838 - -15163/26866. Suppose -n + 2 = -0. Solve -10/7*m + b - n*m**2 = 0 for m.
-1, 2/7
Let l(i) be the first derivative of -3/4*i**4 - 128 + 9/2*i**2 - 6*i + 0*i**3. Factor l(d).
-3*(d - 1)**2*(d + 2)
Suppose -160/13 + 2/13*w**2 - 158/13*w = 0. Calculate w.
-1, 80
Let q = -16090 - -16092. Let t(n) be the second derivative of 0 + 15/2*n**q + 3/4*n**4 + 3/20*n**5 - 9/2*n**3 + 43*n. Solve t(c) = 0.
-5, 1
Suppose -c + 388 - 385 = 0. Let i be c/5 - 57/(-35)*2. Let -9/7*m**4 + 9/7*m + i*m**2 + 3/7*m**3 - 6/7 = 0. Calculate m.
-1, 1/3, 2
Let f = 317 + -307. Let t be (90/(-150))/((-3)/f). Suppose 2/11*l**t - 6/11 + 4/11*l = 0. Calculate l.
-3, 1
Let w(c) be the first derivative of 0*c**2 + 15/4*c**5 + 35/12*c**4 - 13 + 5/6*c**3 + 37*c + 3/2*c**6. Let l(z) be the first derivative of w(z). Factor l(j).
5*j*(j + 1)*(3*j + 1)**2
Factor -17336188 + 17338441 + 2*p**2 - 2256*p + p**2.
3*(p - 751)*(p - 1)
Determine v so that -13068*v - 4/9*v**3 - 431244 - 132*v**2 = 0.
-99
Let j(i) = -9*i - 54. Let v be j(-6). Let f(q) be the second derivative of -1/130*q**5 - 1/13*q**2 - 1/26*q**4 + 15*q - 1/13*q**3 + v. Factor f(b).
-2*(b + 1)**3/13
Suppose 4*t + 2*f = 2, -f = t - 5*f + 4. Suppose -923*q + 920*q + 15 = 0. Factor t + q*r**2 - 5*r + 0.
5*r*(r - 1)
Let w(o) = 9*o**3 - 21*o**2 + 47*o + 7. Let n(y) = y**3 + y**2 + 3*y + 1. Let a(c) = 7*n(c) - w(c). Factor a(g).
-2*g*(g - 13)*(g - 1)
Let x(j) be the first derivative of -11163/10*j**2 - 61/5*j**3 - 1/20*j**4 + 79 - 226981/5*j. Suppose x(t) = 0. Calculate t.
-61
Let p(z) be the third derivative of -1/840*z**8 + 0 + 0*z + 7/300*z**6 + 0*z**4 + 0*z**3 - 2/75*z**5 - 2/525*z**7 - 36*z**2. Suppose p(k) = 0. What is k?
-4, 0, 1
Let f(r) = -5*r**2 + 5*r + 4. Let i(k) = -11*k**2 + 11*k + 9. Let z = -52 - -106. Let t = z - 63. Let c(p) = t*f(p) + 4*i(p). Factor c(w).
w*(w - 1)
Let y = -185 + 425. Let s be (-10)/(y/(-126)) - (-2)/(-8). Factor -3150 + s*m**5 + 3150.
5*m**5
Let m be ((-14 - -9)/((-1)/26))/(-1). Let b be (-2)/(m/145) + 11 + -12. Suppose -b*w - 14/13*w**2 - 2/13 = 0. Calculate w.
-1, -1/7
Suppose 0 = -3*t - 5 + 17. Suppose t - 2 = u. Let x**u + 4*x**2 - 19*x + 29*x = 0. What is x?
-2, 0
Let 2/7*f**2 - 6/7*f + 0 = 0. What is f?
0, 3
Factor 1/6*s**5 + 1079/3*s**2 - 2197/6 + 13/2*s**4 - 169/2*s + 253/3*s**3.
(s - 1)*(s + 1)*(s + 13)**3/6
Let s be 8/(-14) + (21/343)/((-252)/(-8526)). Factor -s*l**2 + 0 + 21*l.
-3*l*(l - 14)/2
Let u(l) be the second derivative of -3*l**5/100 - 126*l**4/5 - 201*l**3/2 - 753*l**2/5 + 750*l. Factor u(k).
-3*(k + 1)**2*(k + 502)/5
Let d be (-10)/15*2361*5/5. Let j = d + 1577. Find a such that 13/3*a**j + 0*a + 7/3*a**2 - 2/3*a**4 + 0 = 0.
-1/2, 0, 7
Let w(s) be the first derivative of -s**5/210 - 25*s**4/14 - 1875*s**3/7 + 3*s**2/2 + 14*s + 190. Let z(p) be the second derivative of w(p). Factor z(a).
-2*(a + 75)**2/7
Let x(o) = o**3 - 113*o**2 + 104*o + 899. Let w be x(112). Factor -3/5*s + 3/5*s**w + 9/5*s**2 - 9/5.
3*(s - 1)*(s + 1)*(s + 3)/5
Let q = 875073/5 - 175014. Factor -18/5 - q*o + 3/5*o**2.
3*(o - 3)*(o + 2)/5
Let q be (33 - 37) + 4 + 0/(-4). Find b, given that q*b + 0 - 5/4*b**2 + 5/4*b**3 + 5/4*b**4 - 5/4*b**5 = 0.
-1, 0, 1
Let g be -8 - (23030/(-1880) + 3/12). Suppose -5*o = -3*v - 16, 5*v = 4*o + 3 - 8. Suppose 3/2*m + 13/2*m**2 - 9 + 1/2*m**g - 7/2*m**v = 0. What is m?
-1, 2, 3
Factor 12*w + 1/3*w**3 + 0 - 4*w**2.
w*(w - 6)**2/3
Let b(l) = -14*l**2 - 12*l + 10. Suppose -3*o - 36 = 5*t + 8, 20 = -o - 3*t. Let i(n) = -2*n**2. Let a(y) = o*i(y) + b(y). Solve a(p) = 0.
1, 5
Let r(n) be the second derivative of -n**7/70 - 2*n**6/5 - 141*n**5/100 + 17*n**4/5 + 5711*n. Solve r(l) = 0 for l.
-17, -4, 0, 1
Let v = 43 + -47. Let k be (18 - (2 - 4)) + v. Factor -15*w**3 - 8*w**2 + 92*w**4 - 177*w**4 + 93*w**4 - w**5 + k*w.
-w*(w - 4)**2*(w - 1)*(w + 1)
Let l be ((-208)/480 - ((-952)/120 + 8))*(-2 + 1). Find y, given that -3/4*y**4 + 3/4*y**2 + 0 + y**3 - 1/2*y - l*y**5 = 0.
-2, -1, 0, 1/2, 1
Let p(t) be the second derivative of -t**6/20 + 9*t**5/20 + t**4/2 - 6*t**3 + 8*t + 14. Suppose p(k) = 0. What is k?
-2, 0, 2, 6
Let h(i) be the second derivative of i**6/15 - 37*i**5/10 - 392*i**4/3 - 3392*i**3/3 - i - 1663. Factor h(t).
2*t*(t - 53)*(t + 8)**2
Let k = -80 - -202. Let u(y) be the first derivative of y**4 + k*y**2 - 2*y**4 + 29 - 120*y**2. Factor u(c).
-4*c*(c - 1)*(c + 1)
Let k(g) be the first derivative of g**3/9 + 31*g**2/6 + 28*g - 1150. Let k(q) = 0. Calculate q.
-28, -3
Let z(x) be the third derivative of x**6/24 - 43*x**5/4 + 680*x**4/3 - 800*x**3 + 251*x**2 - 3*x. Factor z(o).
5*(o - 120)*(o - 8)*(o - 1)
Let v(w) = w**2 + 2*w. Let r be v(-2). Let l = 6298/7835 - 6/1567. Find d, given that r - 4/5*d**3 - 24/5*d**2 + 0*d + l*d**4 = 0.
-2, 0, 3
Let n(z) = -5*z + 18. Let q be n(3). Suppose 7 = r - h - h, q*h = 2*r - 15. Factor -16*o - 13*o + r*o - o**2 - 4*o**2 - 20.
-5*(o + 2)**2
Let a(m) = -m - 1. Let r be a(-6). Suppose 0*k**2 + 8*k**4 + 4*k**r - 4*k + 2*k**2 - 4*k**2 - 6*k**2 = 0. Calculate k.
-1, 0, 1
Let r(m) be the second derivative of -m**7/168 + 2*m**6/9 - 7*m**5/2 + 30*m**4 + 157*m**3/6 + 196*m. Let n(f) be the second derivative of r(f). Factor n(b).
-5*(b - 6)**2*(b - 4)
Let v = 507119/7 + -72445. Let v*t - 8/7*t**2 + 0 + 4/7*t**3 = 0. What is t?
0, 1
Suppose 9*r - 12*r + 192 = -3*h, 62 = r - 2*h. Suppose 64*u - m = r*u - 9, m = -4*u + 15. Factor -6/5*w**u - 2*w + 3/5 + 1/5*w**4 + 12/5*w**2.
(w - 3)*(w - 1)**3/5
Let k(v) be the third derivative of 0*v - 3/7*v**3 - 2/105*v**5 + 27*v**2 + 13/84*v**4 + 0. Solve k(r) = 0 for r.
1, 9/4
Suppose 4*m - 7*r = -76, m + 126*r - 26 = 124*r. Determine w, given that 285/4*w**m - 1 + 26*w = 0.
-2/5, 2/57
Let u(y) be the third derivative of 5*y**8/336 - y**7/14 - 11*y**6/4 - 109*y**5/6 - 425*y**4/8 - 165*y**3/2 + 9757*y**2. Suppose u(l) = 0. What is l?
-3, -1, 11
Let q(m) be the first derivative of m**4/2 - 31*m**2 + 60*m + 1849. Factor q(a).
2*(a - 5)*(a - 1)*(a + 6)
Suppose -266*f + 20 = -261*f + 4*u, -5*f = -2*u + 10. Determine g, given that 1/3*g - 1/6*g**3 + f - 1/6*g**2 = 0.
-2, 0, 1
Suppose 190968/5*j + 8/5*j**5 - 132718*j**2 + 95048/5 + 3474/5*j**4 + 374092/5*j**3 = 0. Calculate j.
-218, -1/4, 1
Factor -44*d**2 - 365*d - 11*d**2 + 16*d**2 - 250 - 3*d**2 - 68*d**2 + 5*d**3.
5*(d - 25)*(d + 1)*(d + 2)
Suppose -741 = -2*y - 737. Let o(n) be the first derivative of 0*n + 0*n**y - 11 + 4/21*n**3 - 2/35*n**5 - 1/14*n**4. Find a, given that o(a) = 0.
-2, 0, 1
Let d(l) be the first derivative of l**4/42 + 16*l**3/21 + 15*l**2/7 + 148*l + 76. Let b(x) be the first derivative of d(x). Let b(n) = 0. What is n?
-15, -1
Determine h, given that 84*h**3 - 779 - 1551 + 930*h**2 + 26*h**4 - 7153 + 400*h - 2517 - 24*h**4 = 0.
-20, -5, 3
Suppose -40*u + 0*u = 10*u. Let h be (3 - u)*(-810)/(-486). Suppose -1/4*y**3 + 3*y**4 - y - 3*y**2 + 5/4*y**h + 0 = 0. What is y?
-2, -1, -2/5, 0, 1
Factor 250/23*t**2 - 10/23*t**4 + 0*t - 50/23*t**3 + 0 + 2/23*t**5.
2*t**2*(t - 5)**2*(t + 5)/23
Suppose 43*i - 330 = -67*i. Suppose 0 = -l - 4*s - 13, 0*s = -4*s - 16. Factor i + 4/3*p**l - 2/3*p**2 - 4*p + 1/3*p**4.
(p - 1)**2*(p + 3)**2/3
Let t(d) = -d**4 - d**3 + 3*d**2 - d - 1. Let n(j) = 10*j**4 - 60*j**3 + 1674*j**2 - 17190*j + 55575. Let i(b) = -2*n(b) - 18*t(b). Solve i(m) = 0.
6, 21
Solve -1560*o + 1671 - 2*o**2 - 109 + 7*o**2 - 7*o**2 = 0 for o.
-781, 1
Let w = -151527