/60 - 2*v**3/3 + 23*v**2/2 + 34. Let l(k) be the second derivative of f(k). Factor l(h).
(h - 2)*(h + 2)
Let g(p) be the second derivative of p**8/20160 + p**7/7560 + p**4/4 - 11*p. Let n(c) be the third derivative of g(c). Factor n(q).
q**2*(q + 1)/3
Factor 4/3*g**4 + 0*g + 16*g**2 + 0 + 32/3*g**3.
4*g**2*(g + 2)*(g + 6)/3
Find m, given that 40/11*m**5 + 4/11 - 18/11*m + 98/11*m**3 - 114/11*m**4 - 10/11*m**2 = 0.
-2/5, 1/4, 1
Let f(i) be the first derivative of i**4/16 + 11*i**3/4 + 36*i**2 + 64*i - 63. Suppose f(y) = 0. What is y?
-16, -1
Let n be (0*(-10)/(-130))/(-9). Solve -2/17*g**3 + n + 8/17*g + 0*g**2 = 0.
-2, 0, 2
Let v(t) = -t**4 + t**3 - t + 1. Let a = -45 - -46. Let w(c) = -3*c**4 + 8*c**3 + 2*c - 2. Let j(x) = a*w(x) + 2*v(x). Factor j(p).
-5*p**3*(p - 2)
Let z(v) = -7*v**2 + 4*v + 17. Let d(t) = 15*t**2 - 9*t - 34. Let y(k) = 6*d(k) + 13*z(k). Let g be y(-5). Factor 0 + 0*w - 1/3*w**g.
-w**2/3
Let n(f) be the third derivative of 2*f**7/105 + 11*f**6/30 + 8*f**5/15 - 10*f**4/3 - 3*f**2 + 1. Factor n(k).
4*k*(k - 1)*(k + 2)*(k + 10)
Solve 3/2*g**5 + 9/2*g - 27 - 6*g**4 - 6*g**3 + 33*g**2 = 0 for g.
-2, -1, 1, 3
Suppose -7*q + 4*q = -138. Solve -21 - j**2 + q + 6*j**2 - 30*j = 0.
1, 5
Let y(a) be the second derivative of -a**5/40 + a**4/24 - 149*a. Solve y(k) = 0.
0, 1
Let o = -1252/3 - -418. Factor 0 + 0*q + 0*q**2 - 10/3*q**3 + o*q**4.
2*q**3*(q - 5)/3
Factor 60*u + 803 - 2*u**2 - 28*u**2 + u**3 - 923 + 52*u + u**3.
2*(u - 10)*(u - 3)*(u - 2)
Let z(w) be the second derivative of -w**7/5040 - w**6/720 - w**5/240 - 3*w**4/4 + 2*w. Let p(g) be the third derivative of z(g). Suppose p(j) = 0. Calculate j.
-1
Let h(u) be the second derivative of -u**4/12 + 4*u**3/3 - 6*u**2 - 9*u + 1. Let h(d) = 0. What is d?
2, 6
Let o(s) = 2*s**5 - 12*s**4 + s**3 + 47*s**2 + 48*s + 19. Let z(f) = -4*f**5 + 12*f**4 - 48*f**2 - 48*f - 20. Let g(w) = 4*o(w) + 3*z(w). Factor g(n).
-4*(n - 2)*(n + 1)**3*(n + 2)
Let j = 1833/110 + -163/10. Find s such that -2/11*s**2 + j - 2/11*s = 0.
-2, 1
Let y = 217727/4 + -54305. Let y*d - 39/4*d**2 - 2197/4 + 1/4*d**3 = 0. Calculate d.
13
Let o(v) be the first derivative of -9/5*v**2 + 9 + 4/5*v - 7/5*v**4 + 12/25*v**5 - 1/15*v**6 + 32/15*v**3. Determine x so that o(x) = 0.
1, 2
Factor -2*u**4 - 28*u**3 - 260*u - 3*u**4 - 150 + 3*u**4 - 160*u**2 + 24*u**2.
-2*(u + 1)*(u + 3)*(u + 5)**2
Solve -70*h - 83 + 3*h**2 + 7 - 11 - 14*h + 0*h**2 = 0 for h.
-1, 29
Let m(c) be the third derivative of -c**5/12 + 25*c**4/24 - 5*c**3 + 15*c**2 + 1. Factor m(p).
-5*(p - 3)*(p - 2)
Let i be (-924)/91 + 10 - (-19)/39. Determine w so that -1/3*w + 1/3*w**4 + 0 + i*w**3 - 1/3*w**2 = 0.
-1, 0, 1
Suppose 0*z = 5*x + z - 122, -2*x - 4*z + 56 = 0. Solve -6*q**2 - 16 - x*q - 4*q**2 + q**2 + q**3 - 2*q**3 = 0.
-4, -1
Factor -147/4 + 36*x + 3/4*x**2.
3*(x - 1)*(x + 49)/4
Let z(o) be the first derivative of 21 - 16/7*o - 8/7*o**2 - 4/21*o**3. Factor z(j).
-4*(j + 2)**2/7
Let z(p) be the third derivative of -p**7/1575 - p**6/180 + 13*p**5/450 - 7*p**4/180 - 100*p**2. Factor z(v).
-2*v*(v - 1)**2*(v + 7)/15
Let i(a) be the first derivative of -a**5/25 + a**4/5 - a**3/5 - 75. Determine v so that i(v) = 0.
0, 1, 3
Let k(t) be the first derivative of 2*t**3/39 + 25*t**2/13 + 48*t/13 + 78. Solve k(y) = 0.
-24, -1
Let v = 4520 - 4518. Factor 18/5 + 8/5*r**v + 21/5*r + 1/5*r**3.
(r + 2)*(r + 3)**2/5
Let x(k) = 2*k**3 - 2*k**2 + 2*k - 8. Let v be x(2). Suppose 117*i**3 + 204*i + 331*i**2 + 13*i**v + 56 - i**3 - 79*i**2 - i**4 = 0. What is i?
-7, -1, -2/3
Suppose 0 = 5*y + 9*t - 13*t - 34, -y = 3*t - 3. Suppose -10 = -z - z. Let 6*d**3 - 20*d + d**5 - 3*d**5 + 5*d**z + 11*d - 9*d**4 + 3 + y*d**2 = 0. What is d?
-1, 1
Let c be 74/10 + -3 - (-11)/(22/(-8)). Solve 0 + 0*h**3 + c*h**4 - 2/5*h**2 + 1/5*h - 1/5*h**5 = 0.
-1, 0, 1
Let x be 1341/(-63) - -21 - (12/7 + -2). Let x - 1/3*q**2 - 1/3*q = 0. What is q?
-1, 0
Let a(x) = 6*x**3 - 10*x**2 + 28*x + 4. Let t(z) = 13*z**3 - 20*z**2 + 60*z + 9. Let o(r) = -9*a(r) + 4*t(r). Factor o(p).
-2*p*(p - 3)*(p - 2)
Find f, given that -3 - 1/8*f**4 - 37/8*f + 9/8*f**3 - 3/8*f**2 = 0.
-1, 3, 8
Suppose -122*n**2 + 260*n + 231*n**2 - 255 - 114*n**2 = 0. Calculate n.
1, 51
Let r(b) = -4*b**2 + 12*b - 5. Let o be r(2). Let 2/5*f**4 - 4/5*f**2 + 1/5*f**5 - 2/5*f**o + 1/5*f + 2/5 = 0. Calculate f.
-2, -1, 1
Solve -5*x**2 + 117 + 132*x + 183 + 19*x - 11*x = 0 for x.
-2, 30
Let z(h) be the third derivative of 2*h**6/15 - 13*h**5/5 - 5*h**4/3 + 6*h**2 + 2. Factor z(g).
4*g*(g - 10)*(4*g + 1)
Let a(k) be the first derivative of -2/39*k**3 + 0*k + 29 + 11/13*k**2. Solve a(j) = 0 for j.
0, 11
Let x be (3 - 328/96)*8/(-3). Factor x*r**2 + 2/9*r**3 + 8/9 + 16/9*r.
2*(r + 1)*(r + 2)**2/9
Let a be 14/2 - (-1 + 0). Factor -3 - 6*y**4 + a*y**3 + 12*y + 7 + 4*y**5 + 8*y**2 - 24*y - 6*y**4.
4*(y - 1)**4*(y + 1)
Suppose 15*j + 2 = 16*j. Let k(z) be the first derivative of -2/35*z**5 - 4/7*z**3 - 4/7*z**j + 5 - 2/7*z - 2/7*z**4. Solve k(n) = 0.
-1
Let x(r) = -r**3 - 25*r**2 - r - 21. Let s be x(-25). Suppose 4*y = 3*i + 9, i + 0 = -s*y - 3. Let -48/7*o**2 + 54/7*o**3 + 8/7*o + y = 0. What is o?
0, 2/9, 2/3
Let w(d) be the second derivative of -d**6/2880 + d**5/480 - 25*d**3/6 - 18*d. Let j(i) be the second derivative of w(i). Find f, given that j(f) = 0.
0, 2
Let d = -38998 - -39004. Find n, given that -d*n - 11/2*n**2 - 1/4*n**4 - 2*n**3 - 9/4 = 0.
-3, -1
Suppose -12*u + 126 = -157 + 223. What is i in 5/3*i**2 + u*i + 10/3 = 0?
-2, -1
Suppose 0 = 4*j - 288 - 332. Let r be (j/(-56))/(-5) + 27/(-63). Let -1/8*p + 1/8*p**2 - r + 1/8*p**3 = 0. What is p?
-1, 1
Let i(a) be the third derivative of -a**11/39600 + a**10/25200 + a**9/25200 - 3*a**5/20 - 6*a**2. Let t(m) be the third derivative of i(m). Factor t(s).
-6*s**3*(s - 1)*(7*s + 2)/5
Let u(w) be the second derivative of w**5/50 - 23*w**4/60 - 34*w**3/15 - 14*w**2/5 - 117*w. Factor u(g).
(g - 14)*(g + 2)*(2*g + 1)/5
Find r, given that -16383/4*r - 1/4*r**3 - 16129/4 - 255/4*r**2 = 0.
-127, -1
Let r be 8/(-20) + 157/5. Suppose -k + 3*k = -4*u + 28, 3*u = -4*k + r. Factor u*l**5 - 5*l**4 - 12*l**5 - 8*l**3 + 4*l**5 + 2*l**5 - 4*l**2.
-l**2*(l + 1)*(l + 2)**2
Let q = 36 - 22. Solve -q*x**3 + 28*x**3 + x**4 - 17*x**3 - 2*x**4 - 2*x**2 = 0 for x.
-2, -1, 0
Let g(m) = -5*m**2 + 15*m - 50. Let w(h) = -h**2 + h - 5. Let q(x) = -5*g(x) + 20*w(x). Factor q(y).
5*(y - 6)*(y - 5)
Let k = -3400/9 - -378. Let n(i) be the first derivative of -k*i**3 + 2/45*i**5 + 5/9*i**2 - 7 - 4/9*i - 1/18*i**4. Factor n(y).
2*(y - 1)**3*(y + 2)/9
Let a = 42 - 30. Suppose 0 = -l, 4*k = -2*l - 3*l + a. Suppose -2*w**4 + 0*w**4 + 2*w**3 + 0*w**k = 0. Calculate w.
0, 1
Let c(y) be the second derivative of -y**8/1344 - y**7/504 + y**6/144 + y**5/24 - 19*y**4/6 - 16*y. Let q(g) be the third derivative of c(g). Factor q(o).
-5*(o - 1)*(o + 1)**2
Let k = 2079/2 - 1039. Let q(t) be the third derivative of 6*t**2 + 0 + 0*t - 3/20*t**5 - k*t**4 + 2*t**3. Let q(r) = 0. What is r?
-2, 2/3
Let r(p) be the first derivative of -24*p + 53 + p**3 - 21/2*p**2. Factor r(l).
3*(l - 8)*(l + 1)
Let w = 11 - 14. Let k be (3/(-21))/(w/6). Determine n, given that 2/7*n + k*n**4 + 6/7*n**3 + 0 + 6/7*n**2 = 0.
-1, 0
Let z(f) = -11*f**4 - 233*f**3 + 318*f**2 - 110*f. Let u(l) = -l**4 - l**3 - l**2 - l. Let g(b) = 2*u(b) - z(b). Determine s so that g(s) = 0.
-27, 0, 2/3
Let q(s) = 3*s**4 - 2*s**3 - 16*s**2 - 20*s - 5. Let x(h) = h**4 + h**3 + h**2 + 1. Let l(v) = -q(v) + 2*x(v). Suppose l(n) = 0. What is n?
-1, 7
Let b(u) be the second derivative of u**7/2100 + u**6/300 - u**5/75 - 8*u**3/3 + 38*u. Let l(y) be the second derivative of b(y). Factor l(x).
2*x*(x - 1)*(x + 4)/5
Let g be 96/(-128)*(-2)/(-3) + 30/28. Solve -8/7*z - g*z**2 + 12/7 = 0.
-3, 1
Let f(z) be the third derivative of 2/165*z**5 - 34*z**2 + 0*z**3 + 0*z - 1/660*z**6 + 0 + 5/132*z**4. Factor f(w).
-2*w*(w - 5)*(w + 1)/11
Let d be (-11 + 8)/(6/8). Let l be 2 - d/8*-4. Solve -3*i**3 + l*i**4 + i**4 - i**5 - 3*i**4 + 2*i**3 = 0 for i.
-1, 0
Let l(p) be the second derivative of p**4/36 + 34*p**3/9 + 65*p**2/2 + 407*p. Suppose l(x) = 0. Calculate x.
-65, -3
Let y(s) = -2*s - 9 - 7*s**2 - 6*s**3 + 5*s**3 - s. Let t be y(-7). Determine v, given that -3*v**2 + 17*v - 5*v + t - 12*v = 0.