3 - 3/2*u**3 + 2*u + 43/6*u**4 = 0.
-1, -2/3, 1, 14
Let k(j) be the second derivative of j**6/210 - j**5/28 + j**4/84 + j**3/2 - 9*j**2/7 + 20*j - 2. Solve k(f) = 0.
-2, 1, 3
Solve 9/5*f**3 + 384/5 + 96/5*f**2 + 336/5*f = 0.
-4, -8/3
Let 272/7 + 4/7*z**2 - 144/7*z = 0. What is z?
2, 34
Let a(j) = -j**2 - j + 16. Let h be a(-4). Factor 0*y**2 + 3/7*y**3 + 0 + 0*y + 3/7*y**5 + 6/7*y**h.
3*y**3*(y + 1)**2/7
Let 16/5*m - 4/5 + 9/5*m**3 - 21/5*m**2 = 0. Calculate m.
2/3, 1
Let l(z) be the first derivative of 8*z**3/3 - 16*z**2 + 32*z - 3. Let y(w) = 2*w**2 - 8*w + 8. Let b(v) = 4*l(v) - 18*y(v). Factor b(j).
-4*(j - 2)**2
Let j(w) be the third derivative of -59/40*w**5 + 0 + 15/8*w**4 - 6*w**2 - 9/8*w**3 + 0*w + 3/8*w**6 - 9/280*w**7. Solve j(h) = 0 for h.
1/3, 3
Let v(f) be the second derivative of -f**5/100 - f**4/15 - 2*f**3/15 - f + 4. Let v(m) = 0. What is m?
-2, 0
Let g(n) = -n**4 - n**3 + n**2 - n. Let p(z) = -4*z**5 + 20*z**4 - 2*z**3 - 35*z**2 - 7*z. Let i(j) = 5*g(j) + 5*p(j). Solve i(q) = 0.
-1, -1/4, 0, 2, 4
Let j be (3 - 4)/(3 - 6 - 6). Let p(t) be the second derivative of -1/18*t**4 + 0 - j*t**3 + 2/3*t**2 - t. Factor p(m).
-2*(m - 1)*(m + 2)/3
Suppose -41*k + 207 = -38*k. Factor 3*v**5 + 0*v**5 + k*v**4 + 3*v**3 - 129*v**4 + 66*v**4.
3*v**3*(v + 1)**2
Let j = -416/23 - -1271/69. Solve 1/3*u**4 - 2/3*u + 0 + u**3 - 1/3*u**5 - j*u**2 = 0 for u.
-1, 0, 1, 2
Let r(v) be the third derivative of v**8/672 - v**6/240 + v**2 + 16*v. Factor r(y).
y**3*(y - 1)*(y + 1)/2
Let a be 3/(-30)*13/(-39). Let i(x) be the second derivative of -x + 0*x**3 + 0 + 1/150*x**6 - 3/100*x**5 + a*x**4 + 0*x**2. Determine d so that i(d) = 0.
0, 1, 2
Solve 81/2 + 1/2*x**2 - 9*x = 0.
9
Let t(d) = 13*d**2 + 450*d - 173. Let y be t(-35). Suppose -3*p - 6 = 2*p + 4*u, p + 2*u = -6. Let -6/7 + p*k - 8/7*k**y = 0. What is k?
3/4, 1
Let d(f) = f**2 - f + 111. Let w be d(0). Let p = w + -106. Factor 0*k**3 + 0 + 0*k - 3/7*k**p + 0*k**2 - 3/7*k**4.
-3*k**4*(k + 1)/7
Let n(z) be the first derivative of -16*z**4 + 22 + 36/5*z**5 - 52/3*z**3 + 32*z**2 + 16*z. Suppose n(k) = 0. What is k?
-1, -2/9, 1, 2
Determine r so that 11/2*r**2 + 3*r + 2*r**3 + 0 - 1/2*r**4 = 0.
-1, 0, 6
Find f such that -2/11*f**2 + 0*f - 2/11*f**5 + 2/11*f**4 + 2/11*f**3 + 0 = 0.
-1, 0, 1
Suppose 0 = -b + 1 + 1. Suppose 2*p + 3*s + 3 = 0, -5 = 5*p - 9*s + 14*s. What is v in -4/3*v - 4/3*v**3 + p - 8/3*v**b = 0?
-1, 0
Let g = -115063/5 + 23016. Determine d so that 0 - 8/5*d - 2*d**3 - 1/5*d**4 - g*d**2 = 0.
-8, -1, 0
Determine p so that -34*p**2 - 72 - 70*p + 14*p**2 + 22*p**2 = 0.
-1, 36
Factor 38*i**2 - 53 - 32*i - 34*i**2 - 27.
4*(i - 10)*(i + 2)
Let h(f) = f**2 - 11*f + 8. Let u be h(11). Let z(b) = -11*b**2 - 5*b + 8. Let i(d) = -4*d**2 - 2*d + 3. Let v(t) = u*i(t) - 3*z(t). Factor v(x).
x*(x - 1)
Let s be (7 + -2)*((-279)/(-90) - 3). Factor 0*m + 0 - 1/2*m**3 - s*m**2.
-m**2*(m + 1)/2
Let r = -8638 - -17277/2. Factor r*i**2 + 81/2 - 9*i.
(i - 9)**2/2
Let a(c) be the second derivative of c**5/50 + 13*c**4/5 - 1021*c. Factor a(w).
2*w**2*(w + 78)/5
Let s(g) be the first derivative of -g**4/14 - 14*g**3 - 1029*g**2 - 33614*g - 459. Factor s(a).
-2*(a + 49)**3/7
Let o(f) be the first derivative of f**3/7 + 3*f**2/2 + 378. Factor o(p).
3*p*(p + 7)/7
Suppose -20/9*j**5 + 0*j + 0 - 8/9*j**4 + 20/9*j**3 + 8/9*j**2 = 0. Calculate j.
-1, -2/5, 0, 1
Suppose -v + 3 = j, -v - 3 + 6 = -3*j. Let g(m) be the second derivative of 2/15*m**v - 1/10*m**4 + 0*m**2 + 6*m + 1/50*m**5 + 0. Factor g(y).
2*y*(y - 2)*(y - 1)/5
Let u(t) = -3*t + 5. Let r be u(2). Let k(a) = a**4 + 3*a**3 + a**2 - 8*a - 7. Let y(j) = -j - 1. Let s(v) = r*k(v) + 5*y(v). Solve s(z) = 0.
-2, -1, 1
Let 0*x - 8/5*x**3 + 3/5*x**4 + 0 + 4/5*x**2 = 0. Calculate x.
0, 2/3, 2
Let s(v) be the third derivative of 2*v**6/75 + 29*v**5/75 + 47*v**4/30 + 4*v**3/3 - 2*v**2 + 8. Factor s(b).
4*(b + 2)*(b + 5)*(4*b + 1)/5
Let r = -202 + 202. Suppose -1/3*n - 1/3*n**2 + r = 0. Calculate n.
-1, 0
Let h(c) be the second derivative of -c**4/30 - 2*c**3/3 - 5*c**2 + 64*c. Factor h(b).
-2*(b + 5)**2/5
Factor 2 - 8/3*q**3 + 20/3*q - 6*q**2.
-2*(q - 1)*(q + 3)*(4*q + 1)/3
Let x = -82 - -109. Let d be (-3)/(x/(-15)) + (-2)/(-6). Determine w so that 0*w - 1/8*w**3 + 1/8*w**5 + 1/8*w**4 - 1/8*w**d + 0 = 0.
-1, 0, 1
Factor 0 + 14/17*o**2 + 2/17*o**4 - 10/17*o**3 - 6/17*o.
2*o*(o - 3)*(o - 1)**2/17
Let s(w) = -2*w**4 - 93*w**3 - 1155*w**2. Let u(d) = 2*d**4 + 94*d**3 + 1154*d**2. Let a(m) = 2*s(m) + 3*u(m). Factor a(x).
2*x**2*(x + 24)**2
Let g(i) be the third derivative of i**8/420 - i**7/105 + i**6/90 + 7*i**3/2 + 6*i**2. Let q(x) be the first derivative of g(x). Solve q(y) = 0 for y.
0, 1
Let p(k) be the third derivative of k**8/84 - 8*k**7/105 + k**6/30 + 2*k**5/3 - 2*k**4/3 - 16*k**3/3 - 88*k**2. Find n, given that p(n) = 0.
-1, 2
Let x(c) = 11*c + 24. Let h be x(-2). Factor 0 + 3/2*w - 15/4*w**h - 21/4*w**3.
-3*w*(w + 1)*(7*w - 2)/4
Let l(c) be the second derivative of 1/130*c**5 + 4/39*c**3 + 2/39*c**4 + 12*c + 0*c**2 + 0. Factor l(w).
2*w*(w + 2)**2/13
Let s(z) be the second derivative of -5/3*z**3 - 15/2*z**2 + 5/12*z**4 - 18*z + 0. Solve s(l) = 0 for l.
-1, 3
Let k(b) be the first derivative of 8*b - 1/12*b**3 + 0*b**2 - 1/12*b**4 - 1/40*b**5 - 8. Let z(l) be the first derivative of k(l). Let z(j) = 0. Calculate j.
-1, 0
Let i(z) = -z**3 + z**2 + 4*z - 3. Let a be i(2). Let g be 3/(-15) - a*87/(-135). Solve -10/9*l**2 + g*l + 2/3*l**3 + 0 = 0 for l.
0, 2/3, 1
Let y(b) be the third derivative of 5/9*b**4 - 1/36*b**6 + 27*b**2 + 0 - 4/315*b**7 + 0*b + 4/9*b**3 + 1/6*b**5. Determine i, given that y(i) = 0.
-2, -1, -1/4, 2
Let i(m) be the first derivative of m**8/336 - m**6/24 - m**5/12 + 29*m**3/3 - 39. Let g(d) be the third derivative of i(d). Factor g(h).
5*h*(h - 2)*(h + 1)**2
Let m(k) be the first derivative of 2*k**3/9 + 20*k**2/3 + 38*k/3 - 259. Suppose m(h) = 0. What is h?
-19, -1
Let s(c) be the second derivative of 0*c**5 + 0 + 8*c + 0*c**3 - 1/6*c**6 + 0*c**2 + 5/12*c**4. Factor s(n).
-5*n**2*(n - 1)*(n + 1)
Let d(u) = -2*u**4 + 22*u**3 - 18*u**2 - 6. Let b(x) = -x**3 - 2*x**2 + 1. Let i(y) = -6*b(y) - d(y). Let i(f) = 0. Calculate f.
0, 3, 5
Let g(t) be the first derivative of 0*t**2 + 4/3*t**3 + 0*t**4 - 1/360*t**6 + 0*t - 1 + 0*t**5. Let z(l) be the third derivative of g(l). Factor z(n).
-n**2
Suppose -5*a + 85 = -5*k, -2*k + 6*k - 5*a = -63. Let b = k - -25. Factor 4/7*y**b - 4/7*y + 2/7*y**4 - 2/7*y**2 + 0.
2*y*(y - 1)*(y + 1)*(y + 2)/7
Let a(z) = 10*z**2. Let i be 5/3 + 3/9. Let x(p) = -3*p**2. Let d(v) = i*a(v) + 7*x(v). Factor d(s).
-s**2
Suppose -36/7*n**2 + 42 + 9*n + 3/7*n**3 = 0. Calculate n.
-2, 7
Let c(w) be the third derivative of w**8/1176 + w**7/245 - w**6/140 - 11*w**5/210 - w**4/14 - 26*w**2. Suppose c(r) = 0. What is r?
-3, -1, 0, 2
Let t(l) be the first derivative of 9*l**6 - 1482*l**5/5 + 20659*l**4/6 - 15090*l**3 + 9072*l**2 - 1944*l + 93. Factor t(w).
2*(w - 9)**3*(9*w - 2)**2/3
Let v(z) be the third derivative of 16*z**7/35 - 586*z**6/15 - 927*z**5/10 - 79*z**4 - 100*z**3/3 + z**2 + 39*z. Suppose v(i) = 0. Calculate i.
-2/3, -1/4, 50
Let c(o) be the second derivative of o**6/72 + 7*o**5/30 - o**4/2 - 7*o**3 - 8*o. Let i(k) be the second derivative of c(k). Factor i(h).
(h + 6)*(5*h - 2)
Let f(k) = 43*k**3 - 553*k**2 - 1877*k - 39. Let x(r) = -7*r**3 + 92*r**2 + 313*r + 6. Let a(s) = -2*f(s) - 13*x(s). Factor a(t).
5*t*(t - 21)*(t + 3)
Let d be -5*2 - 6/(-1). Let b(w) = -2*w - 4. Let f be b(d). Find c such that 5/4*c**2 - 5/2*c**5 - 5/4*c**f + 5/2*c**3 + 0*c + 0 = 0.
-1, -1/2, 0, 1
Let d(r) = -r**4 + r**3 + r**2 + r. Let t = 31 + -32. Let l(f) = -f**4 - 3*f**3 + f**2 + f. Let n(s) = t*d(s) - l(s). Factor n(v).
2*v*(v - 1)*(v + 1)**2
Let o(w) be the first derivative of 2/3*w**2 - 5/18*w**3 + 1/24*w**4 + 11 - 2/3*w. Factor o(u).
(u - 2)**2*(u - 1)/6
Let r = -150 + 302. Suppose z - r = -z. Factor -47*w - 5*w**2 - 4*w**5 + 0*w**5 - z*w**3 - 95*w**2 - 28*w**4 - 16 - 17*w.
-4*(w + 1)**3*(w + 2)**2
Let z(s) be the second derivative of 3*s**5/20 - 3*s**4 + 18*s**3 + 74*s - 1. What is j in z(j) = 0?
0, 6
Suppose 9 = -3*z, 10*s + z - 9 = 7*s. Let c(m) be the first derivative of 0*m - 1/18*m**s + 1 - 2/9*m**3 - 2/9*m**2. Factor c(x).
-2*x*(x