h + 115)/3
Let k(j) be the first derivative of 28/27*j**3 + 20/9*j**2 + 42 - 1/18*j**4 - 1/27*j**6 + 16/9*j - 8/45*j**5. Suppose k(h) = 0. Calculate h.
-2, -1, 2
Let n(v) = -v**2 - 9*v - 15. Let y be n(-6). Factor -12*j**y + j**4 + 437 - 469 + 3*j**4 + 48*j - 8*j**2.
4*(j - 2)**2*(j - 1)*(j + 2)
Factor 17 + 12*i**2 - 231 - 1641*i - 197.
3*(i - 137)*(4*i + 1)
Let w(h) = -16*h**3 - 76*h**2 - 6*h + 12. Let i(d) = -3*d**3 - d**2 - d + 2. Let n(v) = -6*i(v) + w(v). Factor n(s).
2*s**2*(s - 35)
Let a(g) be the third derivative of g**7/42 + 7*g**6/6 + 53*g**5/12 + 65*g**4/12 - 5*g**2 + 17*g. Factor a(l).
5*l*(l + 1)**2*(l + 26)
Let h(p) = -6*p**2 - 69*p + 21. Let n(k) = k**2 + 14*k - 4. Let o(q) = 4*h(q) + 21*n(q). Suppose o(y) = 0. Calculate y.
0, 6
Suppose 0 = 3*l - 2*u - 34, 4*l - 43 = 3*u + 2*u. What is c in l*c**3 + 16*c - 48*c**2 - 3 + 15*c**4 + 3 + 5*c**4 = 0?
-2, 0, 2/5, 1
Let q(x) be the first derivative of -x**4/30 + 2*x**3/5 - 4*x**2/3 + 8*x/5 + 140. Factor q(l).
-2*(l - 6)*(l - 2)*(l - 1)/15
Let l(y) be the first derivative of y**6/45 - y**4/3 + 8*y**3/9 - y**2 + 8*y/15 - 301. Factor l(j).
2*(j - 1)**4*(j + 4)/15
Determine n, given that 3/2*n**4 + 0 + 0*n**2 + 3/2*n**5 + 0*n - 3*n**3 = 0.
-2, 0, 1
Let t = 60 + -60. Let f(u) be the third derivative of 2*u**2 + 1/30*u**5 + 0 + t*u + 1/12*u**4 - 2/3*u**3. Factor f(k).
2*(k - 1)*(k + 2)
Let s = 65 - 63. Let y(o) be the first derivative of 7/6*o**4 + 2/3*o + 2*o**3 + 2 + 5/3*o**s + 4/15*o**5. Factor y(r).
2*(r + 1)**3*(2*r + 1)/3
Let i be (-4 - 58/(-12))*-53. Let u = -43 - i. Factor -1/3*f**2 + 7/6*f - u*f**3 + 1/3.
-(f - 1)*(f + 1)*(7*f + 2)/6
Let i(v) be the first derivative of 0*v**2 - 3/22*v**4 + 11 + 1/11*v**6 - 2/11*v**3 + 0*v + 6/55*v**5. Determine o, given that i(o) = 0.
-1, 0, 1
Let p(x) be the first derivative of 2*x**5/65 + 9*x**4/26 + 10*x**3/13 - 25*x**2/13 - 46. Factor p(d).
2*d*(d - 1)*(d + 5)**2/13
Let p(i) be the first derivative of -24964*i**3/15 - 316*i**2/5 - 4*i/5 + 100. Factor p(y).
-4*(79*y + 1)**2/5
Let u = -6211 + 31058/5. Determine p, given that -9/5*p**3 + 6/5*p + 3/5*p**5 - 3/5*p**2 + 0 + u*p**4 = 0.
-2, -1, 0, 1
Let h be 16/48 + (-13)/(-15). Factor 12/5*p**2 + 1/5*p**4 + 3/5 - 2*p - h*p**3.
(p - 3)*(p - 1)**3/5
Let u = -25/192 - -509/960. Factor -98/5 - 28/5*w - u*w**2.
-2*(w + 7)**2/5
Factor -292*w - 280*w + 20 - 2*w**2 + 590*w.
-2*(w - 10)*(w + 1)
Suppose 3*t = -n + 14, 0*n = -5*n - 20. Let q(k) be the third derivative of k**2 + 0 + 1/540*k**t - 1/54*k**4 + 0*k**3 + 0*k + 1/270*k**5. Solve q(r) = 0 for r.
-2, 0, 1
Let 84*t - 2*t**2 + 5*t**2 - 65 - t**2 - 5*t**2 - 16 = 0. What is t?
1, 27
Let i(o) be the second derivative of 0 - 3/2*o**3 + 1/10*o**6 + 23*o + 13/4*o**4 + 21/20*o**5 - 27*o**2. Factor i(x).
3*(x - 1)*(x + 2)*(x + 3)**2
Factor -666 - 98*r + 3*r**2 - 107*r - 13*r + 3549 + 32*r.
3*(r - 31)**2
Let y = -3156 + 3159. Let k = 1/5 - 0. Factor 0*g + k*g**4 + 0*g**2 + 0 - 2/5*g**y.
g**3*(g - 2)/5
Let i(w) = 2*w**4 + 7*w**3 + 13*w**2 + 3*w - 10. Let f(a) = -a**3 - a**2 - a - 2. Let u(p) = 5*f(p) - i(p). Find s such that u(s) = 0.
-4, -1, 0
Let u(i) be the second derivative of -i**5/50 + 7*i**4/30 - 4*i**3/15 - 12*i**2/5 + 763*i. Factor u(a).
-2*(a - 6)*(a - 2)*(a + 1)/5
Let c(z) be the first derivative of -z**5 - 35*z**4/4 + 40*z**3/3 - 13. Factor c(b).
-5*b**2*(b - 1)*(b + 8)
Let t(q) = -q**3 + 3*q**2 + 2*q - 4. Let a be t(3). Suppose 70*c - 21*c + 40*c = 0. Factor c - 1/3*i**3 - i**a - 2/3*i.
-i*(i + 1)*(i + 2)/3
Let v be 2/4*-1*(0 - 0). Solve -3*f**2 - 3*f + 17*f + v - 12 - 2*f = 0 for f.
2
Suppose 0 = 4*a + 4, -13 = -4*h + 67*a - 66*a. Factor 3/2*g**2 + 3/2*g**h + 0 + 1/2*g**4 + 1/2*g.
g*(g + 1)**3/2
Find v, given that 1/2*v**5 - 3*v**4 - 24*v - 3/2*v**3 + 28*v**2 + 0 = 0.
-3, 0, 1, 4
Factor -5*s**2 + 388 - 224 - 189 + 30*s.
-5*(s - 5)*(s - 1)
Let y = -21 - -27. Let d = y + -6. Find a, given that -7/5*a**4 - 1/5*a - a**2 - 2/5*a**5 - 9/5*a**3 + d = 0.
-1, -1/2, 0
Let d = 1080/37 - 8603/296. Factor -1/8*n + 1/4 - d*n**2.
-(n - 1)*(n + 2)/8
Let f(m) be the second derivative of m**9/6048 + m**8/1920 - m**7/630 - m**6/360 + 25*m**4/12 + 5*m. Let l(c) be the third derivative of f(c). Factor l(b).
b*(b - 1)*(b + 2)*(5*b + 2)/2
Let b(t) be the first derivative of t**7/840 + t**6/180 + 16*t**3/3 + 7. Let h(q) be the third derivative of b(q). Solve h(k) = 0 for k.
-2, 0
Let u(k) be the third derivative of k**8/56 - 2*k**7/105 - 7*k**6/15 - 7*k**5/5 - 23*k**4/12 - 4*k**3/3 - 3*k**2 - 6. Determine r so that u(r) = 0.
-1, -1/3, 4
Solve 1/3*m**3 - 7 + 43/3*m - 23/3*m**2 = 0.
1, 21
Determine t, given that -2/15*t**4 + 4/15 + 2/3*t - 2/15*t**3 + 2/5*t**2 = 0.
-1, 2
Let f(w) = -26*w**2 + 344*w + 7396. Let j(v) = -32*v**2 + 344*v + 7396. Let y(c) = -6*f(c) + 5*j(c). Find h, given that y(h) = 0.
-43
Let p(h) be the second derivative of -h**6/10 - 9*h**5/5 - 9*h**4 + 319*h. Factor p(k).
-3*k**2*(k + 6)**2
Let i(p) = -13*p**3 + 53*p**2 + 195*p + 149. Let v(t) = -6*t**3 + 26*t**2 + 98*t + 74. Let z(d) = 2*i(d) - 5*v(d). Factor z(l).
4*(l - 9)*(l + 1)*(l + 2)
Let b(s) be the first derivative of 2/9*s**3 + 1/3*s**2 + 0*s - 13. Determine q, given that b(q) = 0.
-1, 0
Let y(d) be the second derivative of -d**4/12 + 17*d**3/3 + 35*d**2/2 - 42*d. Suppose y(l) = 0. What is l?
-1, 35
Let b be (20/(-70))/((-2)/70). Find n such that -8*n**2 - 11 + b*n**2 + 3 = 0.
-2, 2
Let q(l) be the second derivative of l**7/231 - l**6/165 - l**5/22 + l**4/66 + 8*l**3/33 + 4*l**2/11 + 97*l. Find z such that q(z) = 0.
-1, 2
Factor 0 + 28/5*s**3 + 136/5*s**2 - 2/5*s**4 + 144/5*s.
-2*s*(s - 18)*(s + 2)**2/5
Let c(g) be the second derivative of g**7/231 + g**6/165 - g**5/22 - 5*g**4/66 + 4*g**3/33 + 4*g**2/11 + 46*g + 2. Solve c(v) = 0.
-2, -1, 1, 2
Let -20*m - 129*m**2 - 36 - 3*m + 57*m + 98*m + 45*m - 12*m**3 = 0. Calculate m.
-12, 1/4, 1
Factor 0*m**2 + 0 + 0*m**3 - 2/13*m**4 + 0*m.
-2*m**4/13
Let r(m) = -m**3 + 13*m**2 - 14*m + 13. Let o be r(12). Let c be (2/21)/(((-11)/12)/o). Factor 0 - 2/7*z + c*z**2.
2*z*(4*z - 1)/7
Let i(j) = 37*j**2 + 321*j + 329. Let p(c) = 20*c**2 + 160*c + 165. Let n(q) = 5*i(q) - 9*p(q). Factor n(z).
5*(z + 1)*(z + 32)
Let l(n) = -11*n**4 + 85*n**3 + 193*n**2 + 97*n - 5. Let c(v) = 5*v**4 - 43*v**3 - 97*v**2 - 49*v + 2. Let p(r) = 5*c(r) + 2*l(r). Find j, given that p(j) = 0.
-1, 0, 17
Let c(i) be the second derivative of i**5/20 - i**4/3 + 2*i**3/3 - 2*i + 348. Suppose c(d) = 0. Calculate d.
0, 2
Let l(v) be the first derivative of -v**4/26 - 40*v**3/39 - 37*v**2/13 - 36*v/13 - 191. Solve l(s) = 0 for s.
-18, -1
Solve 48/7 - 16/7*h - 4/7*h**2 = 0.
-6, 2
Let p = -2571/11 + 33577/143. Determine o, given that -34/13*o + 2/13*o**3 - p*o**2 - 18/13 = 0.
-1, 9
Suppose 2*p - 3*w + 11 = 0, w - 3*w + 6 = -p. Let f(y) = y**2 + 4*y + 3. Let c be f(p). Factor -2*n**2 + 2*n**3 - 2*n**4 + 2*n**2 + 2*n**2 - c*n + n.
-2*n*(n - 1)**2*(n + 1)
Solve -32832*g**2 - 935*g**4 - 492*g**4 + 6912*g + 775*g**4 + 7920*g**3 + 18*g**5 = 0 for g.
0, 2/9, 12
Solve -o + 3 - 1/3*o**3 - 5/3*o**2 = 0.
-3, 1
Factor -3/7*q**3 + 0 + 15/7*q**2 + 6*q.
-3*q*(q - 7)*(q + 2)/7
Let b = -3 + 7. Suppose 3*w + b*f = -2*w + 12, -6 = 3*f. Find c, given that -2 - 6*c**3 + 4*c**3 - w*c**2 + 2*c + 6 = 0.
-2, -1, 1
Let o be -5 + 15 + -1*2. Let f = -57 - -117. Suppose 64*n**3 - 51*n**2 - f*n + 21*n**2 - 74*n**2 + 8*n**2 - o = 0. Calculate n.
-1/4, 2
Let a(g) be the first derivative of -g**6/480 + g**4/96 - 31*g**2/2 + 25. Let v(n) be the second derivative of a(n). Suppose v(h) = 0. What is h?
-1, 0, 1
Let m = 29 + -19. Let u be m/24 - (-3)/9. Factor 3/4*f**4 - 1/2*f**2 - 1/4*f**5 - 1/4 - 1/2*f**3 + u*f.
-(f - 1)**4*(f + 1)/4
Let s(c) = 12*c**3 + 31*c**2 + 17*c. Let k(y) = 2*y**3 + 5*y**2 + 3*y. Suppose 101 = 5*g + 2*j - 69, 3*j = 0. Let d(v) = g*k(v) - 6*s(v). Factor d(z).
-4*z**2*(z + 4)
Factor -4/5*p**3 + 4/5*p**2 + 4/5*p - 4/5.
-4*(p - 1)**2*(p + 1)/5
Let x be (0 - 2) + 8/2. Let a be 32/12 + 2/(-3). Determine i so that -a*i**x + 9 - 5 + i**2 - 3 = 0.
-1, 1
Let z be (0 - (-3 + 4))*-6. Suppose c + 6 = -4*d, 2*c - 4*d = z*c. Factor 11 + 2*f**3 - 7*f**3 + 0*f**2 + 5*f**c + 25*f + 4.
-5*(f - 3)*(f + 1)**2
Let b(p) be the second derivative of -1/168*p**7 + 0*p**2 + 1/120*p**6 + 0 - 1/48*p**4 - 1/12*p**3 - 24*p + 3/80*p**5. De