*4 - 16*x**3 + 2*x**2 - 8*x + 6. Let h(v) = 15*v**4 - 16*v**3 + 2*v**2 - 6*v + 5. Let f(q) = -5*g(q) + 6*h(q). Find t, given that f(t) = 0.
-2/5, 0, 1
Factor -5/2*c**4 - 65/2*c + 0 - 75/2*c**3 - 135/2*c**2.
-5*c*(c + 1)**2*(c + 13)/2
Let v(j) be the second derivative of -j**7/42 + j**6/30 + j**5/10 - j**4/6 - j**3/6 + j**2/2 + 15*j. Suppose v(r) = 0. Calculate r.
-1, 1
Let u(y) be the second derivative of 2*y**6/15 - 12*y**5/5 + 16*y**4 - 128*y**3/3 + 62*y - 4. Factor u(f).
4*f*(f - 4)**3
Suppose 130 - 54 + 12*m - 4*m**3 - 68 = 0. Calculate m.
-1, 2
Let t(q) be the second derivative of q**4/6 + 17*q**3/3 + 30*q**2 - 196*q. Solve t(z) = 0.
-15, -2
Factor -44/5*m + 968/5 + 1/10*m**2.
(m - 44)**2/10
Factor 6/11*h + 2/11*h**2 - 8/11.
2*(h - 1)*(h + 4)/11
Determine z, given that 683*z + 31684 + 219*z - 498*z**2 - 190*z + 502*z**2 = 0.
-89
Let j(a) = -2*a + 54. Let z be j(19). Suppose 0 = -m + 9*m - z. Determine d so that 54*d**5 + 4/3*d - 102*d**4 + 62*d**3 - 46/3*d**m + 0 = 0.
0, 2/9, 1/3, 1
Let g(y) be the third derivative of 0*y**3 - 1/240*y**6 + 0*y - 3*y**2 + 0 + 1/48*y**4 + 0*y**5. Factor g(b).
-b*(b - 1)*(b + 1)/2
Let d = 15557 + -15457. What is m in 15/2*m**3 + 245 - d*m**2 + 595/2*m = 0?
-2/3, 7
Let c(s) = 13*s**2 - 3*s + 2. Let l(r) = 20*r**2 - 4*r + 2. Let u(d) = 3*c(d) - 2*l(d). Determine v so that u(v) = 0.
-2, 1
Let m(j) be the third derivative of j**8/20160 - j**7/560 + j**6/90 + j**5/12 - 2*j**3/3 - 39*j**2. Let b(z) be the third derivative of m(z). Factor b(n).
(n - 8)*(n - 1)
Suppose 0 = -6*p + 4*p - 8. Let u(s) = -1. Let c(x) = x - 3*x + x**2 + 0*x**2 - x - 2. Let o(b) = p*u(b) + 2*c(b). Factor o(f).
2*f*(f - 3)
Let z(q) be the second derivative of -q**7/1260 + q**5/60 + 11*q**4/12 + q. Let y(n) be the third derivative of z(n). Suppose y(u) = 0. Calculate u.
-1, 1
Let a(m) be the second derivative of -m**5/30 + m**4/6 + m**3 + 5*m**2/3 - 36*m - 1. Factor a(k).
-2*(k - 5)*(k + 1)**2/3
Find k, given that -7*k**3 + 5*k**2 + 29*k**4 + 33*k**4 + 9*k**2 - 8*k - 61*k**4 = 0.
0, 1, 2, 4
Find j, given that -16*j - 3*j + 6*j - j**2 - j**3 - 13*j**2 = 0.
-13, -1, 0
Suppose -2*b - 2*t + 22 = 0, -37 = -5*b + 2*t - t. Factor b*k**4 - 3 + 40*k - 3*k**4 - 5 - 30*k**2 - 7.
5*(k - 1)**3*(k + 3)
Let n(l) = -248*l + 2728. Let v be n(11). Suppose v*b - 1/5*b**2 + 4/5 = 0. What is b?
-2, 2
Let n(k) = k**2 - 43*k - 39. Let g(c) = 2*c**2 - 64*c - 58. Let p(b) = 5*g(b) - 8*n(b). What is i in p(i) = 0?
-11, -1
Let q be -2 + -1*(-36)/14. Let c(j) = 15*j**2 + 45*j + 3. Let x be c(-3). Solve 0 + 0*z**2 - q*z**4 - 2/7*z**x + 0*z = 0.
-1/2, 0
Let r = -233736385084/90929213109 + 628/6459417. Let z = 2/2011 - r. Let -z*o**2 - 2/7*o**4 + 10/7*o**3 + 2*o - 4/7 = 0. What is o?
1, 2
Let n be 2/7*(5 - -8)/26. Suppose 6/7*m - 8/7 - n*m**2 = 0. Calculate m.
2, 4
Factor -1600 - 323*m - 4*m**2 - 231*m + 714*m.
-4*(m - 20)**2
Determine m, given that -23*m**4 - 125*m**2 + 0*m + 13*m**2 + 12*m - 31*m**4 + 131*m**3 + 7*m**5 + 16 = 0.
-2/7, 1, 2, 4
Let x be 2*(4 - 21/6). Determine k so that 25*k + 7*k - 810*k**3 + 3 + 6 - x - 198*k**2 = 0.
-2/9, 1/5
Let p(r) be the third derivative of r**5/15 + 32*r**4 + 6144*r**3 - 61*r**2. Suppose p(s) = 0. Calculate s.
-96
Let p be 557 - (5 - (3 + 0)). Determine n, given that 316*n - 75*n**2 - p + 5*n**3 + 59*n - 70 = 0.
5
Let j = 379/1986 + -8/331. Suppose 0 - 1/6*f**2 + j*f**4 + 1/6*f - 1/6*f**3 = 0. Calculate f.
-1, 0, 1
Let h(f) = 83*f - 91*f + 7*f**2 + 0*f**2. Let i(m) = 8*m**2 - 8*m. Let c(y) = -4*h(y) + 3*i(y). Factor c(q).
-4*q*(q - 2)
Let z be (-11 - -15)/((-2)/(-2)). Factor -z*u**2 + 339 + 0*u**4 - 337 + 2*u**4 + 0*u**2.
2*(u - 1)**2*(u + 1)**2
Find t such that 2/7*t**3 + 30/7*t**2 + 54/7*t + 26/7 = 0.
-13, -1
Let i be (13/26)/(3*3/54). Let c(l) be the third derivative of -3*l**2 + 2/5*l**6 + 3/7*l**7 + 0*l**4 + 0*l + 0 + 2/15*l**5 + 0*l**i + 25/168*l**8. Factor c(j).
2*j**2*(j + 1)*(5*j + 2)**2
Let k = -56 - -68. Factor 4*y**2 + k*y**3 - 18*y**4 - 6*y**3 + 2*y + 6*y**2.
-2*y*(y - 1)*(3*y + 1)**2
Solve 998*i**3 + 50*i**2 + 135*i**2 - 353*i**3 + 10*i + 277*i**4 - 2162*i**4 + 1045*i**5 = 0.
-2/19, -1/11, 0, 1
Let y = -199 - -202. Let a(u) be the second derivative of -2*u + 1/63*u**7 + 0*u**y + 2/15*u**5 + 0*u**4 - 4/45*u**6 + 0 + 0*u**2. Factor a(g).
2*g**3*(g - 2)**2/3
Let p(m) = -m**2 + 7 + 0 + 2 + 1 + 11*m. Let s be p(10). Determine a, given that -1 - 3 - 14*a**2 + 18*a + 24*a**4 + s*a**3 + 0*a**2 + 16*a**5 - 48*a**3 = 0.
-2, -1, 1/2
Let l be (-65)/(-143)*(1 + 0). Let s = 69/55 - l. Determine x so that 0*x + 0 + 4/5*x**2 - 2*x**3 + s*x**4 = 0.
0, 1/2, 2
Suppose 3671*m - 3692*m = -42. Factor 1/4*i**m - 1/4 + 0*i.
(i - 1)*(i + 1)/4
Let b be 39/(-6)*(-456)/1976. Find s, given that 0 + 3/2*s**3 - 1/2*s**2 - b*s + 1/2*s**4 = 0.
-3, -1, 0, 1
Let j = 61667/3 + -20555. Factor 1/6*n**2 + 5/6*n + j.
(n + 1)*(n + 4)/6
Let z(q) = -3*q + 54. Let x be z(24). Let h be 8/x*(19/(-2) + 5). Factor -2/11*w**3 + 4/11 + 0*w**h + 6/11*w.
-2*(w - 2)*(w + 1)**2/11
Let 13 + 15/2*k - 6*k**2 - 1/2*k**3 = 0. What is k?
-13, -1, 2
Let x(w) = 2*w**2 + 5*w - 1. Let s(j) = -j. Let v(a) = 3*s(a) + x(a). Let l be v(-2). Let -3/7*b - 9/7*b**l + 0 + 3/7*b**4 + 9/7*b**2 = 0. Calculate b.
0, 1
Let a(g) be the second derivative of g**5/140 + 5*g**4/42 + 2*g**3/3 + 12*g**2/7 - 101*g. What is b in a(b) = 0?
-6, -2
Let w be (0 - -1) + 2 - 0. Determine r, given that 30*r**2 + 7*r**w - 8 - r**4 + 4*r + 6*r**4 + 16*r**3 + 0*r**4 = 0.
-2, -1, 2/5
Let c(l) be the third derivative of -l**7/70 - l**6/40 + 13*l**5/4 + 225*l**4/8 - 2*l**2 - 54*l. Factor c(m).
-3*m*(m - 9)*(m + 5)**2
Let w(a) be the second derivative of -9*a**4/10 - 32*a**3/5 - 4*a**2 - 6*a + 11. What is x in w(x) = 0?
-10/3, -2/9
Let k(q) be the second derivative of q**4/4 + 15*q**3 + 87*q**2/2 + q + 77. Let k(x) = 0. Calculate x.
-29, -1
Factor -10*t**2 + 140*t + 14*t**2 + 20*t.
4*t*(t + 40)
Let z(t) be the second derivative of -t**7/42 + t**6/2 - 23*t**5/10 + 3*t**4/2 + 47*t**3/6 - 33*t**2/2 + 66*t - 8. Suppose z(j) = 0. Calculate j.
-1, 1, 3, 11
Let s(w) be the second derivative of -w**8/36960 + w**7/6930 + w**6/3960 - w**5/330 - 4*w**4/3 + 8*w. Let l(b) be the third derivative of s(b). Factor l(o).
-2*(o - 2)*(o - 1)*(o + 1)/11
Solve -1082 - 9*i - 16*i - 49*i - 287 + 3*i**2 - 4*i**2 = 0 for i.
-37
Suppose 0 = 10*z + 11*z - 1134. Let y be ((-16)/z*-12 - 4)/(-1). Factor -y*f**2 - 2/9 + 2/3*f.
-2*(f - 1)*(2*f - 1)/9
Let a = -74 - -102. Factor 8 - 8*w**2 + 12*w**3 - 6*w**3 - 5*w**3 - 29*w**3 + a*w.
-4*(w - 1)*(w + 1)*(7*w + 2)
Let m be ((-2)/28)/((-5)/(-150)*-15). Factor -m*j**3 - 12/7*j - 6/7*j**2 - 8/7.
-(j + 2)**3/7
Let s(p) = -5*p**3 + 17*p**2 + 29*p + 17. Let d(v) = 17*v**3 - 53*v**2 - 87*v - 52. Let i(a) = -4*d(a) - 14*s(a). Determine w so that i(w) = 0.
-1, 15
Factor -1/7*y**3 + 24/7*y**2 + 0 - 44/7*y.
-y*(y - 22)*(y - 2)/7
Suppose -5*r + 15 = -0*r. Let m(x) be the first derivative of 4/15*x**3 + r - 2/25*x**5 - 2/5*x + 0*x**4 + 0*x**2. Suppose m(v) = 0. Calculate v.
-1, 1
Suppose 22 = 2*m + 14. Let z be (m/(-12))/((-15)/9). Factor 0 - 2/5*p + z*p**2.
p*(p - 2)/5
Let -2/5*v**2 + 2/5*v**3 - 2/5*v + 2/5*v**4 + 0 = 0. What is v?
-1, 0, 1
Suppose 9/5*q**5 + 18/5*q**3 + 0 - 3/5*q + 24/5*q**4 + 0*q**2 = 0. What is q?
-1, 0, 1/3
Suppose 142*q + 18 = 151*q. Let p(j) be the first derivative of 1/9*j**3 + 1/3*j**q - 9 + 0*j. Solve p(o) = 0 for o.
-2, 0
Let k be (-1)/(-4) + 30/8. Let p = 178 - 176. Find g such that -6 + k*g - 2/3*g**p = 0.
3
Let c(u) be the third derivative of 0*u + 1/132*u**4 + 0 - 12*u**2 + 1/33*u**3 - 1/330*u**5 - 1/660*u**6. Let c(v) = 0. What is v?
-1, 1
Find h, given that -576/5 + 332/5*h**2 - 384*h - 14/5*h**3 = 0.
-2/7, 12
Let m(u) = u**3 + 12*u**2 + 8*u + 31. Let p be m(-12). Let l = p - -65. Let 0 + 2/3*o**3 + l*o - 2/3*o**2 = 0. Calculate o.
0, 1
Let t(v) = -v + 9 - 5 + 4. Let u be t(6). Solve 3*p**4 + 3*p**3 + 3*p**2 - 2*p**u - 4*p**2 - 3*p = 0 for p.
-1, 0, 1
Suppose 5*c - b + 10 = 0, -c = 3*c + 4*b - 16. Let m(f) = f**2 - 1. Let x(d) = 5*d**2 - 6*d + 1. Let y(h) = c*x(h) - 4*m(h). Factor y(q).
-3*(q - 1)*(3*q + 1)
Let l(h) be the second derivative of -h**5/110 + 5*h**4/66 - 8*h**3/33 + 4*h**2/11 - 38*h. Find v such that l(v) = 0.
1, 2
Let p(d) = 23*d - 3*d**2 + 2*d**2 - 14*d + 8 + 