. Let t(o) = -10*o**2 + 2. Let v(u) = -5*t(u) + w(u). Factor v(q).
-(q - 444)*(q - 1)**2
Suppose -2*t - 10 = 0, -v + 2*t + t + 18 = 0. Determine q so that -5*q**5 - 6*q - 30*q**2 + 30*q**4 + 29*q**5 - 3*q - 6*q**v - 9*q**3 = 0.
-1, -3/4, -1/2, 0, 1
Let p(g) = g - 6. Let v be p(10). Determine z, given that -56*z + 2*z**3 + z**2 + 0*z**3 + 30*z - z**v + 24*z = 0.
-1, 0, 1, 2
Let a(y) be the third derivative of -9/20*y**5 - 40/3*y**3 - 1/840*y**7 + 0*y + 4 - 19/6*y**4 - 14*y**2 - 17/480*y**6. Factor a(v).
-(v + 4)**3*(v + 5)/4
Let h(j) be the first derivative of -j**3/18 + 11*j**2/12 - 4*j - 2728. Let h(l) = 0. What is l?
3, 8
Let m be (652/2119)/(2/26). Let p(o) be the first derivative of 0*o + 4/3*o**3 + 1/2*o**m - 5 + o**2. Factor p(s).
2*s*(s + 1)**2
Factor -2/9*q**2 - 190/3*q + 0.
-2*q*(q + 285)/9
Factor -3/5*p**4 - 288*p - 1452/5*p**2 - 372/5*p**3 + 0.
-3*p*(p + 2)**2*(p + 120)/5
Let c(q) = -3*q**2 + 329*q - 984. Let k(n) = 7*n**2 - 659*n + 1974. Let s(j) = -15*c(j) - 6*k(j). Factor s(y).
3*(y - 324)*(y - 3)
Let l(d) be the third derivative of -d**6/360 + 8*d**3/3 - 131*d**2. Let x(a) be the first derivative of l(a). Factor x(n).
-n**2
Suppose -13*b + 11*b + 18 = 2*t, 21 = 3*t. Let k = -5 - -8. Let 0*l**k + 2/21*l**4 + 0 - 2/21*l**b + 0*l = 0. Calculate l.
-1, 0, 1
Let p(h) be the second derivative of h**7/16380 + h**6/195 - 5*h**5/156 + 3*h**4/4 + 3*h**2/2 + 78*h. Let u(a) be the third derivative of p(a). Factor u(f).
2*(f - 1)*(f + 25)/13
Determine p so that -21/2*p**5 - 141/2*p**4 + 24*p - 126*p**3 + 0 - 42*p**2 = 0.
-4, -2, -1, 0, 2/7
Let x = 45 - 36. Let w = -1 + x. Determine t, given that 45*t**5 + 44*t**5 + 2*t**3 + w*t**2 - 90*t**5 + 7*t + 2 - 2*t**4 = 0.
-1, 2
Suppose -84098304 - 828*r**2 + 457056*r + 1/2*r**3 = 0. Calculate r.
552
Let g(b) be the first derivative of -24*b - 15*b**3 + b**4 + 11*b**3 + 40*b + 111. Let g(k) = 0. Calculate k.
-1, 2
Let n = -64/11 - -232/55. Let t = n - -12/5. Determine s, given that 0*s**2 - 2/5*s**4 + 2/5 - t*s + 4/5*s**3 = 0.
-1, 1
Let y(q) = q**2 - q - 40. Let z(m) = -2*m**2 - 124*m + 30. Let i(v) = -4*y(v) - z(v). What is c in i(c) = 0?
-1, 65
Let i = 82 + -80. Solve -14*b**3 + 42*b**3 + 80 + 219*b + 316*b**i + 149*b = 0 for b.
-10, -1, -2/7
Let r be -2 - 7/(-2) - (-321)/214. Let y(q) be the second derivative of 1/10*q**4 + 6/5*q**2 + 0 + 18*q + 3/5*q**r. Factor y(d).
6*(d + 1)*(d + 2)/5
Let s = 1236 + -1230. Let f be s - (-2 - -1) - 5 - 0. Solve 0 - 2/23*h**3 + 2/23*h + 0*h**f = 0.
-1, 0, 1
Let l be ((200/(-24))/5)/(120/(-16)). Let p be (6/1*(-12)/(-54))/3. Factor 4/9 - p*r**2 + 2/9*r**3 - l*r.
2*(r - 2)*(r - 1)*(r + 1)/9
Let n(v) be the first derivative of -19 - 5/4*v**2 - 1/24*v**4 - 3/2*v - 7/18*v**3. Factor n(z).
-(z + 1)*(z + 3)**2/6
Let z(s) be the second derivative of s**5/20 + 19*s**4/3 - s**3/6 - 38*s**2 - 1170*s. Factor z(f).
(f - 1)*(f + 1)*(f + 76)
Let g be (-34 - 3066/(-84))*4. Factor -5/4*h**2 + 0 + g*h.
-5*h*(h - 8)/4
Suppose 4*c = 109 - 65. Suppose -45*h**3 - 63*h - 5*h**2 + 0*h**2 + c*h**4 + 108*h - 6*h**4 = 0. Calculate h.
-1, 0, 1, 9
Let w(r) be the third derivative of -11/150*r**5 - 9/20*r**4 + 0 + 0*r + 147*r**2 + 6/5*r**3. Suppose w(n) = 0. What is n?
-3, 6/11
Suppose 1600/7 - 4/7*i**3 - 1760/7*i + 164/7*i**2 = 0. Calculate i.
1, 20
Let t be 17/4 - 2/8. Factor -7*b**2 - 34*b + 6*b**2 - 31*b - t*b**2.
-5*b*(b + 13)
Let u(y) be the first derivative of 3*y**4/16 + 205*y**3/4 + 3978*y**2 + 7803*y - 1162. Factor u(g).
3*(g + 1)*(g + 102)**2/4
Let r(c) be the first derivative of 0*c**2 + c + 3/14*c**3 - 18 + 1/28*c**4. Let y(p) be the first derivative of r(p). Factor y(a).
3*a*(a + 3)/7
Let t(y) = 9*y**2 + 13*y - 73. Let u be t(-14). Suppose 0 = 9*f + u - 1527. Factor -9/5*g**3 + 0 + 6/5*g + 3*g**f.
-3*g*(g - 2)*(3*g + 1)/5
Let i(z) = 5*z**2 + 35*z - 15. Let d(f) = -7*f**2 - 52*f + 24. Let p be (2/5)/((-3)/(-360)*6). Let c(m) = p*i(m) + 5*d(m). Solve c(j) = 0 for j.
-4, 0
Let x(y) be the first derivative of -y**6/540 - 2*y**5/135 + y**4/36 + 2*y**3/3 - 4*y**2 + 3*y - 17. Let m(h) be the second derivative of x(h). Factor m(g).
-2*(g - 2)*(g + 3)**2/9
Factor -246/17*j**2 + 2/17*j**3 + 486/17*j - 242/17.
2*(j - 121)*(j - 1)**2/17
Let m(p) = 5*p**3 + 131*p**2 + p - 125. Let h(s) = -15*s**3 - 391*s**2 - s + 375. Let n(z) = 3*h(z) + 8*m(z). Determine i so that n(i) = 0.
-25, -1, 1
Let d(u) be the first derivative of -4*u**5/5 + 62*u**4 + 4*u**3/3 - 124*u**2 + 1529. Factor d(v).
-4*v*(v - 62)*(v - 1)*(v + 1)
Suppose -10*f + 368 = 88. What is w in -34*w**4 - 32*w**4 + 90*w**4 - f*w**4 + w + 3*w**2 = 0?
-1/2, 0, 1
Let k(x) be the third derivative of -x**7/5880 + x**6/360 + 33*x**3 - 148*x**2. Let a(b) be the first derivative of k(b). Suppose a(f) = 0. What is f?
0, 7
Let t(l) be the first derivative of -188 - 1/2*l**3 + 10*l - 7*l**2. Factor t(x).
-(x + 10)*(3*x - 2)/2
Let n(u) be the second derivative of u**5/150 - 14*u**4/15 + 36*u**3/5 - 64*u**2/3 - u - 429. Factor n(k).
2*(k - 80)*(k - 2)**2/15
Let g(p) = 3*p**3 - 67*p**2 + 223*p + 200. Let s be g(18). Factor 1/6*f**s + 14/3 - 8/3*f.
(f - 14)*(f - 2)/6
Let u(z) = -z + 14. Let x be u(12). Let l(p) = -p**2 + 4*p - 1. Let g be l(x). Factor v**g - v**5 - 12*v + 13*v - v.
-v**3*(v - 1)*(v + 1)
Let c(r) = -r**2 - r + 3*r - 7*r + 1 + 6*r. Let n be 2*(7/(-28) + (-79)/4). Let p(j) = 7*j**2 - 4*j - 11. Let h(q) = n*c(q) - 5*p(q). Factor h(m).
5*(m - 3)*(m - 1)
Let x = -127996 - -63101963/493. Let c = 3/29 - x. Solve c*j**3 + 0 + 2/17*j**4 + 0*j - 6/17*j**2 = 0 for j.
-3, 0, 1
Let j(i) be the second derivative of i**6/30 + 9*i**5/100 - 61*i**4/30 + 4*i**3/5 + 39*i - 1. Determine a, given that j(a) = 0.
-6, 0, 1/5, 4
Let b(o) = -48*o**3 - 3*o**2 + 5. Let u(y) = 72*y**3 - 8 + 4*y**2 + 17*y + 14*y - 31*y. Let k(i) = 8*b(i) + 5*u(i). Find w such that k(w) = 0.
-1/6, 0
Factor 46*b - 23*b**2 - 529 - 4*b**2 - 18*b**2 + 44*b**2.
-(b - 23)**2
Factor 3/4*r**4 + 9*r + 0 - 3/4*r**2 - 9*r**3.
3*r*(r - 12)*(r - 1)*(r + 1)/4
Let u = 135 - 48. Let b = u + -84. What is o in -17*o - 4*o**2 - 8 + o**3 + 0*o**2 + 3*o + o**b = 0?
-1, 4
Let k = 10/6543 - -45781/13086. Suppose 5/2*b**3 + 0 - k*b**2 + b = 0. What is b?
0, 2/5, 1
Let m be ((0 - 0)/(3/(-3)))/(-1). Suppose m = -4*i - u + 19, -5*u - 55 = -11*i + 6*i. Suppose 2 - 67*l - 65*l + 136*l - i*l**2 = 0. Calculate l.
-1/3, 1
Let g(n) be the first derivative of 3*n**4/4 + 6*n**3 - 27*n**2/2 - 42*n - 1861. Find a such that g(a) = 0.
-7, -1, 2
Let o(h) be the third derivative of 0 + 0*h**3 + 0*h - 24/5*h**5 - 140*h**2 + 11/40*h**6 - 1/210*h**7 + 32/3*h**4. What is n in o(n) = 0?
0, 1, 16
Let l(f) be the third derivative of -7/8*f**4 + 0*f + 147/2*f**3 - 27 - 1/40*f**6 - f**2 - 11/20*f**5. Factor l(o).
-3*(o - 3)*(o + 7)**2
Let m(j) = -j**3 + 12*j**2 + 8*j - 95. Let y be m(12). Let 103*t + 10*t**2 - y - 5 - 20*t**3 - 83*t + 4*t**4 + t**4 - 9 = 0. What is t?
-1, 1, 3
Factor 27/2*w**3 + 3/4*w**4 + 36*w**2 + 69/2*w + 45/4.
3*(w + 1)**3*(w + 15)/4
Suppose -5225 = -14*l - 997. Suppose -322 + l = -10*t. Let -1/2*i**t + 4*i - 8 = 0. What is i?
4
Let o(v) be the second derivative of -3/10*v**5 - 1/6*v**4 + 0 - 68*v - 1/15*v**6 + v**3 + 2*v**2. Find l such that o(l) = 0.
-2, -1, 1
Let o = 76242 + -388248/5. Let h = o + 1408. Factor 7/10*k**2 - 1/10 + 1/5*k + h*k**3.
(k + 1)**2*(4*k - 1)/10
Let g(i) = -3*i**4 - 8*i**3 - i**2 + 12*i. Let w(j) = -3*j**4 - 9*j**3 + 12*j. Let n(l) = 3*g(l) - 4*w(l). What is k in n(k) = 0?
-4, -1, 0, 1
Factor 1007/4*x**2 + 0 + 0*x - 1/8*x**3.
-x**2*(x - 2014)/8
Determine r, given that 2752/3*r**3 - 182/3*r**4 - 16192/3*r**2 + 1/3*r**5 + 42752/3*r - 42496/3 = 0.
4, 166
Determine c so that -28*c**2 - 59/2*c + 1/2*c**3 + 57 = 0.
-2, 1, 57
Let d = 1021 - 1156. Let f = 135 + d. Find q such that 0 - 4/3*q**2 + f*q = 0.
0
Determine m so that -528/23 - 526/23*m + 2/23*m**2 = 0.
-1, 264
Let r = -145415 - -145418. Determine z so that 24/7*z**r + 0*z + 0 - 2/7*z**4 - 72/7*z**2 = 0.
0, 6
Let r = 1168/8179 - -3/57253. Factor -1/7*l**3 + 1/7*l**4 + 1/7*l + 0 - r*l**2.
l*(l - 1)**2*(l + 1)/7
Suppose 0 = -8*j + 4*j. Suppose -3*g + 70 + 115 = 5*d, -3*g = j. Factor y**4 + 0*y**4 + 37 - d.
y**4
Let o be (42/(-84))/(2*(-3)/192). Let 72*y**2 + o*y - 7*y - 4 + 1 - 6 - 74*y**2 = 0. Calculate y.
3/2, 3
Let z = -15/497 +