4 = -5*b. Suppose 575*j + m = 594*j. Factor -3/4*t + t**j - 1/4 + 0*t**2.
(t - 1)*(2*t + 1)**2/4
Let r(x) = 2*x**2 + 4*x - 5. Let f be r(4). Let q = f - 21. Factor -k**4 + 24*k**5 + 4*k**3 - 5*k**4 - q*k**5.
2*k**3*(k - 2)*(k - 1)
Suppose 0 = -2*q - 7*p + 12*p - 1, -5*p - 15 = 0. Let r be q/14 - (-3198)/574. Solve 0 - 1/2*w**2 + 0*w**3 + 1/4*w + 1/2*w**4 - 1/4*w**r = 0.
-1, 0, 1
Let l(r) = 12*r**2 - 2. Let i = 363 - 373. Let y(d) = 4*d**2 - 1. Let c = -4 + 7. Let j(a) = c*l(a) + i*y(a). Factor j(m).
-4*(m - 1)*(m + 1)
Suppose -37*r - 7*r = -1452. Suppose r*n - 4*n + n + n**2 - 16*n = 0. Calculate n.
-14, 0
Let a(y) = -y**3 - 29*y**2 - 92*y + 202. Let j be a(-25). Let t(h) be the first derivative of 1/3*h**j + 2/27*h**3 - 20 + 4/9*h. Suppose t(g) = 0. What is g?
-2, -1
Let d(u) = -u**3 + 11*u**2 + u - 9. Let q be d(11). Let 157*a + 67*a**3 + 2*a**4 + 16 - 51*a**3 + 42*a**q - 113*a = 0. Calculate a.
-4, -2, -1
Suppose 78*m - 18 = 72*m. Let 900*u**2 + 189288 + 659278 - 54000*u + 231434 - 5*u**m = 0. Calculate u.
60
Let g(n) be the third derivative of 0 + 1/15*n**5 - 1/240*n**6 + n - 13/48*n**4 + 1/2*n**3 - 88*n**2. Suppose g(q) = 0. What is q?
1, 6
Let k = 1937/6 - 964/3. Solve 0 + k*r - 2*r**2 = 0.
0, 3/4
Factor -1422/5*q + 1/5*q**2 + 505521/5.
(q - 711)**2/5
Let v(i) = 0 - 4 + 141*i - 6*i**2 - 151*i. Let t be v(-1). Factor 1/2*m**3 + 2*m**2 + t + 0*m.
m**2*(m + 4)/2
Let a(b) = 27*b**3 + 17*b**2 - 4*b - 6. Let w(c) = -2*c**3 + c + 1. Suppose 16*v - 15*v = -5. Let t(n) = v*a(n) - 30*w(n). Factor t(k).
-5*k*(k + 1)*(15*k + 2)
Let f = 12190 - 365699/30. Let r(l) be the second derivative of 1/135*l**6 + 0*l**2 - 1/27*l**3 + 1/18*l**4 - f*l**5 + 0 - 8*l. Factor r(m).
2*m*(m - 1)**3/9
Let y(g) = g**3 - 161*g**2 + 6878*g - 19182. Let x(l) = -5*l**3 + 804*l**2 - 34389*l + 95901. Let q(u) = 2*x(u) + 11*y(u). Solve q(i) = 0 for i.
3, 80
Let q(o) be the second derivative of o**5/15 + o**4/3 + 2*o**3/3 + 46*o**2 - 3*o + 1. Let l(g) be the first derivative of q(g). Factor l(u).
4*(u + 1)**2
Let y(l) be the second derivative of l**5/60 - 59*l**4/18 - 242*l**3/9 - 244*l**2/3 + 8*l - 20. Factor y(g).
(g - 122)*(g + 2)**2/3
Let m(p) be the first derivative of 68 + 0*p**3 + 12/25*p**5 + 2/5*p**4 - 2/3*p**6 + 0*p**2 + 0*p. Factor m(f).
-4*f**3*(f - 1)*(5*f + 2)/5
Let j = 361391/42 - 53604/7. Let m = j + -946. Factor 5/6*v**2 + 5/6*v**3 - m*v - 5/6.
5*(v - 1)*(v + 1)**2/6
Let u(d) = d**3 + 11*d**2 + 32*d + 26. Let z(h) = 3*h**3 + 31*h**2 + 93*h + 79. Let p(o) = 7*u(o) - 2*z(o). Factor p(k).
(k + 1)*(k + 2)*(k + 12)
Let z = -5500 + 5503. Find b such that -14/9*b**4 + 38/9*b**z - 16/9*b**2 + 0 - 8/9*b = 0.
-2/7, 0, 1, 2
Let t(s) be the third derivative of -s**7/210 + s**6/12 + 7*s**5/5 + 23*s**4/3 + 64*s**3/3 - s**2 + 8*s - 28. Solve t(j) = 0.
-2, 16
Let j(m) be the third derivative of m**5/30 + 439*m**4/12 - 1144*m**2. Suppose j(q) = 0. What is q?
-439, 0
Let t be 20/(4 - 9) - -1*6. Suppose 0 = -3*h + 5*b - 19, 6*h - h = t*b. Factor -5/7*v - 3/7 + 2/7*v**h.
(v - 3)*(2*v + 1)/7
Let 33 + 143*j - 106*j**3 - 32*j**3 - 4038*j**4 + 193*j + 4023*j**4 + 27 + 153*j**2 = 0. What is j?
-10, -1, -1/5, 2
Let m be (-7 + 1948/280)/(6/(-8)). Let t(d) be the first derivative of 6 - 3/14*d**4 + 0*d**3 + 0*d - m*d**5 + 0*d**2. Factor t(z).
-2*z**3*(z + 3)/7
Let u(l) be the second derivative of l**6/48 + 9*l**5/8 + 405*l**4/16 + 1215*l**3/4 - 35*l**2/2 + 24*l. Let p(z) be the first derivative of u(z). Factor p(g).
5*(g + 9)**3/2
Let r(k) be the first derivative of 0*k + 1/5*k**5 - k**4 + 0*k**2 - 165 + k**3. Factor r(q).
q**2*(q - 3)*(q - 1)
Let x = -274 - -285. Factor 72 - 8*k - x*k - 8*k**2 + 4*k**3 - 17*k.
4*(k - 3)*(k - 2)*(k + 3)
Let l(z) = 27*z**4 - 198*z**3 + 420*z**2 - 204*z - 5. Let m(f) = 33*f**4 - 198*f**3 + 423*f**2 - 204*f - 6. Let n(b) = -6*l(b) + 5*m(b). Solve n(u) = 0.
-68, 0, 1
Let s(q) be the first derivative of 9*q**4/5 + 176*q**3 + 1736*q**2/5 + 1152*q/5 + 3902. Factor s(u).
4*(u + 72)*(3*u + 2)**2/5
Let q(k) be the first derivative of -k**3/15 + 41*k**2/5 - 32*k + 4137. Let q(a) = 0. Calculate a.
2, 80
Suppose 10 = 2*f + h, -13*f = -15*f + 4*h - 10. Let j(q) be the first derivative of 12 + 0*q**4 + 0*q**2 - 4/5*q**5 + 0*q + q**6 + 0*q**f. Solve j(l) = 0 for l.
0, 2/3
Suppose 2*s + 16 = -147*b + 151*b, -s + b - 3 = 0. Determine w so that -8/5*w**s - w + 10 - 1/5*w**3 = 0.
-5, 2
Let -153188*h**3 - 2*h**5 + 674040*h**2 - 336200*h + 56950*h**3 - 165794*h**3 - 77450*h**3 + 1644*h**4 = 0. Calculate h.
0, 1, 410
Find v such that -58725/4*v**3 - 23565/4*v**2 - 3/4 - 2379/4*v = 0.
-1/5, -1/783
Determine u, given that -12464*u**3 - 10*u + 12460*u**3 + 21*u - 191*u - 56*u**2 = 0.
-9, -5, 0
Let n(a) be the second derivative of a**6/10 + 12*a**5/5 + 13*a**4 + 24*a**3 - 77*a. Let n(t) = 0. What is t?
-12, -2, 0
Let l(j) be the second derivative of j**7/210 + j**6/15 - j**3/6 - 13*j**2/2 + 33*j. Let d(a) be the second derivative of l(a). Determine q so that d(q) = 0.
-6, 0
Suppose 30*d + 46*d - 50*d = 0. Let i(h) be the first derivative of 13 + 2/9*h**3 + 0*h + d*h**2. Find l, given that i(l) = 0.
0
Suppose -6*n - 44 + 80 = 0. Suppose 2*r = -3*r + 15. Factor 9*u**r - 6*u**2 - 3*u + 0 + n - 6*u**3.
3*(u - 2)*(u - 1)*(u + 1)
Suppose 815*a - 1189*a + 0 = 1511*a - 0. Find o such that -2/3*o**4 + 0 + 10/3*o**3 + a*o + 28/3*o**2 = 0.
-2, 0, 7
Let o(t) be the first derivative of t**4/40 + 121*t**3/30 - 124*t**2/5 + 50*t + 2561. Let o(v) = 0. Calculate v.
-125, 2
Let i(f) = 4*f + 85. Let h be i(-11). Determine z so that 2*z**4 + 16*z**3 - 44*z - 4*z**2 + 4*z**2 - 9 - 4*z**2 + h - 2*z**2 = 0.
-8, -2, 1
Find l, given that -4717580*l - 4708900 - 12061*l**2 + 3377*l**2 + 4846*l**3 - 4850*l**3 = 0.
-1085, -1
Let v(d) be the third derivative of 3/112*d**8 + 2/5*d**6 + 0*d**5 + 0 - 19/70*d**7 + 0*d**4 + 0*d**3 + 0*d - 61*d**2. Factor v(i).
3*i**3*(i - 1)*(3*i - 16)
Let m(h) = -h**3 + 3*h**2 - 3*h + 2. Let r be m(2). Let x = 897146 - 897144. Factor r + 2/17*s**x + 14/17*s.
2*s*(s + 7)/17
Let a(f) be the third derivative of -2*f**7/525 - f**6/600 + 7*f**5/60 + f**4/5 - 6*f**3/5 - 11504*f**2. What is k in a(k) = 0?
-2, 3/4, 3
Determine n, given that 12*n**2 + 44/3*n**4 + 0*n + 76/3*n**3 + 0 + 4/3*n**5 = 0.
-9, -1, 0
Factor -1250 + 75/2*h**2 + 250*h - 5*h**3 - 1/2*h**4.
-(h - 5)**2*(h + 10)**2/2
Let y(j) = -11*j - 28. Let n be y(-3). Determine w, given that -n + 2*w**2 + 14297*w - 3 - 14291*w = 0.
-4, 1
Let b(v) be the third derivative of -1/1176*v**8 + 1/84*v**4 + 2/735*v**7 + 0*v + 5 + 0*v**3 - 1/105*v**5 + 0*v**6 + 5*v**2. Factor b(q).
-2*q*(q - 1)**3*(q + 1)/7
Let f(d) be the third derivative of -d**5/60 + 59*d**4/24 - 123*d**3 + 822*d**2 - 3. What is v in f(v) = 0?
18, 41
Let i(c) be the third derivative of -c**7/70 - 27*c**6/5 - 5723*c**5/10 + 2943*c**4 - 11881*c**3/2 + 49*c**2 + 4*c. Factor i(o).
-3*(o - 1)**2*(o + 109)**2
Let r be (-18)/(-36)*28/77. Factor 26/11*d - r*d**3 + 20/11 + 4/11*d**2.
-2*(d - 5)*(d + 1)*(d + 2)/11
Let a(d) be the first derivative of -133 + 2*d**2 - 1/15*d**5 + 2/3*d**4 + 0*d - 19/9*d**3. Suppose a(u) = 0. What is u?
0, 1, 3, 4
Factor -761/4*m**2 + 1525/4*m - 1/4*m**3 - 763/4.
-(m - 1)**2*(m + 763)/4
Let a(l) be the third derivative of -l**7/840 + l**6/24 + 47*l**5/240 - 11*l**4/16 - 3371*l**2. Factor a(v).
-v*(v - 22)*(v - 1)*(v + 3)/4
Let a(r) be the third derivative of 1/16*r**4 + 5*r**2 + 0*r**3 + 1/40*r**5 + 0*r - 3. Factor a(m).
3*m*(m + 1)/2
Let y = 4974 - 3482. Factor 10270*q**3 + y*q + 53*q + 6199*q**2 + 90 + 1830*q**3 + 1941*q**2.
5*(5*q + 2)*(22*q + 3)**2
Let p = 148/43 - 1289/387. Let z(g) be the third derivative of 4*g**2 - p*g**3 + 0*g + 1/180*g**5 + 1/72*g**4 + 0. Factor z(b).
(b - 1)*(b + 2)/3
Suppose 3*w = 6*r, 4*w - 3*r = 9 - 9. Let c(d) be the second derivative of w*d**3 + 0 - d - 8/5*d**2 - 1/25*d**5 + 1/5*d**4. Solve c(v) = 0.
-1, 2
Suppose 0 = 11*s - 74 - 47. Suppose 3 - 1 = -5*f - 4*i, s = f - 3*i. What is a in 0*a**f + 0*a**3 + 0 + 0*a + 2/15*a**5 + 4/15*a**4 = 0?
-2, 0
Let t(y) be the first derivative of y**5/20 - 13*y**4/4 + 169*y**3/2 - 2197*y**2/2 - 13*y + 20. Let v(d) be the first derivative of t(d). Factor v(c).
(c - 13)**3
Let g = -410/1589 + 11306/1589. Find p such that 0 - 3/7*p**4 + g*p - 60/7*p**2 + 24/7*p**3 = 0.
0, 2, 4
Fact