3
Let z(s) = -5*s**2 - 22*s - 23. Let p(w) = 15*w**2 + 67*w + 68. Suppose 4*m + 2*i = -16, 3*i + 3 = -3*m - 12. Let o(c) = m*p(c) - 8*z(c). Solve o(l) = 0.
-4, -1
Suppose -2*m = -5*t + 14, 5*m - 4 = -4*t - 6. Let u(v) be the third derivative of 1/36*v**4 + 0 - 2/45*v**3 + 0*v + 5*v**t + 7/450*v**5. Factor u(z).
2*(z + 1)*(7*z - 2)/15
Factor 246/7*o**3 + 3/7*o**4 + 4791/7*o**2 + 756 - 1476*o.
3*(o - 1)**2*(o + 42)**2/7
Let i = -86 + 86. Let t(g) be the first derivative of i*g + 0*g**2 + 3/2*g**4 - 2/3*g**3 - 6/5*g**5 + 1/3*g**6 - 5. Factor t(b).
2*b**2*(b - 1)**3
Suppose 7*v - 4*v + 3 = -3*y, 0 = -5*v - 3*y + 3. Factor 45*h**2 + h**5 - 84*h**2 + h**4 - 2*h**v + 38*h**2 + h**3.
h**2*(h - 1)*(h + 1)**2
Let b(h) = 119*h - 81*h**2 + 23*h**3 - 16 + 16*h - 36*h. Let o(c) = -116*c**3 + 404*c**2 - 496*c + 80. Let t(n) = -16*b(n) - 3*o(n). Solve t(a) = 0 for a.
1/5, 2
Determine j so that -596*j + 3829*j**3 - 1937*j**3 - 448*j**2 - 1912*j**3 - 168 = 0.
-21, -1, -2/5
Let g be (1 - (-8)/2) + -1. Solve -8*o**2 - g*o**3 - 88*o + 84*o + 0 + 0 = 0.
-1, 0
Let q = 22 - 11. Factor -q*p**2 - 3*p - 4*p - 1 + 2*p + 7.
-(p + 1)*(11*p - 6)
Let p(o) be the second derivative of -81*o**6/10 + 162*o**5/5 - 54*o**4 + 48*o**3 - 24*o**2 - 11*o + 2. Factor p(q).
-3*(3*q - 2)**4
Suppose 4*w = -18*u + 17*u + 19, -3*w + 3*u - 12 = 0. What is x in 1/2 + 3/4*x**w - 1/4*x**2 - 1/4*x**4 - 3/4*x = 0?
-1, 1, 2
Suppose 2*q = 2*w - 2, -3*w + 5*q - q = -2. Suppose 33 = 5*k - 3*d, -2*k + 0*d = w*d - 10. Let -6*t**2 - 62 - 4*t**2 + 80 - k*t - 2*t**3 = 0. What is t?
-3, 1
Let w be -19*80/(-190)*(-2 - 19/(-8)). Determine z so that -4/3*z - 56/3*z**4 + 8/3 + 4*z**5 - 16*z**2 + 88/3*z**w = 0.
-1/3, 1, 2
Let r(d) = -7*d**2 + 5*d - 4. Let s(h) = h**2. Let y(t) = 5*r(t) + 30*s(t). Factor y(n).
-5*(n - 4)*(n - 1)
Let y(r) be the second derivative of -r**5/105 - 2*r**4/21 - 8*r**3/21 + 13*r**2/2 + 19*r. Let h(t) be the first derivative of y(t). Let h(u) = 0. Calculate u.
-2
Let c be 9/(-3) + 1 - (0 - 5). Let o(m) be the first derivative of 0*m - 1 + 3/2*m**2 - 3/8*m**4 + 1/2*m**c. Factor o(k).
-3*k*(k - 2)*(k + 1)/2
Let g(t) be the second derivative of -t**4/18 + 40*t**3/9 + 28*t**2 + 646*t. Factor g(q).
-2*(q - 42)*(q + 2)/3
Let k be (-51)/(-3)*(-2)/4. Let b = -33/4 - k. Factor 0 + b*i + 0*i**2 - 1/4*i**3.
-i*(i - 1)*(i + 1)/4
Let s = -53855/2198 - -2/1099. Let b = -24 - s. Suppose -3/2*g + b*g**3 + 0 + g**2 = 0. What is g?
-3, 0, 1
Let t(c) be the third derivative of -c**8/1008 - c**7/315 + c**6/180 + 2*c**5/45 + 7*c**4/72 + c**3/9 - 44*c**2 + 2. Determine b, given that t(b) = 0.
-1, 2
Let s(y) be the first derivative of -98*y**6/15 - 182*y**5/25 + 38*y**4/5 + 74*y**3/15 - 28*y**2/5 + 8*y/5 + 93. Find k such that s(k) = 0.
-1, 2/7, 1/2
Factor 0 - 117/4*j - 9/4*j**3 - 177/2*j**2.
-3*j*(j + 39)*(3*j + 1)/4
Let u(m) be the first derivative of 8/9*m + 15 - 5/36*m**4 - 14/9*m**2 + 22/27*m**3. Factor u(i).
-(i - 2)**2*(5*i - 2)/9
Factor -62/13*z + 116/13 + 2/13*z**2.
2*(z - 29)*(z - 2)/13
Let j(v) be the third derivative of -1/12*v**5 + 1/42*v**7 + 0*v + 0 + 39*v**2 - 1/8*v**4 - 1/168*v**8 + 0*v**3 + 1/24*v**6. Suppose j(x) = 0. Calculate x.
-1, -1/2, 0, 1, 3
Let w(l) = l**3 - 12*l**2 - 14*l + 16. Suppose g - 3*y - 4 = 0, -2*y = 5*g - 0*g - 71. Let n be w(g). Factor 3*d**3 + d - d - 3*d**2 + 0*d**n - 3*d + 3*d**4.
3*d*(d - 1)*(d + 1)**2
Let h(q) be the first derivative of 2*q**6/9 - 8*q**5/3 + 17*q**4/3 - 32*q**3/9 + 186. Factor h(f).
4*f**2*(f - 8)*(f - 1)**2/3
Suppose 0 = 53*b - 60*b + 84. Let h be b/(-8) + 21/6. Suppose -4/7*l + 0 - 6/7*l**3 + 10/7*l**h = 0. What is l?
0, 2/3, 1
Let o = -540 + 544. Let j(p) be the first derivative of -2 + 3/4*p**o + 4*p**3 + 6*p**2 + 0*p. Factor j(w).
3*w*(w + 2)**2
Let d(m) be the third derivative of 2/105*m**7 + 0*m**5 + 0 + 3*m**2 + 0*m**3 + 0*m + 0*m**6 + 0*m**4. Factor d(s).
4*s**4
Let q(n) be the second derivative of 7*n**6/720 + n**5/48 - n**4/24 - 13*n**3/3 + 22*n. Let u(m) be the second derivative of q(m). Factor u(a).
(a + 1)*(7*a - 2)/2
Let r(v) be the first derivative of v**5/10 + 7*v**4/8 + 3*v**3 + 5*v**2 + 4*v - 14. Factor r(k).
(k + 1)*(k + 2)**3/2
Let j be (-16)/20 - (-56)/20. Let 25/4 - 5/2*h + 1/4*h**j = 0. Calculate h.
5
Let j be 7 + 8/8 - 6. Let a(v) be the first derivative of -2 + j*v + 3/2*v**2 + 1/3*v**3. Factor a(f).
(f + 1)*(f + 2)
Find w, given that -35*w**2 - 25 + 112*w**3 - 76*w**4 - 12*w**2 + 16*w**5 - 4*w + 29 = 0.
-1/4, 1/2, 2
Let t(h) be the first derivative of -2*h**3/63 + 8*h**2/21 - 32*h/21 + 19. Factor t(d).
-2*(d - 4)**2/21
Determine w so that 2*w**4 + w**4 - 243*w**2 + 75*w**3 - 55216 + 55132 + 249*w = 0.
-28, 1
Factor 41*a**3 + 63375*a + 641516 + 975*a**2 - 36*a**3 + 731609.
5*(a + 65)**3
Let k(b) be the second derivative of b**9/83160 + b**8/18480 - b**6/1980 - b**5/660 - 2*b**4/3 + 7*b. Let p(v) be the third derivative of k(v). Factor p(d).
2*(d - 1)*(d + 1)**3/11
Let n = 3/6880 - -13739/48160. Solve -n*q**5 + 2*q**4 + 8/7 - 38/7*q**3 + 50/7*q**2 - 32/7*q = 0 for q.
1, 2
Let -1/3*h**3 + 0 + h + 2/3*h**2 = 0. Calculate h.
-1, 0, 3
Let u(l) = -l**4 + l**3 - l**2 + 1. Let b(j) = j**4 - 10*j**2 + 4*j + 5. Let x(h) = 3*b(h) - 12*u(h). Factor x(f).
3*(f - 1)**2*(f + 1)*(5*f + 1)
Let c(w) be the second derivative of -2*w**7/63 - 2*w**6/45 + 2*w**5/15 + 2*w**4/9 - 2*w**3/9 - 2*w**2/3 - 299*w. Factor c(k).
-4*(k - 1)**2*(k + 1)**3/3
Factor 132/7*z - 54*z**2 + 48/7.
-6*(7*z - 4)*(9*z + 2)/7
Factor 8 + 20/3*z**2 - 68/3*z.
4*(z - 3)*(5*z - 2)/3
Let m = -25 - -19. Let i(y) = y**4 + 5*y**2 - 6*y + 4. Let d(o) = 2*o**4 - o**3 + 6*o**2 - 5*o + 4. Let w(x) = m*i(x) + 4*d(x). Let w(v) = 0. What is v?
-2, 1, 2
Let z = -41 - -43. Suppose z*t + t = -t. Solve 1/3*y**4 - 4/3*y + t + 0*y**2 + y**3 = 0.
-2, 0, 1
Let 360*d**2 - 66*d + 66*d**3 + 2*d**4 - 150 - 213 + d**4 = 0. What is d?
-11, -1, 1
Let b(z) = 2570*z**4 - 6720*z**3 - 2785*z**2 - 270*z. Let w(g) = 1284*g**4 - 3360*g**3 - 1393*g**2 - 135*g. Let k(o) = 2*b(o) - 5*w(o). Factor k(s).
-5*s*(s - 3)*(16*s + 3)**2
Let p be 12/(-30) - 1044/(-10). Determine k, given that -2*k**3 - 104 + 3*k**4 + 3*k**2 + p - 4*k**3 = 0.
0, 1
Let g(k) = 2*k - 1. Let f be g(3). Suppose -5*j = f*x - 15, -5*j + 3*x + 0*x + 15 = 0. Factor -6*o**4 + 2*o + 6*o**2 + 5*o - 4*o**j - 3*o.
-2*o*(o - 1)*(o + 1)*(3*o + 2)
Let j = -10297/3 - -3433. Suppose 1/6*g**5 + 2/3*g**4 + j*g**2 + 0 + g**3 + 1/6*g = 0. Calculate g.
-1, 0
Let r = 518 - 518. Suppose -4*q + 3*p = 4, 0*q + 5*p = -2*q + 24. What is o in -o**q + r + 1/4*o = 0?
0, 1/4
Let p = -3148 - -3150. What is i in -2*i - 13/2*i**3 - 1/2*i**5 + 0 - 3*i**4 - 6*i**p = 0?
-2, -1, 0
Let c = -49 - -43. Let n be ((-28)/c)/(24/9). Let 0*q - n*q**4 + 9/4*q**3 - 1/2*q**2 + 0 = 0. Calculate q.
0, 2/7, 1
Let s be -2*(-2)/(-4)*-1. Let j be -2*(-1)/(1/s). What is p in j*p**2 - 2*p - 3*p + p = 0?
0, 2
Let n(u) = u**2. Let x be n(2). Suppose 10 - 25 = -5*y. Solve x*c**2 - 13*c**3 - c - 6*c**y + 9*c + 7*c**3 = 0.
-2/3, 0, 1
Let b(j) = j**2 - 9*j - 14. Let t be b(11). Suppose t*v - 5*v**2 + 87 + v**3 - 46 - 45 = 0. Calculate v.
1, 2
Let z(d) be the second derivative of d**4/3 + 208*d**3/3 + 5408*d**2 + 48*d. Factor z(v).
4*(v + 52)**2
Let h be (-4 - (-6 - 0))/((-4)/550). Let w be h/(-375) - (-3)/5. Determine c so that c**3 - 4/3*c + w*c**2 + 0 = 0.
-2, 0, 2/3
Suppose 3*t + 56 = -2*g, 4*t = -6*g + g - 84. Let v be (-2)/(-4) + 4/t. Factor 0*j - 1/4*j**5 + 0*j**2 + 0 + 0*j**3 + v*j**4.
-j**4*(j - 1)/4
Let m be (1 + -1)/(-5 + 4). Let k = 1107 + -1107. Solve -2/3*w**3 + m + 1/3*w**2 - w**4 + k*w = 0 for w.
-1, 0, 1/3
Let i(g) be the first derivative of g**7/210 + g**6/45 - g**5/30 - g**4/3 + 20*g**3/3 - 25. Let s(b) be the third derivative of i(b). Factor s(f).
4*(f - 1)*(f + 1)*(f + 2)
Let d(g) be the first derivative of 1/30*g**3 + 5 + 1/20*g**6 + 0*g - 1/50*g**5 - 3/40*g**4 + 0*g**2. Let d(r) = 0. What is r?
-1, 0, 1/3, 1
Let a be 11/(11/(-4)) - -14*2/4. What is g in 8/3*g + 0 + 2*g**a - 16/3*g**2 = 0?
0, 2/3, 2
Factor 51/4*l**2 + 4913 + 1/8*l**3 + 867/2*l.
(l + 34)**3/8
Let a be -6 + (-1135)/25*-3. Let h = a + -130. Factor 1/5*p**3 + 0*p**2 + h*p**4 + 0*p + 0.
p**3*(p + 1)/5
Let s(z) be the second derivative of -z**7/210 - z**6/40 - z**5/20 - z**4/24 - 39*z**2/2 - 31*z. Let n(p) be the f