, 1/2, 1
Factor -61*o - 123/2 + 1/2*o**2.
(o - 123)*(o + 1)/2
Factor -2571/7*z**2 - 552120/7*z - 549552/7 - 3/7*z**3.
-3*(z + 1)*(z + 428)**2/7
Factor -140/9*i + 38/9*i**2 - 176/9 + 2/9*i**3.
2*(i - 4)*(i + 1)*(i + 22)/9
Let l(m) be the first derivative of m**5/27 + m**4/6 + 8*m**3/27 + 15*m**2 - m - 65. Let w(u) be the second derivative of l(u). Suppose w(q) = 0. Calculate q.
-1, -4/5
Let x(y) be the first derivative of 7 + 3*y**2 + 1/2*y**3 + 2*y - 1/4*y**4. Let t(k) be the first derivative of x(k). Solve t(g) = 0 for g.
-1, 2
Let j be 8/(-5)*((-11112)/(-624) - 18). Let w(d) be the first derivative of -1/26*d**4 - 16 + 3/13*d**2 - j*d + 0*d**3. Factor w(a).
-2*(a - 1)**2*(a + 2)/13
Suppose -5*s + 21 - 11 = 0. Suppose 5*y = 5, -s*o + 2*y + 1 = -y. Factor -2/5*d**5 + 2/5*d**o - 2/5*d**4 + 2/5*d**3 + 0 + 0*d.
-2*d**2*(d - 1)*(d + 1)**2/5
Let a(b) = -b**3 + 32*b**2 + 36*b - 71. Let v be a(33). Factor -13*h**5 - v*h**4 + 57*h**2 + 53*h**2 - 17*h**3 - 112*h**2.
-h**2*(h + 1)**2*(13*h + 2)
Suppose 7 = -12*i + 103. Suppose -2*n - 2*n = 0, -5*n = 4*a - i. Factor -8/5*q - 2/5*q**a + 0.
-2*q*(q + 4)/5
Let q(a) = 33*a**2 + 1464*a + 4325. Let m(b) = -80*b**2 - 3660*b - 10812. Let t(y) = 5*m(y) + 12*q(y). Factor t(s).
-4*(s + 3)*(s + 180)
Suppose 43 + 46 = 762*r + 89. Solve 27/2*f**4 + 30*f**3 + 3/2*f**5 + 18*f**2 + 0 + r*f = 0.
-6, -2, -1, 0
Let n be 8*(-4)/(-64)*4. Factor -37*w**2 - 19*w**n + 12*w**2 + 16*w.
-4*w*(11*w - 4)
Factor -201*x - 27*x + 6*x + 211*x**2 - 1224 - 10*x**2 + 3*x**3.
3*(x - 3)*(x + 2)*(x + 68)
Let k be 6/10 + ((-231)/(-15) - 10). Let r(l) be the third derivative of 1/15*l**5 - k*l**2 - 1/30*l**6 + 1/6*l**4 - 2/3*l**3 + 0 + 0*l. What is u in r(u) = 0?
-1, 1
Let i(o) = -3*o**3 - 7*o**2 - 6*o - 17. Let u be i(-3). Find b such that 105*b**3 - 104 + 230*b - 66 + 205*b - 24*b**4 - 365*b**2 + u*b**4 = 0.
1, 2, 17
Let h(s) = -25*s**2 - 6*s - 2. Let t(l) = 25*l**2 + 4*l + 3. Let b(i) = -4*i + 82. Let g be b(20). Let r(k) = g*t(k) + 3*h(k). Factor r(x).
-5*x*(5*x + 2)
Let v(i) be the second derivative of i + 726/5*i**2 - 4 + 1/20*i**4 + 22/5*i**3. Factor v(k).
3*(k + 22)**2/5
Let z be 50/40*(16 + (-1040)/75). Factor -56/15*r + 2/15*r**3 - z - 14/15*r**2.
2*(r - 10)*(r + 1)*(r + 2)/15
Suppose 138*h = 310*h - 136*h - 72. What is l in h*l - 1/3*l**2 + 7/3 = 0?
-1, 7
Let t(j) be the third derivative of j**7/42 - 53*j**6/120 + 49*j**5/30 + 19*j**4/2 + 12*j**3 - 2*j**2 + 242*j. Factor t(l).
(l - 6)**2*(l + 1)*(5*l + 2)
Factor -2682 + 3128 + 2*y**2 + 14*y - 155*y - 307*y.
2*(y - 223)*(y - 1)
Determine z, given that 12785*z + 175 + 3*z**2 - 807 - 12935*z - 2056 = 0.
-14, 64
Suppose 0 = 17*q + 11880 + 1754. Let g = q + 1613/2. Solve -g*n - 3/4*n**3 + 21/4*n**2 + 0 = 0 for n.
0, 1, 6
Let p(b) = -124*b**2 + 344*b + 11180. Let f(r) = -46*r**2 + 114*r + 3727. Let x(h) = -8*f(h) + 3*p(h). Suppose x(u) = 0. Calculate u.
-19, 49
Let f(b) = 29*b**2 + 4*b - 16. Let v(y) = 16*y**2 + 3*y - 8. Let l(u) = -5*f(u) + 9*v(u). Factor l(g).
-(g - 8)*(g + 1)
Factor -11/2*i**3 - 109/2*i**2 + 0 + 119/2*i + 1/2*i**4.
i*(i - 17)*(i - 1)*(i + 7)/2
Let d = 833731/2 + -416865. Factor -d*q - 1/3 + 14/3*q**3 + 9/2*q**2.
(q + 1)*(4*q + 1)*(7*q - 2)/6
Factor -1/4*n**3 - 2 - 7/2*n - 7/4*n**2.
-(n + 1)*(n + 2)*(n + 4)/4
Let f(x) be the second derivative of x**6/15 + 21*x**5/10 + 19*x**4/6 - 7*x**3 - 20*x**2 + 2330*x. Factor f(s).
2*(s - 1)*(s + 1)**2*(s + 20)
Let s(x) be the first derivative of 5*x**3/3 + 325*x**2 - 173. Solve s(i) = 0 for i.
-130, 0
Let -226/3*s + 25538/3 + 1/6*s**2 = 0. What is s?
226
Let a be (133980/(-6600))/((-14)/30) - 30. Suppose -3/2*w**2 - a - 9*w = 0. Calculate w.
-3
Let d(a) = -a + 28. Let w be d(26). Factor -540*p + 1085*p - 19*p**w - 543*p.
-p*(19*p - 2)
Let k(o) be the first derivative of 2*o**6/3 + 24*o**5/5 - 15*o**4 + 32*o**3/3 + 96. Suppose k(t) = 0. What is t?
-8, 0, 1
Factor 2/5*y**3 + 0 + 126/5*y + 128/5*y**2.
2*y*(y + 1)*(y + 63)/5
Let x(y) = 9*y**4 + 42*y**3 + 51*y**2 - 204*y + 114. Let o(l) = -10*l**4 - 43*l**3 - 53*l**2 + 205*l - 113. Let u(r) = 6*o(r) + 7*x(r). Factor u(w).
3*(w - 1)**2*(w + 4)*(w + 10)
Let b be (-2 + -3)/(1 + 42/(-12)). Factor 1306 + 5*j**3 - 1306 + 57*j**b + 13*j**2.
5*j**2*(j + 14)
Let p(a) be the second derivative of 1/18*a**4 + 4 + 14/3*a**2 + 5*a - 5/3*a**3. Let p(i) = 0. What is i?
1, 14
Let m = -1/1035 - -2083/13455. Let d(x) be the first derivative of 1/13*x**2 + 0*x + 3/26*x**4 + 18 + m*x**3 + 2/65*x**5. Determine w so that d(w) = 0.
-1, 0
Let i be 1972/18734 + ((-12)/(-22))/(285/40). Factor i*r**2 + 4232/11 - 184/11*r.
2*(r - 46)**2/11
Let g = 869/4 + -39097/180. Let n(r) be the second derivative of 13/9*r**4 + 6*r + 8/3*r**3 + 2/5*r**5 + 8/3*r**2 + 0 + g*r**6. Factor n(s).
4*(s + 1)**2*(s + 2)**2/3
Let g be (1 - -321)*(-68)/136. Let m = -643/4 - g. Solve -1/3*l**2 + 1/6 + m*l**3 - 1/12*l = 0.
-2/3, 1
Suppose 4*b = -3*d, -5*d - 3 = b - 20. Factor d + w**2 - 11 + 12*w + 18.
(w + 1)*(w + 11)
Let z(k) be the third derivative of -k**7/1050 + 79*k**6/600 - 23*k**5/30 + 19*k**4/15 - 3534*k**2. Determine u, given that z(u) = 0.
0, 1, 2, 76
Find j such that 12326*j + 2856 + 12391*j - 2*j**2 - 24851*j = 0.
-84, 17
Find b, given that -840*b + 6*b**2 + 358*b - 1080 + 414*b - 2*b**2 = 0.
-10, 27
Let o = 361531/2 - 180765. Let -1/2*t**4 - 1/6*t**5 - 1/6*t**2 + 0 - o*t**3 + 0*t = 0. What is t?
-1, 0
Let 130*v**2 + 6272*v - 19208/3 + 2/3*v**3 = 0. What is v?
-98, 1
Let g(y) = -y + 10. Let x = 43 - 37. Let l be g(x). Factor 5 + 6*t**2 - l + 0 - 3*t**4 - 4.
-3*(t - 1)**2*(t + 1)**2
Let v(d) be the second derivative of -d**6/30 + 71*d**5/10 - 5701*d**4/12 + 7810*d**3 - 54450*d**2 - 4006*d. Factor v(f).
-(f - 66)**2*(f - 5)**2
Let b = -934 + 4672/5. Let z = 152 - 150. Factor 18/5 + b*n**z + 12/5*n.
2*(n + 3)**2/5
Suppose -68*j + 70*j + 12 = 0. Let d be 1/(40/2028)*(-195)/j. Factor d*z**5 + 123/4*z + 879/2*z**2 + 14703/4*z**4 + 3/4 + 4875/2*z**3.
3*(z + 1)**2*(13*z + 1)**3/4
Let j be (-57)/247*(-13)/18. Let g(d) be the third derivative of -4/3*d**3 + 0*d + 1/210*d**7 + 0 + 1/10*d**5 + j*d**4 - 25*d**2 - 1/24*d**6. Factor g(x).
(x - 2)**3*(x + 1)
Let w(m) be the second derivative of -125*m - 5*m**3 + 0 - 20*m**2 - 5/12*m**4. Find n such that w(n) = 0.
-4, -2
Suppose -a - a = -12. Let z(q) = 4*q**3 - q. Let n(y) = 6*y**3 - 7*y - y - y**3 + 6*y. Let w(h) = a*z(h) - 5*n(h). Factor w(k).
-k*(k - 2)*(k + 2)
Let u = 122185131/992134 - 1/76318. Let o = u - 123. Find z, given that -o*z**2 - 50/13 + 20/13*z = 0.
5
Let l(y) be the second derivative of y**4/12 + 143*y**3 - 859*y**2/2 - 7962*y. Find b such that l(b) = 0.
-859, 1
Suppose 3/8*o**4 + 3*o - 21/8 + 9/4*o**2 - 3*o**3 = 0. What is o?
-1, 1, 7
Let n(l) be the first derivative of -98*l - 84 - 7/2*l**2 - 1/24*l**3. Solve n(h) = 0 for h.
-28
Let i(q) be the second derivative of 1/100*q**5 + 0*q**3 + 0*q**2 + 5/12*q**4 + 14*q + 0. Factor i(s).
s**2*(s + 25)/5
Let p(y) be the second derivative of -y**7/7 + 298*y**6/75 - 519*y**5/50 + 136*y**4/15 - 12*y**3/5 + 6830*y. Suppose p(w) = 0. Calculate w.
0, 1/5, 2/3, 1, 18
Let n(k) be the third derivative of -k**6/240 + 23*k**5/120 + 41*k**4/24 - 26*k**3/3 + 2*k**2 - 496*k. Factor n(v).
-(v - 26)*(v - 1)*(v + 4)/2
Let v(o) be the third derivative of o**6/840 - 131*o**5/105 + 17161*o**4/42 + 4*o**2 + 217*o. Factor v(f).
f*(f - 262)**2/7
Let t(h) be the third derivative of -11/525*h**7 + 0 + 0*h + 20/3*h**3 + 13/3*h**4 + 1/420*h**8 + 120*h**2 + 109/150*h**5 - 7/75*h**6. What is a in t(a) = 0?
-2, -1/2, 5
Let f be ((-550)/(-1056))/((-57)/(-456)). Factor -5/3 - 5/2*i**2 + 5/6*i**3 - f*i + 5/6*i**4.
5*(i - 2)*(i + 1)**3/6
Let y(m) = -25*m - 32. Let a be y(-4). Let c = 72 - a. Factor 10*h - c*h**2 + 3*h**2 - 4*h**2.
-5*h*(h - 2)
Factor 0 - 147*i**2 + 13/4*i**3 + 135/4*i.
i*(i - 45)*(13*i - 3)/4
Let i(x) be the second derivative of x**6/6 + 39*x**5 + 9875*x**4/4 - 31205*x**3/3 + 7304*x. Solve i(r) = 0.
-79, 0, 2
Let y(f) = -5*f**2 - 2*f + 4. Let t = 187 - 187. Let x be y(t). Factor 0*b - 4/13*b**2 + 0 - 14/13*b**x + 18/13*b**3.
-2*b**2*(b - 1)*(7*b - 2)/13
Let o = 758 + -774. Let b be (-40)/32*o/35. What is t in 2/7 - b*t + 2/7*t**2 = 0?
1
Let u(d) be the first derivative of 16/3*d**3 + 1/720*d**6 + 1/48*d**4 + 1/120*d**5 + 13 + 0*d + 0*d**2. Let t(y