 0, 1, 11
Suppose -g = -2*l - 8, -3*g + 18 = -5*l - 4. Let d be l/(-10) - (-3)/(-195)*-87. What is q in -d + 74/13*q - 14/13*q**2 = 0?
2/7, 5
Let x be (-605)/(-88) - 2/(-16). Suppose -x*u - 3 = -52. Factor -3*z**2 - 8*z**2 - 5 - z**2 - 10*z + u*z**2.
-5*(z + 1)**2
Let q(g) be the second derivative of -g**4/6 + 2326*g**3/3 - 1352569*g**2 - 827*g. Let q(t) = 0. Calculate t.
1163
Let f(t) = -9*t**2 + 73*t + 28. Let k(i) = 9*i**2 - 72*i - 27. Suppose j = -a + 6, -5*j + j + a = -9. Let o(y) = j*f(y) + 4*k(y). Factor o(x).
3*(x - 8)*(3*x + 1)
Factor 10 + 34 - 26 + 16*y - 73*y**2 + 71*y**2.
-2*(y - 9)*(y + 1)
Suppose -5*t = r - 0*r + 29, -2*t = -4*r - 28. Let a be 5 - (4 + -4 - r/3). Factor -71*p**a - 37*p**2 + 3*p**3 + 1319*p - 23*p - 5184.
3*(p - 12)**3
Let w(s) be the first derivative of 1/40*s**6 - 9/80*s**5 - 19*s + 7 + 3/8*s**3 - 1/16*s**4 + 0*s**2. Let g(z) be the first derivative of w(z). Factor g(t).
3*t*(t - 3)*(t - 1)*(t + 1)/4
Suppose 0 = 2*g + 6 - 106. Let g + 5*b**3 + 11*b**2 - 4*b**2 + 9*b**2 - 95*b + 24*b**2 = 0. What is b?
-10, 1
Determine m so that -6*m + 1/5*m**4 + 0 + 4/5*m**3 - 11/5*m**2 = 0.
-5, -2, 0, 3
Let u(l) be the third derivative of -l**6/60 - l**5/30 - 38*l**2 - 3. Factor u(d).
-2*d**2*(d + 1)
Let u(x) = -x**3 - 761*x**2 - 840*x. Let c(q) = 2*q**3 + 746*q**2 + 840*q. Let r(m) = 5*c(m) + 6*u(m). Factor r(y).
4*y*(y - 210)*(y + 1)
Let f(i) be the third derivative of i**7/70 - 3*i**6/40 - 5*i**5/4 + 75*i**4/8 + 612*i**2 - 5. Determine w, given that f(w) = 0.
-5, 0, 3, 5
Let 200/9*w - 2/9*w**3 + 14/3*w**2 + 0 = 0. What is w?
-4, 0, 25
Let q be (-5)/25 - (-2 - 2)/20. Suppose 9*w + q*w = w. Find a, given that 0 + 1/2*a**4 + w*a**3 - 1/4*a**5 + 1/4*a - 1/2*a**2 = 0.
-1, 0, 1
Let a(q) = 19*q**4 + 117*q**3 + 60*q**2 - 607*q - 14. Let d(s) = -32*s**4 - 196*s**3 - 100*s**2 + 1012*s + 24. Let x(c) = 12*a(c) + 7*d(c). Factor x(r).
4*r*(r - 2)*(r + 5)**2
Find d, given that -1/2*d**5 + 3/2*d**4 - 83/2*d**2 - 75*d + 100 + 31/2*d**3 = 0.
-5, -2, 1, 4, 5
Factor 8/3*x**2 + 0 + 0*x - 7/6*x**4 + x**3.
-x**2*(x - 2)*(7*x + 8)/6
Let f(w) = -2*w**3 - 27*w**2 + 45*w - 46. Let x(u) = u**3 + 12*u**2 - 23*u + 22. Let i(o) = -2*f(o) - 5*x(o). What is s in i(s) = 0?
-9, 1, 2
Let y(d) be the third derivative of d**5/390 - 79*d**4/52 + 236*d**3/39 + 3808*d**2. Factor y(t).
2*(t - 236)*(t - 1)/13
Let c(w) be the first derivative of -w**4/4 - 203*w**3/9 - 164*w**2/3 + 44*w + 8168. Determine a, given that c(a) = 0.
-66, -2, 1/3
Let p(w) be the first derivative of -74*w**5/75 + 61*w**4/10 - 572*w**3/45 + 44*w**2/5 + 16*w/15 + 1833. Solve p(r) = 0.
-2/37, 1, 2
Let p(c) = -c**2. Let a = 38 - 35. Let x(o) = 2*o - a*o**3 + 6*o - 6*o**2 + o + 6. Let q(n) = 6*p(n) - x(n). Factor q(y).
3*(y - 2)*(y + 1)**2
Let y = 502 + -313. Let k be 2/(-3) - (-180)/y. Suppose 4/7*p + 6/7*p**2 + k*p**3 + 0 = 0. Calculate p.
-2, -1, 0
Let g(j) be the first derivative of -1/5*j**5 + 1/12*j**6 + 1/4*j**2 + 2/3*j**3 - 1/4*j**4 - j + 22. Suppose g(d) = 0. Calculate d.
-1, 1, 2
Let f(r) be the first derivative of -1/18*r**3 - 1/3*r**2 + 1/6*r**4 + 162 + 1/30*r**5 + 0*r. Factor f(s).
s*(s - 1)*(s + 1)*(s + 4)/6
Let u = 42 - 37. Let g(h) = -h**3 - 7*h**2 - h - 2. Let t be g(-7). Factor 15*m**3 - 34*m**u + 5*m**2 - 15*m**2 + 14*m**t + 2*m - 7*m + 20*m**4.
-5*m*(m - 1)**2*(2*m + 1)**2
Let t(o) be the third derivative of -8*o**7/245 - 31*o**6/84 - 67*o**5/210 - o**4/14 - 2*o**2 - 132. Determine v so that t(v) = 0.
-6, -1/3, -1/8, 0
Let g(o) be the first derivative of o**4 + 280*o**3 + 1656*o**2 + 3296*o + 3000. Factor g(l).
4*(l + 2)**2*(l + 206)
Let y be 12/14 + 2/(-7). Let s = 2/936391 + 1872768/6554737. Let 0*w + s*w**2 + 0 - y*w**3 + 2/7*w**4 = 0. Calculate w.
0, 1
Let w(u) = -3*u**2 + 28*u - 9. Let o(h) = -10*h**2 + 109*h - 29. Let c(q) = 6*o(q) - 26*w(q). Determine l so that c(l) = 0.
10/9, 3
Let m(p) = -2*p**3 - 8*p**2 - 2*p - 1. Let a be m(-4). Let r be (-2)/a + 1156/714. Factor -r - 4/3*k - 1/3*k**2.
-(k + 2)**2/3
Let c(y) be the third derivative of 4*y**2 + 2*y + 1/30*y**5 - 1/60*y**6 + 7/4*y**4 - 15*y**3 + 0. Factor c(r).
-2*(r - 3)**2*(r + 5)
Find g, given that -80*g**2 - 27*g**2 - 18*g**2 - 381*g - 80 + 1391*g = 0.
2/25, 8
Let g(f) be the third derivative of 0*f**5 - 30*f + 0*f**6 + f**2 + 0 + 0*f**4 + 1/210*f**7 + 0*f**3 + 1/1344*f**8. Find l, given that g(l) = 0.
-4, 0
Suppose -5*o + 49 = -2*t, 28 = 2*o + 587*t - 592*t. Let m(h) be the first derivative of 5/9*h**3 - h**2 + 1/3*h + o. Let m(i) = 0. Calculate i.
1/5, 1
Let u(m) be the third derivative of -5*m**8/336 + m**7/6 - 5*m**6/24 - 7*m**5/12 + 5*m**4/4 + m**2 - 486. Find k such that u(k) = 0.
-1, 0, 1, 6
Let l(t) be the third derivative of -t**6/24 + 591*t**5/4 - 1746405*t**4/8 + 344041785*t**3/2 - 445*t**2. Factor l(m).
-5*(m - 591)**3
Let p(v) be the third derivative of -v**5/300 + 9*v**4/10 + 22*v**3/3 + 5684*v**2. Factor p(u).
-(u - 110)*(u + 2)/5
Let k(v) be the third derivative of v**8/8400 - v**7/3150 - v**6/900 + v**5/150 + 17*v**4/12 + 45*v**2. Let m(d) be the second derivative of k(d). Factor m(a).
4*(a - 1)**2*(a + 1)/5
Let n(p) be the third derivative of p**8/1512 + 2*p**7/945 - 2*p**6/45 - 5*p**5/27 - 25*p**4/108 + 6*p**2 - 5*p. Determine k, given that n(k) = 0.
-5, -1, 0, 5
Let o(q) = -29*q**3 - 64*q**2 + 135*q - 70. Let x(t) = 255*t**3 + 575*t**2 - 1215*t + 630. Let b(l) = -35*o(l) - 4*x(l). What is k in b(k) = 0?
-14, 1
Suppose 242*m - 121*m - 20 = 116*m. Let w(l) be the third derivative of -l**2 - 1/30*l**5 + 1/6*l**m + l**3 + 0*l + 0. Suppose w(o) = 0. Calculate o.
-1, 3
Let p(z) = 12*z**3 - 105*z**2 - 318*z. Let c(q) = 10*q**3 - 106*q**2 - 318*q. Let f(l) = 7*c(l) - 6*p(l). Solve f(u) = 0 for u.
-53, -3, 0
Let k = -384 - -384. Let g(a) = -47*a**2 + 100*a - 8. Let i be g(2). Factor 0*f**3 + k - 4/3*f + 2*f**2 - 2/3*f**i.
-2*f*(f - 1)**2*(f + 2)/3
Let w = 13751 - 151259/11. Factor -10/11*c**2 + 0 - w*c**3 - 12/11*c.
-2*c*(c + 2)*(c + 3)/11
Let -5*z**2 + 30 - 1144*z + 2*z**2 + 1153*z = 0. What is z?
-2, 5
Let o(a) = -4*a - 19. Let r(c) = 5*c**2 - 20160*c + 20280885. Let p(t) = -5*o(t) + r(t). Find z such that p(z) = 0.
2014
What is g in -3/7*g**5 + 0 - 207*g**3 - 2145/7*g**2 - 948/7*g - 255/7*g**4 = 0?
-79, -4, -1, 0
Let u(m) = 11*m**3 - 135*m**2 + 978*m - 836. Let y(b) = 35*b**3 - 405*b**2 + 2935*b - 2505. Let t(d) = -10*u(d) + 3*y(d). Suppose t(l) = 0. Calculate l.
1, 13
Let o(a) = 19*a**2 + 8533*a - 4477571. Let h(f) = 5*f**2 + 2134*f - 1119394. Let w(y) = -23*h(y) + 6*o(y). Let w(j) = 0. Calculate j.
1058
Let a(l) be the first derivative of l**3/6 + 889*l**2 + 1580642*l + 581. Factor a(b).
(b + 1778)**2/2
Let l(r) = 113*r - 6890. Let f be l(61). Let v(p) be the second derivative of 0 - 4*p**2 - 5/3*p**f - 1/6*p**4 + 29*p. Factor v(a).
-2*(a + 1)*(a + 4)
Let z(c) be the first derivative of 2*c**3/3 + 30*c**2 + 112*c - 12438. Factor z(t).
2*(t + 2)*(t + 28)
Let o(p) = 20*p. Let g be o(2). Let r be 55/(-5)*1/(-1) - 2. Find x such that -40*x - 4 - 4 - 19*x**2 - g*x**2 + r*x**2 = 0.
-2/5
Let f be (-23)/(-2)*2238/8579. What is b in 9*b**f - 98 - 109/2*b**2 + 126*b - 1/2*b**4 = 0?
2, 7
Let b(s) = -10*s + 276. Let g be b(27). Let v(y) = -y**2 + 11*y + 2. Let x be v(6). Let -2*p**3 - 4*p**5 + 26*p**3 + x*p**2 + g*p + 6*p = 0. What is p?
-1, 0, 3
Let c be 4 + 232/(-60) + 54264/8820 + -4. Solve 2 - c*f + 2/7*f**2 = 0.
1, 7
Suppose 0*x = 6*x - 1 - 35. Let g(y) be the third derivative of 1/10*y**4 - 1/300*y**6 + 0 - 6/5*y**3 - 1/1050*y**7 + 0*y + 11/300*y**5 - x*y**2. Factor g(j).
-(j - 2)**2*(j + 3)**2/5
Suppose 0 = -l + 6, 3*p - 567 = -6*l - 522. Let 39/7*q**p + 3/7*q**2 - 6*q - 24/7 + 3/7*q**5 + 3*q**4 = 0. What is q?
-4, -2, -1, 1
Let p be 14/(-16)*(-9)/(20/(-2880)*-168). Factor p*j**3 + 65*j - 1/4*j**4 - 42 - 69/2*j**2.
-(j - 21)*(j - 2)**3/4
Let h(f) be the third derivative of 21*f**2 - 19/4*f**4 + 0*f + 6*f**3 + 0 - 1/12*f**6 + 16/15*f**5. Solve h(u) = 0 for u.
2/5, 3
Suppose 3*l = -176 + 99 + 83. Factor -22/3*s + 121/3 + 1/3*s**l.
(s - 11)**2/3
Let m be -2 + 2 - 0 - (-72)/18. Suppose -4*s = -m*h - 8 - 8, 4*h = 5*s - 16. Factor 1/6*p**2 - 1/6*p**4 - 1/6*p + s + 1/6*p**3.
-p*(p - 1)**2*(p + 1)/6
Let i = 67 + -67. Suppose -89*x + 84*x + 25 = i. What is h in h**4 - 12*h**2 + 16*h**2 - x*h**4 = 0?
-1, 0, 