q - 289*q - 740*q. Solve 0 - 7/2*p - 13/4*p**2 + 1/4*p**q = 0 for p.
-1, 0, 14
Factor -295/2*r + 0 + 1/6*r**2.
r*(r - 885)/6
Determine a, given that 1070/7*a**2 - 4/7*a**3 + 538/7*a - 536/7 = 0.
-1, 1/2, 268
Let o(w) = -57*w**2 - 26*w - 21. Let k(u) = 64*u**2 + 28*u + 21. Let s(y) = 8*k(y) + 9*o(y). Let s(l) = 0. What is l?
-7, -3
Factor -274/11 + 2/11*d**2 - 272/11*d.
2*(d - 137)*(d + 1)/11
Factor 0 - 1/6*t**2 + 35/6*t.
-t*(t - 35)/6
Let r be 8 + -1 + 10270/(-1580). Factor 8*a - r*a**3 + 0 + 35/3*a**2.
-a*(a - 24)*(3*a + 2)/6
Let q(x) be the first derivative of -3*x**2/2 + 9*x - 2. Let z be q(2). Factor 14*i**z + 8 + 30*i**3 - 34*i**3 - 14*i**2 - 8*i - 8*i.
2*(i - 2)*(i + 1)*(5*i - 2)
Let v = 109/143 + -7/572. Let m(s) be the first derivative of -15/2*s**2 + 13 + v*s**4 + 0*s - 4*s**3. Factor m(k).
3*k*(k - 5)*(k + 1)
Suppose 4*b + 20 = -20*z, -7*b + 6*b - 5 = 4*z. Find u, given that 3/4*u**2 + 0*u + z - 1/4*u**3 = 0.
0, 3
Suppose 4*n - 40*a = 236, -n - 2 = n + 4*a. Let s(w) be the second derivative of 1/11*w**2 + 0*w**3 + n*w - 1/66*w**4 + 0. What is b in s(b) = 0?
-1, 1
Let v = 73 + -54. Suppose 5*z = 3*a + v, 3*a - 16 = -2*z - 0*a. Find g such that -10*g**3 - 10*g**2 + 5*g + g - 3 - g + 5*g**z + 8 + 5*g**4 = 0.
-1, 1
Let s(q) be the third derivative of q**6/1020 - 9*q**5/85 + 35*q**4/68 - 52*q**3/51 + 119*q**2 + 10. Factor s(p).
2*(p - 52)*(p - 1)**2/17
Factor 1 - 495*s + 5*s**4 - 1 - 177*s**3 - 2*s**4 + 2005*s**2 - 1336*s**2.
3*s*(s - 55)*(s - 3)*(s - 1)
Factor -4*s**3 - 1825 + 20*s**2 + 522*s + 1649 + s**3 - 3*s**3.
-2*(s - 11)*(s + 8)*(3*s - 1)
Let r = 1733/540 + -16/5. Let s(h) be the third derivative of 2/27*h**3 - 7*h**2 - 1/270*h**5 - r*h**4 + 0*h + 0. Determine w so that s(w) = 0.
-2, 1
Let s(a) be the third derivative of 2/9*a**3 - a + 0 - 1/24*a**4 - 1/180*a**5 + 61*a**2. Factor s(d).
-(d - 1)*(d + 4)/3
Let i(g) = g**2 - g - 40. Let z(a) = -2*a**2 - 8*a + 138. Let r(o) = -3*i(o) - z(o). Determine n, given that r(n) = 0.
2, 9
Solve 344/3*j**3 - 64/3*j - 152*j**2 + 8/3*j**5 + 128 - 30*j**4 = 0.
-3/4, 2, 4
Let s = -5456 + 5456. Let b(i) be the third derivative of -49/12*i**4 + 0*i**3 + 0 - 16*i**2 - 1/60*i**6 + s*i - 7/15*i**5. Find m, given that b(m) = 0.
-7, 0
Find p such that 53 + 37 + 44 + 4*p**2 - 24*p - 242 = 0.
-3, 9
Suppose 150*i - 323 = 153*i + q, 0 = -5*q - 25. Let d = 106 + i. Determine y, given that 105/2*y**2 + d + 3/2*y**4 + 147/2*y - 39/2*y**3 = 0.
-1, 0, 7
Let f(a) = -29*a**4 - 225*a**3 + 5742*a**2 - 32430*a + 44366. Let s(q) = 5*q**4 + 37*q**3 - 957*q**2 + 5405*q - 7394. Let y(u) = -6*f(u) - 35*s(u). Factor y(x).
-(x - 23)**2*(x - 7)*(x - 2)
Let l(y) = 140*y**3 + 4117*y**2 - 31947*y + 12285. Let o(d) = -20*d**3 - 588*d**2 + 4564*d - 1756. Let s(c) = 4*l(c) + 27*o(c). Suppose s(p) = 0. Calculate p.
-36, 2/5, 6
Suppose 30 = -2223*c + 2220*c + 2*u, u = -c + 15. Let d = 5 - 2. Let -14/5*t**4 + 144/5*t**d - 78*t**2 + 20*t + c = 0. What is t?
0, 2/7, 5
Let c(v) be the first derivative of v**5 + 155*v**4/2 + 2395*v**3 + 36890*v**2 + 283220*v - 354. Factor c(l).
5*(l + 14)**2*(l + 17)**2
Solve 0 + 22*f**3 - 186*f**2 + 494/3*f - 2/3*f**4 = 0 for f.
0, 1, 13, 19
Let d(y) be the first derivative of 2*y**5/25 + 3*y**4/5 - 152*y**3/15 + 186*y**2/5 - 234*y/5 - 534. Find c such that d(c) = 0.
-13, 1, 3
Let d be (4*4/(-32))/(2/(-8)). Factor -d - 21502*h**3 + 21534*h**3 - 4*h**4 - 48*h**2 + 2.
-4*h**2*(h - 6)*(h - 2)
Suppose 3*z = 4*i - 0*i - 13, 0 = 4*i - 16. Determine f so that -z + 182*f**2 - 170*f**2 - 3*f - 5 + 9*f**3 = 0.
-1, 2/3
Let p(d) = -3*d**3 - 8*d**2 - 4*d - 4. Let z(w) = 11*w**3 + 31*w**2 + 18*w + 18. Let t(m) = 9*p(m) + 2*z(m). Factor t(x).
-5*x**2*(x + 2)
Let i(h) be the first derivative of -3*h**3 + 17*h**2 - 1/4*h**4 - 24*h + 246. Determine j, given that i(j) = 0.
-12, 1, 2
Let o(j) = 8*j**3 + 180*j**2 + 5382*j + 45639. Let n(i) = 22*i**3 + 542*i**2 + 16146*i + 136914. Let r(h) = 3*n(h) - 8*o(h). What is t in r(t) = 0?
-39, -15
Let k(s) = 12*s**3 + 205*s**2 + 162*s + 5. Let c(x) = -4*x**2 + 1. Let a(y) = 5*c(y) - k(y). Factor a(p).
-3*p*(p + 18)*(4*p + 3)
Let p(t) be the first derivative of -3*t**4/4 - 38*t**3 - 504*t**2 + 1037. Factor p(j).
-3*j*(j + 14)*(j + 24)
Let d be 2/((4 - 6) + 4) + 10. Let -d*z**3 - 11*z**4 + z**5 - 4*z**3 - 2*z**5 + 36*z**2 - 9*z**3 = 0. Calculate z.
-6, 0, 1
Let w(f) be the third derivative of 101*f**5/30 - 4*f**4 - f**2 - 7*f - 130. Factor w(t).
2*t*(101*t - 48)
Let -80*j**2 + 12*j**2 - 104247*j**3 + 104557*j**3 - 18*j**4 = 0. Calculate j.
0, 2/9, 17
Suppose 24 = 3*l + 5*n, -3*l + 0*n + 2*n = -3. Let d be ((-15)/9 + 3)*l. Suppose -5*o**5 - 3*o**4 - 5*o**4 + 3*o**d + 3*o**4 = 0. Calculate o.
-2/5, 0
Suppose 137*s - 3965 = 132*s. Factor -5254*x + 105*x - 838*x**2 - 3*x**3 + 31944 + s*x + 1036*x**2.
-3*(x - 22)**3
Let c be 10/2 - 13/((-91)/(-21)). Let z(n) = 5*n**2 - 4*n. Let f(l) = l**2 - l - 1. Let k(t) = c*z(t) + 2*f(t). Factor k(w).
2*(w - 1)*(6*w + 1)
Let w(n) be the second derivative of n**6/30 + 2*n**5 + 3838*n. Factor w(v).
v**3*(v + 40)
Let z(k) be the third derivative of -7*k**6/30 - 34*k**5/3 - 881*k**4/6 - 476*k**3/3 + 3654*k**2 + k. Factor z(d).
-4*(d + 7)*(d + 17)*(7*d + 2)
Let d be 7/(-8)*172/(-903). Solve 0 + d*b**2 + 29/6*b = 0.
-29, 0
Let l(k) be the second derivative of -19 - 39/40*k**5 - k - 675/2*k**2 - 109/16*k**4 - 1/40*k**6 + 195/2*k**3. Factor l(f).
-3*(f - 2)**2*(f + 15)**2/4
Let a(f) = -f**3 + 2*f**2 + f - 9. Let x be a(-7). Let q = -421 + x. Determine z, given that 24/5*z**q - 3*z**5 - 3/5*z**3 + 0*z + 0 - 6/5*z**2 = 0.
-2/5, 0, 1
Let -2*q**3 - 5898*q**2 - 4379587*q - 2309099*q + 890952*q - 1485965980 - 829438811 + 415680617 = 0. Calculate q.
-983
Let a(t) be the second derivative of -t**5/300 - 13*t**4/60 - 135*t**2/2 + 41*t. Let k(p) be the first derivative of a(p). Factor k(i).
-i*(i + 26)/5
Let c be (-1)/(-8) + (-7)/(-280)*115. Let l be c*32/(-24) - -6. Factor 9/2*x + 2*x**l + 1.
(x + 2)*(4*x + 1)/2
Suppose 12*k - 73 = -25. Solve k*i**3 + 17*i**2 + 35*i**2 + 44*i + 13 + 116*i + 131 = 0.
-9, -2
Suppose 390*d - 934 = -154. Let z(g) be the third derivative of 0*g**5 - 1/1200*g**6 + 0 - 35*g**d + 1/80*g**4 - 1/30*g**3 + 0*g. Determine s so that z(s) = 0.
-2, 1
Let d(p) be the first derivative of p**5/5 - 7*p**4/2 + 20*p**3 - 36*p**2 - 1011. Factor d(h).
h*(h - 6)**2*(h - 2)
What is z in -5/6*z**4 - z**3 + 1/2 - 1/6*z**5 + 1/3*z**2 + 7/6*z = 0?
-3, -1, 1
Let s(w) be the first derivative of 5*w**7/126 + 2*w**6/9 - w**5/6 - 5*w**4/3 + 5*w**3/2 - 46*w - 69. Let t(o) be the first derivative of s(o). Factor t(k).
5*k*(k - 1)**2*(k + 3)**2/3
Let g(u) be the third derivative of u**8/84 + 16*u**7/105 - u**6/30 - 8*u**5/15 - 8*u**2 - 52. Determine f so that g(f) = 0.
-8, -1, 0, 1
Let o be 5/(-1915)*(-4 + 7). Let h = 2693/1532 + o. Suppose -1/4*g - 3/4 + 1/4*g**3 - g**4 + h*g**2 = 0. What is g?
-1, -3/4, 1
Let f be 714 + -767 - (3 - 56). Find y such that f - 5/4*y**4 + 0*y + 5/4*y**2 - 15/4*y**5 + 15/4*y**3 = 0.
-1, -1/3, 0, 1
Suppose 115*n - 110*n = 2775. Factor -7*w**2 + 82 + 73 - n*w - 44 - 2*w**2 + 75.
-3*(w + 62)*(3*w - 1)
Let u be (-1 - 4) + 11 + 32. Find j such that -38 + 4*j**2 - 8*j + u = 0.
0, 2
Let b be ((-38)/(-171))/((-4)/(-18)). Let k(i) = -10*i**2 + 10. Let m(a) = -2*a**2 + a + 1. Let j(z) = b*k(z) - 6*m(z). Factor j(w).
2*(w - 2)*(w - 1)
Suppose -25*f = -4*f - 42. Factor -88 - 120*n**f + 196*n**3 - 38 + 249*n - 199*n**3.
-3*(n - 1)**2*(n + 42)
Let l = 304109/1166 + 1311/106. Let z = l + -273. Factor z + 4/11*c + 2/11*c**2.
2*(c + 1)**2/11
Let g(p) be the first derivative of -p**6 + 44*p**5/5 + 34*p**4 - 452*p**3/3 + 175*p**2 - 72*p - 1926. What is n in g(n) = 0?
-4, 1/3, 1, 9
Let s be 84*(-115)/(-16100) + 309/35*1. Factor -54/7 + 18*y - s*y**2 + 10/7*y**3.
2*(y - 3)**2*(5*y - 3)/7
Suppose 163*n = 159*n + 248. Let t be 0*((-2)/(-9) - n/(-558)). Find r such that 0*r**2 + 0*r - 2/17*r**5 + 2/17*r**3 + t*r**4 + 0 = 0.
-1, 0, 1
Let k(u) be the first derivative of -u**6/180 + 91*u**5/30 - 8281*u**4/12 - 266*u**3/3 + 10. Let p(t) be the third derivative of k(t). Solve p(r) = 0 for r.
91
Let j(u) be the third derivative of 5*u**2 - 11/480*u**6 + 0*u - 2/105*u**7 - 1/120*u**5 - 4 + 0*u**3 - 1/192*u**8 + 0*u**4. Solve j(n) = 0 for n.
-1, -2/7, 0
Let k(h) be the 