*(t - 1)
Let q = 583420 + -583415. Solve -3/4*r**4 + 13/4*r**3 + 7/4*r**2 + 5 - 9*r - 1/4*r**q = 0 for r.
-5, -2, 1, 2
Factor -2/9*b**3 + 154/9*b**2 - 100/3*b + 0.
-2*b*(b - 75)*(b - 2)/9
Suppose 0 = 3*s + z - 155, 5*s - 3*z - 184 = 79. Solve -6*w**3 + 28*w**2 - 10*w + 2*w**3 + 18*w + 20 - s*w = 0 for w.
1, 5
Let c(k) be the first derivative of 2*k**5/75 + 6*k**4/5 + 776*k**3/45 + 384*k**2/5 + 2048*k/15 - 5672. Factor c(l).
2*(l + 2)**2*(l + 16)**2/15
Let a be 3/(-2) + (17360/(-160))/(-31). Factor 0*l + 2/3*l**5 + 2*l**3 + a*l**4 + 2/3*l**2 + 0.
2*l**2*(l + 1)**3/3
What is l in -2/13*l**5 + 834/13*l**2 + 40/13*l - 768/13 - 66/13*l**4 - 38/13*l**3 = 0?
-32, -4, -1, 1, 3
Let f be ((-32)/18 - -3) + 8/(-36). Suppose -f + 5 = c. Let -1/6*r - 1/6*r**5 + 0*r**2 + 0*r**c + 0 + 1/3*r**3 = 0. What is r?
-1, 0, 1
Solve 136*g + 12*g**2 + 8*g**2 - 183 - 54*g + 39 - 54*g + g**3 = 0.
-18, -4, 2
Let d(k) be the first derivative of 10*k**5 + 665*k**4/2 - 5038*k**3/3 + 927*k**2 - 180*k + 120. Suppose d(g) = 0. What is g?
-30, 1/5, 3
Let o(x) be the first derivative of 2*x**5/65 - 3*x**4/26 - 4*x**3/13 + 8*x**2/13 + 1076. Factor o(l).
2*l*(l - 4)*(l - 1)*(l + 2)/13
Let x(w) be the second derivative of 21/2*w**2 + 0 + 1/21*w**4 + 2/105*w**5 - 1/140*w**6 + 0*w**3 - 21*w. Let p(j) be the first derivative of x(j). Factor p(k).
-2*k*(k - 2)*(3*k + 2)/7
Find v such that -13*v**2 + 405 - 7*v**2 + 381 - 114 - 388*v = 0.
-21, 8/5
Determine j so that -30/11 - 4/11*j - 2/11*j**4 + 32/11*j**2 + 4/11*j**3 = 0.
-3, -1, 1, 5
Let u(p) = 23*p**2 - 498*p + 62502. Let a(b) = -11*b**2 - b - 1. Let c(f) = -6*a(f) - 3*u(f). Let c(k) = 0. Calculate k.
250
Suppose 31 = 31*c + 37*c - 241. Let w(o) be the second derivative of 0*o**2 + 0 + 1/20*o**5 + 2/3*o**3 - 7*o - 5/12*o**c. Suppose w(i) = 0. What is i?
0, 1, 4
Let z(q) = -q**2 + 33*q + 76. Let g be z(35). Suppose -3*x**4 - 14*x**3 - g*x**4 + 6 - 33*x**2 - 19*x**3 - 3*x = 0. What is x?
-2, -1, 1/3
Suppose -2*i + 3 = o - 2*o, i + 6 = -2*o. Let y be ((-4)/4)/(o/9). Determine g, given that 6*g**3 - y*g**4 - 12 - 7*g + 9*g**2 - 12*g + 7*g = 0.
-1, 2
Let y = -216 - -803. Let x = -587 + y. Factor 2/3*d**2 - 2*d**3 + x + 0*d.
-2*d**2*(3*d - 1)/3
Suppose 4*g - 49 = g + 2*l, -3*g + 4*l = -47. Factor 108*p - 120 - 73*p**2 - 168 - 4*p**3 - 348*p + g*p**2.
-4*(p + 2)*(p + 6)**2
Let n(b) be the first derivative of 2*b**5/15 - 17*b**4/6 + 88*b**3/9 - 28*b**2/3 - 326. Factor n(u).
2*u*(u - 14)*(u - 2)*(u - 1)/3
Factor -42436/7*g + 0 - 3296/7*g**2 - 64/7*g**3.
-4*g*(4*g + 103)**2/7
Let y(k) be the third derivative of -k**6/300 + 43*k**5/5 - 9245*k**4 + 15901400*k**3/3 - 23*k**2 - 24. Solve y(j) = 0.
430
Factor -1/9*s**2 + 194/9*s - 760/9.
-(s - 190)*(s - 4)/9
Find h such that -5*h + 20*h - 7*h**2 + h**3 + 325621 + 3*h**2 - 14*h**2 - 325587 = 0.
-1, 2, 17
Let c = -30143 - -30145. Let 2 - 2/3*a**c - 4/3*a = 0. Calculate a.
-3, 1
Factor -11*o**2 + 130*o - 186*o - 192 + 7*o**2.
-4*(o + 6)*(o + 8)
Let w(a) = 16*a**3 - 198*a**2 + 107*a - 55. Let q(i) = 7*i**3 - 84*i**2 + 53*i - 28. Let v(p) = -5*q(p) + 2*w(p). Suppose v(l) = 0. Calculate l.
1, 2, 5
Let s(o) = -8*o**5 - 22*o**3 - 46*o**2 - 26*o + 10. Let j(i) = i**5 + i**2 + i - 1. Let z be (-209)/(-171) - 2/9. Let v(y) = z*s(y) + 10*j(y). Factor v(k).
2*k*(k - 4)*(k + 1)**2*(k + 2)
Let x(w) be the third derivative of 0*w - 3/80*w**5 - 1/2*w**3 - 23/96*w**4 - 2*w**2 + 1/840*w**7 - 1 + 1/160*w**6. Factor x(o).
(o - 3)*(o + 1)**2*(o + 4)/4
Let p(q) = 10*q**2 - 18*q - 114. Let b be p(-7). Let t = b - 502. Factor 8/3*c**2 + 4/3*c**3 + t + 4/3*c.
4*c*(c + 1)**2/3
Let s(v) be the second derivative of 0 + 0*v**2 + 1/32*v**4 - 47*v + 1/160*v**5 - 5/24*v**3. Suppose s(n) = 0. What is n?
-5, 0, 2
Let g(l) be the first derivative of l**7/210 - 7*l**5/30 + l**4 - 97*l**3/3 - 93. Let z(n) be the third derivative of g(n). Let z(p) = 0. What is p?
-3, 1, 2
Suppose 83 = -12*n - 25. Let y be (6/n)/((-2)/42). Find u such that 10*u**4 + 11*u**3 - y*u**5 - 10*u**2 + u**3 - u**5 + 3*u**3 = 0.
-1, 0, 2/3, 1
What is z in -9*z**3 - 19/4*z**4 - 5/4*z**2 - 1/2*z**5 + 0 + 7/2*z = 0?
-7, -2, -1, 0, 1/2
Let r = 2647/179 - 1437820/1253. Let v = r + 1143. What is c in 24/7*c - v - 2/7*c**2 = 0?
6
Let u be ((-89)/(-1335))/((-3)/(-3)). Let m(x) be the second derivative of u*x**4 - 4/5*x**2 - 2*x + 0 - 2/15*x**3. Factor m(i).
4*(i - 2)*(i + 1)/5
Let b be 5/15*(-3)/(-2). Let i be (-3 - 0)*(-4248)/2360*(-10)/(-12). Factor -4*x**4 + 0 + 11*x**3 - 12*x**2 + i*x + b*x**5.
x*(x - 3)**2*(x - 1)**2/2
Suppose 2/7*m**4 - 696/7*m**2 + 392*m - 2720/7 - 2/7*m**3 = 0. What is m?
-20, 2, 17
Let m(c) be the third derivative of c**5/72 + 115*c**4/144 + 25*c**3/2 + 1197*c**2. Suppose m(v) = 0. Calculate v.
-18, -5
Factor 990*p - 2552 + 223*p - 467*p + 914*p - 4*p**2 + 896.
-4*(p - 414)*(p - 1)
Let o(t) = t**2 + 1171*t + 12760. Let y be o(-11). Solve 4/15*m**2 + 2/15*m + y + 2/15*m**3 = 0 for m.
-1, 0
Let m(r) = 45*r**3 + 114*r**2 + 48*r + 6. Let s(u) = 89*u**3 + 219*u**2 + 96*u + 11. Let w(x) = -5*m(x) + 3*s(x). Determine v so that w(v) = 0.
-1, -1/14
Let g be (-11 - -10)/3*(0 - -1367). Let i = 456 + g. Factor 1 + 5/3*z**2 - 7/3*z - i*z**3.
-(z - 3)*(z - 1)**2/3
Let k(w) = w**3 + w**2 + w + 1. Suppose -13*y = -6*y + 28. Let l(z) = 6*z**2 + 8*z + 2. Let h(v) = y*k(v) + 2*l(v). Determine p so that h(p) = 0.
-1, 0, 3
Let a(z) = 3*z**2 + 171*z + 208. Let l(w) = w**2 + 85*w + 108. Let b(s) = -3*a(s) + 5*l(s). Factor b(k).
-4*(k + 1)*(k + 21)
Let l(x) = 625*x**4 + 7695*x**3 - 25270*x**2 + 12285*x - 75. Let k(q) = 17*q**4 + 208*q**3 - 683*q**2 + 332*q - 2. Let f(n) = 75*k(n) - 2*l(n). Factor f(j).
5*j*(j - 2)*(j + 11)*(5*j - 3)
Let n(i) be the third derivative of -5/8*i**4 + 0 + 7/60*i**5 + 0*i + 1/3*i**3 - 294*i**2. Find l such that n(l) = 0.
1/7, 2
Suppose 2*c - 7*c = -2*f + 26, 0 = f + 4*c + 13. Let d be -2*((-21)/6 - -2). Factor -8*q**3 + 3*q + 2*q**f + 4*q**2 + 7*q**d.
q*(q + 1)*(q + 3)
Solve -2890*p**4 + 55*p**3 - 2406*p**2 + 47*p**5 + 7862*p**3 + 4971*p**3 + 3*p**5 - 6530*p**2 + 1696*p = 0.
0, 2/5, 4, 53
Let x(q) = q**2 - 1026*q + 4. Let o be x(0). Suppose 0*m + 2/5*m**o - 12*m**2 + 0 - 2/5*m**3 = 0. What is m?
-5, 0, 6
Let g = 25 - 23. Suppose -43 - 161 = -g*b. Factor 0*y**2 - 2*y**2 + b - 12*y - 118.
-2*(y + 2)*(y + 4)
Let w = 318 + -319. Let x be (w - -3)*(25 + -19). Factor -x*n - 3/2*n**3 + 24 - 21/2*n**2.
-3*(n - 1)*(n + 4)**2/2
Let f(t) = -1. Let v(n) = -11*n - 8. Let z(c) = 5*f(c) - v(c). Let u be z(9). Suppose -g**3 - 3*g**3 + 98*g**2 - u*g**2 = 0. Calculate g.
-1, 0
Let h(c) be the third derivative of -c**7/525 + c**6/50 - 11*c**5/150 + c**4/10 + 27*c**2 + 8*c + 2. Factor h(i).
-2*i*(i - 3)*(i - 2)*(i - 1)/5
Let i be (7/(175/40))/(6/15). Let z be 1 + (-1036)/(-10) + i/10. Factor 4*n**2 + z*n - 105*n - n**4.
-n**2*(n - 2)*(n + 2)
Let 17/2*y**2 - 1/2*y**3 + 19*y + 0 = 0. What is y?
-2, 0, 19
Suppose 272 = -f + 2*n + 290, -27 = f + 3*n. Factor -4/15*l - 2/5*l**3 + 2/15*l**5 + 2/15*l**4 + f - 2/3*l**2.
2*l*(l - 2)*(l + 1)**3/15
Let t(l) be the first derivative of 264 + 0*l**2 - 1/69*l**6 - 5/46*l**4 + 0*l**3 + 0*l + 12/115*l**5. Factor t(s).
-2*s**3*(s - 5)*(s - 1)/23
Let j(i) be the third derivative of -i**5/240 - 13*i**4/12 + 259*i**3/8 + 10094*i**2. Factor j(p).
-(p - 7)*(p + 111)/4
Solve 68236*u**2 - 728*u**4 - 60*u**5 - 19*u + 355*u + 1764*u**3 - 65468*u**2 = 0 for u.
-14, -1, -2/15, 0, 3
Let u(h) be the first derivative of 1/10*h**5 + 1/24*h**6 - 1/6*h**3 + 0*h + 0*h**2 - 1/16*h**4 + 30. Suppose u(t) = 0. Calculate t.
-2, -1, 0, 1
Let p be (360/480)/((-15)/(-48)*6). Determine o so that 22/15*o**2 - 4/15*o**4 + 2/15*o**3 + p + 22/15*o = 0.
-1, -1/2, 3
Suppose -32/23*k - 160/23 + 2/23*k**2 = 0. What is k?
-4, 20
Let j(h) be the first derivative of 27/5*h**3 - 9/25*h**5 - 116 - 132/5*h**2 + 51/20*h**4 + 144/5*h - 1/10*h**6. Find n such that j(n) = 0.
-4, 1, 3
Let i(k) be the third derivative of 86*k**2 - 1/30*k**7 + 0*k**3 + 7/60*k**6 + 0*k**4 + 0 + 1/336*k**8 + 0*k - 2/15*k**5. Factor i(d).
d**2*(d - 4)*(d - 2)*(d - 1)
Let t(j) be the first derivative of j**6/15 - 4*j**5/25 - 11*j**4/5 + 16*j**3/15 + 117*j**2/5 + 36*j - 9154. Determine u, given that t(u) = 0.
-3, -2, -1, 3, 5
Let i = -828049 + 828051. Factor -10*l - 1/2*l**3 + 9/2*l**i + 6.
-(l