12*s**3 + 8*s + 8*s - s**4.
-(s - 4)**3*(s + 1)
Determine b, given that 1279/4*b**2 + 1/4*b**3 + 1283 - 1282*b = 0.
-1283, 2
Solve 136/5*h**4 - 4/5*h**5 + 284/5*h**3 + 0 + 144/5*h**2 + 0*h = 0 for h.
-1, 0, 36
Suppose -2408*a - 1152*a + 12312 + 1928 = 0. Find u such that 0*u**3 + 3/2*u**a - 3/2*u**2 + 0*u + 0 = 0.
-1, 0, 1
Let m(o) be the second derivative of o**6/420 - o**5/120 - 5*o**4/168 - 13*o**3/6 + o**2 - 59*o. Let u(l) be the second derivative of m(l). Solve u(t) = 0.
-1/2, 5/3
Factor -322/3 + 58/3*o**2 + 2/3*o**3 + 262/3*o.
2*(o - 1)*(o + 7)*(o + 23)/3
Factor 22/7*x**3 + 1/7*x**4 + 272/7*x + 153/7*x**2 - 64.
(x - 1)*(x + 7)*(x + 8)**2/7
Let n(h) = 10*h**3 - 4*h - 3. Let v(j) = -6*j**3 - 2*j**2 + 4*j + 2. Let i(g) = 4*n(g) + 6*v(g). Factor i(a).
4*a*(a - 2)*(a - 1)
Determine b so that -3*b**2 + 40*b - 162*b - 1161 - 63*b + 29*b = 0.
-43, -9
Let f(a) = 6*a - 120. Let x be f(16). Let i be 2 + 0/2*6/x. Factor 3/4*y + 0 - 1/4*y**3 + 1/2*y**i.
-y*(y - 3)*(y + 1)/4
Let -89*w**4 - 453 + 762*w - 768 + 917*w**3 - 840*w + 1723*w**2 + 2*w**5 - 1417*w + 163 = 0. What is w?
-2, -1/2, 1, 23
Let u(j) be the third derivative of -j**6/180 - 41*j**5/45 + 253*j**4/36 - 170*j**3/9 - 3093*j**2. Find r, given that u(r) = 0.
-85, 1, 2
Suppose -7*h + 345 = 303. Let i(y) be the third derivative of -9*y**2 + 0 + 0*y + 1/180*y**h - 4/3*y**3 + 1/90*y**5 - 2/9*y**4. Factor i(z).
2*(z - 3)*(z + 2)**2/3
Factor -141/2*k - 1/2*k**4 + 217/2*k**2 - 198 - 39/2*k**3.
-(k - 3)**2*(k + 1)*(k + 44)/2
Let t(g) be the second derivative of -g**7/21 + 4*g**6/15 + 18*g**5/5 + 37*g**4/3 + 61*g**3/3 + 18*g**2 - 102*g + 3. Factor t(c).
-2*(c - 9)*(c + 1)**3*(c + 2)
Suppose 4*i - 2*f - 77794 = 0, -5*i - f - 45905 = -143165. Factor 145*z**2 + i - 19451 + 35*z**3 + 20*z.
5*z*(z + 4)*(7*z + 1)
Factor 20/3*m + 16 - 2/3*m**2.
-2*(m - 12)*(m + 2)/3
Let s(u) be the second derivative of -u**7/1764 - u**6/240 - u**5/420 + 107*u**4/6 + 33*u + 4. Let j(c) be the third derivative of s(c). Factor j(z).
-(z + 2)*(10*z + 1)/7
Let f be (-2)/4 + 13794/1778. Let y = 7/254 + f. What is c in -y*c**3 - 12/7*c - 48/7*c**2 + 0 - 15/7*c**4 = 0?
-2, -1, -2/5, 0
Suppose -2*d - d + 23*d = 0. Let o(n) be the second derivative of 1/15*n**6 - 8*n + d*n**2 + 1/14*n**4 + 0 - 2/21*n**3 + 6/35*n**5. Factor o(b).
2*b*(b + 1)**2*(7*b - 2)/7
Let s(c) be the third derivative of 41*c - c**2 + 11/26*c**4 - 1/390*c**5 + 0 - 363/13*c**3. Factor s(j).
-2*(j - 33)**2/13
Let 2652*h**2 - 2639 + 66484 - 1130*h - 2647*h**2 = 0. What is h?
113
Let h = 461 + -459. Suppose 26 + 10 - 20*s**h + 0*s**2 + 4*s**3 + 45*s - 33*s = 0. Calculate s.
-1, 3
Let w(h) = 7*h**2 + 40*h - 101. Suppose 4*p = -43*p - 94. Let s(x) = 5*x**2 - x - 1. Let y(l) = p*s(l) + w(l). Solve y(z) = 0 for z.
3, 11
Let j = -8 - -18. Let w be -1*j - (-5 + 7). Let l(k) = -k**2 - 7*k + 2. Let p(g) = -g + 1. Let h(n) = w*p(n) + 3*l(n). Find c such that h(c) = 0.
-2, -1
Let u = -32 - -31. Let d be (-5 - u - -4)/2. Factor d*t**3 + 3*t**3 - 2*t + 3*t**4 + 3*t**3 - 4*t - 3.
3*(t - 1)*(t + 1)**3
Let q = -504 + 318. Let v = 188 + q. Solve -3/5*w**v + 3/5*w + 6/5 = 0 for w.
-1, 2
Let n(q) be the first derivative of 5*q**3/3 + 75*q**2/2 + 180*q - 116. Solve n(d) = 0 for d.
-12, -3
Suppose -589073 = -5*z + 3*l, 0*l = -4*z + 5*l + 471248. Factor 117817*p**3 - 2*p**4 + 2*p**2 - z*p**3.
-2*p**2*(p - 1)*(p + 1)
Let n(c) be the third derivative of c**6/60 + 34*c**5/15 + 84*c**4 - 1728*c**3 - 3*c**2 - 29. Solve n(u) = 0 for u.
-36, 4
Suppose -4*x + 24 = -2*x. Suppose 13*u - 10*u = x. Factor 27*l**4 + l**3 - 24*l**u - 7*l + l - 3 + 5*l**3.
3*(l - 1)*(l + 1)**3
Let 185/2*g**2 + 15*g + 15*g**3 + 0 = 0. Calculate g.
-6, -1/6, 0
Factor -20 - 1/2*j**3 + 37/2*j + 2*j**2.
-(j - 8)*(j - 1)*(j + 5)/2
Let t = -83270 - -83274. Factor -1 - t*o**2 + 7/2*o + o**4 - 1/2*o**5 + o**3.
-(o - 1)**4*(o + 2)/2
Let z(l) be the third derivative of -3*l**8/896 - 43*l**7/6720 + l**6/1440 - 149*l**3/6 - l**2 - 2*l. Let c(h) be the first derivative of z(h). Factor c(m).
-m**2*(m + 1)*(45*m - 2)/8
Let u be (5/2)/(113/2260). Let d be (-10)/u*10/(-3). Factor 2*r**2 + d*r - 2/3*r**3 - 2.
-2*(r - 3)*(r - 1)*(r + 1)/3
Let n(k) be the third derivative of -k**5/36 - 155*k**4/9 - 410*k**3/3 + k**2 - 353. Factor n(y).
-5*(y + 2)*(y + 246)/3
Let k be (-32)/17 - (-1)/(-51)*6. Let z be ((-5)/k + 0)*(-4122)/(-45). Let -51*n**2 - 9*n**3 + 235*n - 46*n + 12*n**3 + 14 + z = 0. What is n?
-1, 9
Let u = -285597/28 - -82076/7. Let j = -1525 + u. Let -j + 9/8*p**3 - 11/8*p - 3/2*p**2 = 0. Calculate p.
-1/3, 2
Suppose 166/11*p - 80 + 2/11*p**2 = 0. What is p?
-88, 5
Suppose -354 = -3*m - 2*c, -70*m - 792 = -76*m + 3*c. What is w in 108 - m*w + 75/4*w**2 - 3/4*w**3 = 0?
1, 12
Let m(k) be the third derivative of 7*k**4/12 + k**3/3 + 2*k**2. Let g be m(2). Factor c**4 + 30*c**3 - c**2 - 52*c**3 + g*c**3 - 17*c**4.
-c**2*(4*c - 1)**2
Let o(i) be the third derivative of -i**7/420 - i**6/36 + 2*i**5/15 + 4*i**4 + i**3 + i**2 + 36. Let g(c) be the first derivative of o(c). Solve g(p) = 0.
-4, 3
Let m(j) = -5*j**3 - 23*j**2 - 40*j - 18. Let w(g) = 15*g**3 + 14*g**2 + 273*g + 54*g**2 + 53 - 153*g. Let v(q) = 7*m(q) + 2*w(q). Determine y so that v(y) = 0.
-2, -1
Let o(h) be the first derivative of 0*h**2 + 1/6*h**3 + 0*h - 3*h**4 + 125. Determine v, given that o(v) = 0.
0, 1/24
Factor -53 + 32*z + 498*z + 203 + 930 - 2*z**2 - 3*z**2.
-5*(z - 108)*(z + 2)
Let c(j) = -6*j**2 + 1149 - 1149 + 4*j**4 + 50*j - 22*j**3. Let a(m) = -m**5 + 17*m**4 - 89*m**3 - 23*m**2 + 201*m. Let l(k) = 4*a(k) - 18*c(k). Solve l(v) = 0.
-3, -2, 0, 2
Suppose 0 = -3*a + 2*v - 166 - 20, -4*v + 192 = -3*a. Let d be -4 + (3/(-1))/(45/a). Factor 0 - 5/3*f**3 + d*f - 10/3*f**2.
-5*f**2*(f + 2)/3
Let z be (-2 + -1)/((-380)/133) + -1. Let t(x) be the second derivative of z*x**5 + 0 - 1/6*x**3 - 1/6*x**2 + 10*x + 1/36*x**4. Factor t(h).
(h - 1)*(h + 1)*(3*h + 1)/3
Suppose -4*q + 148 = 4*p, 5*p - 2*q + 179 = 10*p. Factor -l**4 - 4 - 3 + 7 - 60*l**2 - 4*l**4 - p*l**3.
-5*l**2*(l + 3)*(l + 4)
Let n = -115 - -120. Suppose -2*i - 9 = -c + i, 2*i = n*c - 110. Find q, given that 3*q**3 - 32 - 15*q - 12*q - c*q**2 + 32 = 0.
-1, 0, 9
Let d(n) be the second derivative of -n**5/5 + 17*n**4/12 + 22*n**3/3 - 6*n**2 + 362*n. Suppose d(u) = 0. What is u?
-2, 1/4, 6
Let m(n) = 4*n**4 + 289*n**3 + 295*n**2 - 324*n - 292. Let b(k) = 2*k**4 + 145*k**3 + 147*k**2 - 160*k - 146. Let p(u) = -14*b(u) + 6*m(u). Factor p(j).
-4*(j - 1)*(j + 1)**2*(j + 73)
Let k(x) be the first derivative of 10*x**3/3 + 3175*x**2/2 - 1590*x - 2546. Factor k(f).
5*(f + 318)*(2*f - 1)
Suppose 3*v - 14*v = 39*v + 13*v. What is m in -2/7*m**2 + v*m**3 + 0 + 2/7*m**4 + 0*m = 0?
-1, 0, 1
Let l(z) = -z**3 - 4*z**2 + 2. Let t be l(-4). Let b be ((-4)/6)/(17/51 - (-6)/(-9)). Let 7/4*x**t + 1/4*x**3 + b*x - 4 = 0. What is x?
-4, 1
Let p(v) be the first derivative of -18*v**5/25 + 77*v**4/2 + 2612*v**3/3 + 1496*v**2 + 2688*v/5 - 10671. Find i, given that p(i) = 0.
-12, -1, -2/9, 56
Let l(j) = -134*j + 28. Let x be l(-9). Factor -2*t**2 + 1258*t - 8 - 14 - x*t.
-2*(t - 11)*(t - 1)
Factor -2912*q**3 - 12*q**4 - 201076*q + 220548*q + 2816 + 32820*q**2 + 61*q**4.
(q - 44)*(q - 16)*(7*q + 2)**2
Suppose 8*l**5 + 1716*l**2 - 126*l**4 - 698*l**3 - 493*l**3 - 3828*l - 9*l**5 - 1440 - 2*l**5 - 5172*l**2 = 0. What is l?
-30, -8, -2, -1
Let p be 252/(-40) + 5 - (616/(-33))/14. Let a(n) be the third derivative of 1/2*n**4 + p*n**5 + 3*n**3 + 20*n**2 + 0*n + 0. Factor a(w).
2*(w + 3)**2
Suppose 3*l + 1133 = 19*g - 24*g, 5*l + 5*g = -1885. Let m = l - -378. Factor -3/5*j**3 - 3/5 - 9/5*j**m - 9/5*j.
-3*(j + 1)**3/5
Suppose -774360*y = -774234*y. Factor 2/3*c**2 + y*c - 1/6*c**5 + 0 + 5/6*c**4 - 4/3*c**3.
-c**2*(c - 2)**2*(c - 1)/6
Solve 81*q - 32*q - 100*q**2 + 216 + 29*q + 24*q + 18*q**3 - 4*q**3 = 0 for q.
-1, 3, 36/7
Suppose 69*k - 86 - 121 = 0. Let c(w) be the second derivative of -5/27*w**k - 1/54*w**4 + 0 - 2/3*w**2 + 4*w. Factor c(b).
-2*(b + 2)*(b + 3)/9
Suppose 2*w = 3*y - 27 + 13, 5*w = -5. Suppose 0 = -10*b + 13*b + 4*x - 10, 2*x = -y*b + 10. Let -4/3 - 2/3*h**2 - b*h = 0. What is h?
-2, -1
Suppose 14*b - 81*b + 201 = 0. Let j(n) be the third derivative of -1/15*n**5 - 10/3*n**b + 0 + n**4 + 0*n + 21*n**2. Find l such that j(l) = 