o).
-2*(o - 1)**3/13
Suppose 14*g - 6*w + 24 = 12*g, 3*g = 2*w - 1. Let r(q) be the second derivative of -7/78*q**4 + 3/130*q**5 - 1/13*q**2 + 5/39*q**g - 5*q + 0. Factor r(p).
2*(p - 1)**2*(3*p - 1)/13
Let v(d) = -12*d**3 + 6*d**2 + 12*d - 10. Let y(x) = -11*x**3 + 6*x**2 + 11*x - 12. Let n(u) = 6*v(u) - 4*y(u). Determine p so that n(p) = 0.
-1, 3/7, 1
Let s(h) be the second derivative of -2/39*h**3 + 0*h**2 - 1/130*h**5 + 0 + 102*h + 1/26*h**4. Solve s(a) = 0.
0, 1, 2
Let m = 4815 + -4810. Let o(l) be the third derivative of -1/90*l**6 - 1/45*l**m - 1/630*l**7 + 0*l**4 + 0 - 5*l**2 + 0*l + 0*l**3. Find s, given that o(s) = 0.
-2, 0
Suppose -29/4 - 31/4*s**2 + 1/4*s**3 + 59/4*s = 0. Calculate s.
1, 29
Let l(b) = -6240*b - 485*b**2 - 5765 + 8*b**3 - 25*b**3 + 7*b**3. Let a(s) = -5*s**3 - 242*s**2 - 3120*s - 2883. Let t(i) = -5*a(i) + 3*l(i). Factor t(n).
-5*(n + 1)*(n + 24)**2
Let c = 29903 - 29903. Factor c - 1/2*a**3 - 1/2*a**2 + 0*a.
-a**2*(a + 1)/2
Let k(m) = 6*m - m**2 - 7*m + 0*m**2 + 0*m**3 + m**3. Let y(i) = i**4 + i**3 + i**2 - 9*i + 1. Suppose 46 - 31 = -3*w. Let b(c) = w*k(c) + y(c). Factor b(r).
(r - 1)**4
Let f(g) be the first derivative of -g**4 - 56*g**3 - 558*g**2 - 952*g - 12601. Factor f(d).
-4*(d + 1)*(d + 7)*(d + 34)
Let h(m) be the second derivative of m**4/78 + 118*m**3 + 407277*m**2 + 166*m + 15. Solve h(x) = 0 for x.
-2301
Let j(v) = 2*v - 1. Let q be j(3). Let i be 407/55 - 8/20. Solve -q*n + 10*n + 9 + 3*n**2 + i*n = 0 for n.
-3, -1
Let f(j) be the second derivative of 12*j + 0 + 0*j**2 + 5/24*j**4 - 2/3*j**3 + 0*j**5 - 1/72*j**6. Let w(v) be the second derivative of f(v). Solve w(m) = 0.
-1, 1
Determine y so that 11385*y - 125*y**4 - 14410*y**3 - 1502*y**2 - 1461*y**2 + 885*y**3 + 561*y**2 + 4860 - 193*y**2 = 0.
-108, -3/5, 1
Factor 23/2*h + 0 + 2/3*h**3 + 95/6*h**2.
h*(h + 23)*(4*h + 3)/6
Solve 0 - 81/4*o - 3/8*o**3 - 87/8*o**2 = 0 for o.
-27, -2, 0
Suppose 0 = 2*b + 3 + 9. Let l be 1*b*4/(-8). Find c such that -l*c**3 + 3 + 34*c**2 + 3*c - 15*c**2 - 22*c**2 = 0.
-1, 1
Let s(a) be the third derivative of -a**6/320 + 27*a**4/64 - 27*a**3/8 - 1630*a**2. Factor s(g).
-3*(g - 3)**2*(g + 6)/8
Suppose -138 = -57732*b + 57686*b. Find p, given that -15*p**2 - 150*p - 500 - 1/2*p**b = 0.
-10
Let u(y) be the third derivative of 0 - 1/2*y**3 + y**2 + 17/240*y**5 + 80*y - 1/120*y**6 + 11/24*y**4. Determine x so that u(x) = 0.
-2, 1/4, 6
Let a(y) be the second derivative of 1/4*y**5 + 5/12*y**4 - 188*y - 5/42*y**7 + 0*y**3 - 1/6*y**6 + 0 + 0*y**2. Let a(j) = 0. Calculate j.
-1, 0, 1
Let v = 15818 + -237268/15. Factor -1210/3*t**2 - 44/3*t - v.
-2*(55*t + 1)**2/15
Let o(f) be the second derivative of 95*f + 3/16*f**4 + 0 - 27/2*f**2 + 0*f**3 + 1/80*f**5. What is g in o(g) = 0?
-6, 3
Let z be 5/45*(6/(-4) + (-78)/(-4)). Let g = 1199/7 - 171. Factor -8/7*t**z - 6/7*t + 0 - g*t**3.
-2*t*(t + 1)*(t + 3)/7
Let w(d) be the first derivative of d**6/18 - 34*d**5/15 + 143*d**4/6 + 100*d**3/9 - 799*d**2/6 - 578*d/3 - 2357. Suppose w(v) = 0. What is v?
-1, 2, 17
Suppose 2*u = -4*c - 2, -3*c + 2*u + 1 = -15. Suppose -15 = -2*z - 3*d, -124 + 149 = -c*z + 5*d. What is i in z + 9/5*i - 3/5*i**2 = 0?
0, 3
Let v(u) = 3*u**2 + 4*u - 5. Let g be v(1). Suppose g*i = 11*i - 18. Factor 1/2*o + 2*o**i - 3/2.
(o + 1)*(4*o - 3)/2
Let z(c) be the first derivative of 2/9*c**3 + 21 - 8/9*c - 4/9*c**2 + 2/45*c**5 + 2/9*c**4. Determine g so that z(g) = 0.
-2, -1, 1
Let v(l) = 17*l**2 - 71*l - 264. Let r be v(-4). Let s = r + -1458/5. Suppose -s + 2/15*g**3 + 14/15*g - 2/3*g**2 = 0. Calculate g.
1, 3
Let j be 56/(-56) + 0 + 3. Suppose -4*q = 2*y - 4, 5*y = -j*q + 6*y + 6. Factor 4/5*c**q - 8/5 - 4/5*c.
4*(c - 2)*(c + 1)/5
Suppose 2295 = 11*b + 304. Factor -40*r**4 - b*r**2 + 39*r**4 + 169*r**2 - 6*r**3 - 8*r.
-r*(r + 2)**3
Factor -381/2*p**3 + 8910*p**2 + 3/2*p**4 + 1329696 - 180792*p.
3*(p - 36)**3*(p - 19)/2
Let h(b) = b**3 - 83*b**2 + 90*b + 176. Let k(g) = -2*g**3 - 5*g**2 + g + 2. Let n(d) = 5*h(d) + 5*k(d). Factor n(v).
-5*(v - 2)*(v + 1)*(v + 89)
Let h(z) be the second derivative of z**4/2 - 22*z**3/3 + 7*z**2 - 2232*z. Factor h(b).
2*(b - 7)*(3*b - 1)
Factor -1454*x + 759988 + 986417 + 5*x**2 - 1212*x - 3244*x.
5*(x - 591)**2
Let b be ((-15)/50*-5)/(27 - 4824/192). Factor -2*q + 6/5*q**2 - b.
2*(q - 2)*(3*q + 1)/5
Let i(l) be the first derivative of -5*l**3/18 + 2395*l**2/2 - 3441615*l/2 + 5667. What is q in i(q) = 0?
1437
Suppose -5*z + z + 10 = -3*i, 5*z - 30 = -5*i. Suppose 4*j - 23 = -5*p + i*j, 6 = p - j. Factor -442 - p*w**2 + 15*w + 442.
-5*w*(w - 3)
Let l(d) be the third derivative of -4*d**7/105 - 17*d**6/60 - 8*d**5/15 - d**4/4 - 1467*d**2. Find b, given that l(b) = 0.
-3, -1, -1/4, 0
Let k(h) be the first derivative of -h**3/4 - 15*h**2/2 + 2223*h/4 + 1948. Factor k(x).
-3*(x - 19)*(x + 39)/4
Let r(i) be the second derivative of -11*i**7/42 - 247*i**6/90 - 157*i**5/20 - 313*i**4/36 - 2*i**3 + 10*i**2/3 - 619*i. Determine q, given that r(q) = 0.
-5, -1, -2/3, 2/11
Let u(i) = -13*i - 12 + 3*i**2 + 2 - 2*i**2 - 4*i. Let j be u(18). Factor 7*a**2 - 9*a - 10*a**3 + 15*a**3 - j*a**3 + 5*a**2.
-3*a*(a - 3)*(a - 1)
Let s = 179261 - 179258. Factor 5*u**2 - 3/2*u - 6*u**3 + 0 + s*u**4 - 1/2*u**5.
-u*(u - 3)*(u - 1)**3/2
Solve 8090837*o**4 - 240*o**2 - 62*o - 8090839*o**4 - 406*o - 270 - 44*o**3 = 0 for o.
-15, -3, -1
Let g be (299 - 286) + (-15 - -7). Find w such that 0*w**3 + 0*w**2 + 0 + 0*w - 2/5*w**4 - 2/5*w**g = 0.
-1, 0
Let s(u) be the third derivative of 49*u**5/18 + 77*u**4/18 + 121*u**3/45 + 10*u**2 - 101*u. Factor s(v).
2*(35*v + 11)**2/15
Let w(c) be the third derivative of c**5/20 - c**4/3 + c**3 + c**2. Let z(p) = -9 + 95*p + p**2 + 8 - 178*p + 82*p. Let v(y) = w(y) - 2*z(y). Factor v(x).
(x - 4)*(x - 2)
Find d, given that 18*d**2 - 59/3*d**3 - 232/3 + 1/3*d**4 + 236/3*d = 0.
-2, 1, 2, 58
Let w(n) be the first derivative of n**3/9 + 4*n**2 - 52*n/3 - 249. What is p in w(p) = 0?
-26, 2
Let r be (((-20)/6)/(1330/(-228)))/((-12)/(-5082)). Factor -2/9*g**2 - 44/3*g - r.
-2*(g + 33)**2/9
Let k = -6 + 8. Factor 3*i**3 + 2*i**2 - 6*i + i**k - 5*i**2 - i**2.
3*i*(i - 2)*(i + 1)
Suppose -3*b - b = -20. Suppose -7*o - 3 = -4*o + 5*t, 5*t = -4*o + 1. Factor j**4 - o*j**5 + b*j**5 - 3*j**3 - 11*j**2 + 10*j**2 + 2*j.
j*(j - 1)**2*(j + 1)*(j + 2)
Factor 43*m**3 - 40*m**3 - 5*m**2 - 22*m - 53*m + 88*m + 40 - 71*m.
(m - 5)*(m + 4)*(3*m - 2)
Let g = -150 - -1140. Factor g*q**3 - 453*q**4 - 16 + 420*q**2 + 16 + 40*q - 152*q**4.
-5*q*(q - 2)*(11*q + 2)**2
Suppose -50 = 46*a - 45*a + 4*o, 7*a = -2*o - 12. Factor 3/8*v + 1/8*v**4 - 5/8*v**a + 0 + 1/8*v**3.
v*(v - 1)**2*(v + 3)/8
Factor -318828 - 4/3*h**2 + 1304*h.
-4*(h - 489)**2/3
Let n(w) = -w**3 - w**2 - 4. Let m(v) = -4*v**3 + 46*v**2 - 182*v - 256. Let d(s) = m(s) - 6*n(s). Factor d(p).
2*(p - 4)*(p + 1)*(p + 29)
Let r(c) = c**2 - 7*c + 8. Let x be r(6). Let s be 0 + 24/(-20)*5/(-2). Solve 32*q**s - 11*q**4 - q**4 + 3 + 6 - 5 - 24*q**x = 0.
-1/3, 1
Factor -2/5*y**2 - 336/5 + 338/5*y.
-2*(y - 168)*(y - 1)/5
Suppose -686 = 6*q + 43*q. Let y be (12/q)/((-140)/490). Factor 2/9*b + 0 + 5/9*b**2 + 2/9*b**y.
b*(b + 2)*(2*b + 1)/9
Let h(q) = -7*q**3 - 154*q**2 - 237*q + 346. Let d(m) = -m**3 - 26*m**2 - 39*m + 58. Let p(z) = -13*d(z) + 2*h(z). Factor p(i).
-(i - 31)*(i - 1)*(i + 2)
Let y = 320026 + -320021. Determine f so that 0 - 26/3*f**4 + 26/3*f**2 - 169/3*f + 1/3*f**y + 56*f**3 = 0.
-1, 0, 1, 13
Factor 4/7*z**5 - 288/7*z - 128/7 - 208/7*z**2 + 12/7*z**4 - 40/7*z**3.
4*(z - 4)*(z + 1)*(z + 2)**3/7
Let r(h) be the first derivative of -6 + 36*h + 4/3*h**3 + 12*h**2. Factor r(f).
4*(f + 3)**2
Find x, given that 40/3 + 12*x + 8/3*x**2 = 0.
-5/2, -2
Let r = 8304 + -8304. Let o(z) be the third derivative of -1/180*z**5 + 0*z + 0 + 18*z**2 + r*z**3 - 1/72*z**4. Factor o(n).
-n*(n + 1)/3
Let y be ((-104)/(-6312))/(726/711 - 1). Let v = y + 5/263. Suppose 2/5 + 2/5*t**2 + v*t = 0. What is t?
-1
Let j = 67 - 64. Find y such that y**5 + 3*y**5 + 17*y**4 + 670*y + 20*y**j - 670*y + 4*y**2 = 0.
-2, -1/4, 0
Let l(k) be the first derivative of -81/5*k + 176 - 1/15*k**3 + 9/5*k**2. Factor l(p).
-(p - 9)**2/5
What is b in 227*b + 34*b + 684 + 65*b + 100*b**2 + 4*b**3 + 158*b + 8*b = 0?
-19, -3
Let c = -24680 + 24680. Fa