2/9*a**3 + 84. Determine o so that y(o) = 0.
-9, 2, 3
Let k be (256/768)/(1*(-2)/60). Let g(h) = 6 + 1 - 1 + 7*h + h**2. Let w(n) = -4*n**2 - 22*n - 18. Let o(z) = k*g(z) - 3*w(z). Suppose o(l) = 0. Calculate l.
-1, 3
Factor 384/7 - 20*x + 4/7*x**2.
4*(x - 32)*(x - 3)/7
Let h(t) be the second derivative of 0*t**3 - 103*t - 1/80*t**5 + 1/2*t**2 - 1/16*t**4 + 0. Find l, given that h(l) = 0.
-2, 1
Let h = -5119 + 5127. Let q(k) be the first derivative of -5/4*k**4 + 1/5*k**5 - h*k + 24 + 2*k**3 + 2*k**2. What is f in q(f) = 0?
-1, 2
Let u(m) = 159*m**2 + 711*m - 1969. Let q(w) = 29*w**2 + 141*w - 394. Let i(n) = 22*q(n) - 4*u(n). Factor i(f).
2*(f - 3)*(f + 132)
Suppose 2*c + 4312 = 522. Let m = c + 1897. Suppose -1/2*v + 1 - 1/2*v**m = 0. Calculate v.
-2, 1
Let c(g) be the second derivative of 0*g**2 - 2 + 0*g**3 + 2*g - 1/2*g**5 - 1/6*g**6 + 0*g**4. Factor c(r).
-5*r**3*(r + 2)
Find b, given that 128/5 - 1/5*b**2 - 28/5*b = 0.
-32, 4
Let d(g) be the third derivative of 2/105*g**7 + 0*g**3 + 0 + 0*g + 37/15*g**6 + 1369/15*g**5 + 0*g**4 + 153*g**2. Solve d(n) = 0 for n.
-37, 0
Suppose -8*k - 140 + 156 = 0. Factor 3*l**k + l**2 + 5*l**2 - 72 + 75*l - 12*l**2.
-3*(l - 24)*(l - 1)
Let r = 26236 + -52469/2. Factor 57/2*h**4 + 51/4*h + 27/4*h**5 + 93/2*h**3 + r + 36*h**2.
3*(h + 1)**4*(9*h + 2)/4
Let t be (-8)/78*(-59709)/3062. Let -13/3*v + 0 - 1/3*v**t = 0. What is v?
-13, 0
Determine v, given that -315/4*v + 33/4*v**2 + 162 = 0.
3, 72/11
Suppose 703*v - 20 = 693*v. Factor 16*u**4 + 12*u**3 + 6*u**v - 9 - 12*u + 0*u**4 - 13*u**4 + 0*u**2.
3*(u - 1)*(u + 1)**2*(u + 3)
Suppose 604*p - 600*p + 256 = 0. Let f be p/(-512) - 11*21/(-72). Find v such that 1 + v**2 + f*v = 0.
-3, -1/3
Suppose 20 = 4*i, 4*o - 3*i - 3 = -2*i. Suppose 42 = 10*k + o. Factor 33 - 4*r**2 - 33 + r**k.
r**2*(r - 2)*(r + 2)
Let s be ((-9)/66)/3*(-1 + 8 + -11). Determine w, given that 0*w + 0 - 2/11*w**5 - 6/11*w**2 + 6/11*w**4 + s*w**3 = 0.
-1, 0, 1, 3
Factor 1684*g + 0*g**2 + 1190*g - 456300 - 3*g**2 - 534*g.
-3*(g - 390)**2
Let s(t) = -9*t**2 + 317*t - 374. Let f be s(34). Let h(k) be the third derivative of f*k + 1/20*k**5 + 0 + 0*k**3 + 0*k**4 - 28*k**2. What is o in h(o) = 0?
0
Suppose 0 = -r - 53 + 58. What is m in -3*m**5 + m**4 + 4*m**r + 20*m**3 + 23*m**3 - 48*m**3 + 3*m**2 = 0?
-3, 0, 1
Suppose 4*f = 2*m - 5 + 7, -3*m + f = -7. Let h(v) = -2*v**2 - 11*v - 3. Let g(x) = -3*x**2 - 10*x - 4. Let c(y) = m*g(y) - 4*h(y). Factor c(p).
-p*(p - 14)
Suppose 0 = 738*h - 741*h + 5*m - 90, 0 = -2*h + m - 11. Solve 2/9*l**h - 32/9*l**4 + 0 - 224/9*l**2 + 52/3*l**3 + 98/9*l = 0 for l.
0, 1, 7
Let v(l) = -2*l**3 + 2*l**2 + 2*l + 3. Let o(m) = 22*m**3 - 1016*m**2 + 124972*m - 246046. Let b(c) = -2*o(c) - 20*v(c). Let b(u) = 0. What is u?
2, 248
Let i(c) = -6*c**3 + 694*c**2 + 3239*c + 2574. Let v(a) = -20*a**3 + 2428*a**2 + 11336*a + 9008. Let k(l) = 24*i(l) - 7*v(l). Factor k(n).
-4*(n + 1)*(n + 4)*(n + 80)
Factor -28*o**3 + 619*o - 17*o - 4*o**4 - 218*o + 400 + 36*o**2 + 76*o.
-4*(o - 4)*(o + 1)*(o + 5)**2
Let q(l) be the third derivative of -l**6/48 - 19*l**5/24 + 205*l**4/48 - 35*l**3/4 + 771*l**2. What is z in q(z) = 0?
-21, 1
Find t, given that 151*t**2 - 76 - 80*t**2 - 4*t**3 + 6*t + 3*t**3 - 5*t + 5 = 0.
-1, 1, 71
What is u in 1017/2*u**3 + 625/8 + 25763/4*u**2 + 2825/2*u + 81/8*u**4 = 0?
-25, -1/9
Let m(h) be the first derivative of -h**4/12 + h**3 + 7*h**2/2 + 62*h - 50. Let p(k) be the first derivative of m(k). Suppose p(l) = 0. What is l?
-1, 7
Let u(d) = -3*d**2 + 76*d + 54. Let v be u(26). Factor 116*c**v - 6 - 235*c**2 + 12*c**3 + 134*c**2 - 21*c.
3*(c - 1)*(c + 2)*(4*c + 1)
Let m = -14103176/9 + 1567020. Determine s so that 16/3*s - 44/9*s**3 - m*s**5 - 8/9*s**2 - 8/3*s**4 + 32/9 = 0.
-2, -1, 1
Suppose 29*i**2 - 12*i**2 + i**2 - 105*i - 1550 - 13*i**2 = 0. Calculate i.
-10, 31
Solve 0 + 49/4*c**3 + 11/2*c**2 + 0*c - 15/4*c**4 = 0 for c.
-2/5, 0, 11/3
Let h(b) be the first derivative of -7*b**5/20 + 45*b**4/16 - 95*b**3/12 + 75*b**2/8 - 9*b/2 - 1168. Find k, given that h(k) = 0.
3/7, 1, 2, 3
Suppose 22 = 9*q + 2*q. Determine c, given that 12 - 23 + 9 + 68*c - 578*c**q = 0.
1/17
Let g(x) be the first derivative of x**5/15 + 29*x**4/6 + 36*x**3 - 227*x**2/2 + 24. Let b(a) be the second derivative of g(a). Suppose b(r) = 0. Calculate r.
-27, -2
Suppose 0 = 3*y - 4*w - 18 - 0, -73*w = -77*w - 12. Factor 50/11*g**4 + 112/11*g**y - 32/11*g - 130/11*g**3 + 0.
2*g*(g - 1)*(5*g - 4)**2/11
Let y(f) be the first derivative of f**4/9 - 700*f**3/27 + 5162*f**2/3 - 3364*f - 907. Factor y(u).
4*(u - 87)**2*(u - 1)/9
Let 150/7*p - 1700/7 + 2/7*p**2 = 0. What is p?
-85, 10
Let a(l) be the third derivative of -l**7/210 + 3*l**6/5 + 191*l**5/30 + 10*l**4 - 231*l**3/2 - 4*l**2 + 277. Factor a(s).
-(s - 77)*(s - 1)*(s + 3)**2
Suppose -u = -26*u + 750. Factor 18*j**2 - 24*j**2 + 8*j**2 - u*j + 3*j**3 + 25*j**2.
3*j*(j - 1)*(j + 10)
Let y(j) be the first derivative of j**4/20 - j**3/2 + 6*j**2/5 - 72*j - 33. Let g(x) be the first derivative of y(x). Factor g(w).
3*(w - 4)*(w - 1)/5
Suppose 0 = 2*w + 109 - 49. Let n be (-11)/w - (1467/135 - 11). Factor -h + n*h**3 - 3/4*h**2 + 1/4*h**4 + 1.
(h - 1)**2*(h + 2)**2/4
Determine w so that -2984/21*w**2 - 134/3*w**4 + 14/3*w**5 - 128/21 + 2864/21*w**3 + 1088/21*w = 0.
2/7, 1, 4
Let x = -327883 - -983671/3. Suppose 2/3*t**3 - x*t + 0 + 20/3*t**2 = 0. Calculate t.
-11, 0, 1
Let v(f) = f**3 + 148*f**2 - 451*f + 304. Let r be v(-151). Let j(p) be the first derivative of -38 - 9*p**3 - 3/2*p**r + 0*p. Let j(c) = 0. Calculate c.
-1/9, 0
Let s(k) be the third derivative of 1/240*k**5 + 160*k**2 + 0*k**3 - 1/160*k**6 + 0 + 1/32*k**4 - 1/840*k**7 + 0*k. What is i in s(i) = 0?
-3, -1, 0, 1
Suppose 1 = 3*h + 4*y - 11, 0 = 4*h + 3*y - 23. Solve 2*b**3 + 349*b - 1210 + 108*b**2 + 3*b**3 + 36*b - h*b**2 = 0.
-11, 2
Let i(h) be the second derivative of 5/18*h**3 + 19/180*h**6 + 53/72*h**4 + 0*h**2 + 23/40*h**5 + 0 - 42*h - 1/36*h**7. Let i(c) = 0. What is c?
-1, -2/7, 0, 5
Suppose 0 = -2*n - 4*d + 8, -8*d = -n - 11*d + 5. Suppose 3 + 316*z**2 - 3 + 309*z**2 + 5*z**3 - 615*z**n = 0. What is z?
-2, 0
Let u(k) be the first derivative of 1/12*k**2 + 0*k + 82 - 1/9*k**3 + 1/24*k**4. Factor u(z).
z*(z - 1)**2/6
Let b(w) = 43*w**3 + w + 1. Let i be b(-1). Let g = i + 45. Let 3*o**2 + 2*o - 9*o**g - 3*o + 3*o**3 + 4*o = 0. What is o?
0, 1
Suppose -55*t = 397 - 562. Let m(d) be the third derivative of 0 - 36*d**2 - 1/6*d**t - 1/72*d**5 + 0*d - 17/144*d**4. Suppose m(b) = 0. Calculate b.
-3, -2/5
Let x be ((-384)/20 - (-1007)/53)/(9/(-240)). Solve -x*n - 40/3 + 2/3*n**2 = 0 for n.
-2, 10
Let i = -87087/20 + 17419/4. Suppose -26/5*r**2 - 24/5*r + i = 0. What is r?
-1, 1/13
Factor 16*b**4 + 20*b**5 + 50*b - b**5 - 48 - 24*b**3 + 20*b + 46*b - 64*b**2 - 15*b**5.
4*(b - 1)**3*(b + 3)*(b + 4)
Let j(r) = -58*r**3 + 25640*r**2 - 32870*r + 7468. Let d(l) = 23*l**3 - 10256*l**2 + 13148*l - 2990. Let p(y) = -12*d(y) - 5*j(y). Solve p(v) = 0 for v.
2/7, 1, 365
Suppose 0 = 2*a - 5*p + 2*p - 81, -3*a - 5*p + 112 = 0. Suppose -27 = -a*y + 30*y. Factor -3/2*f**2 - 3/2 + y*f.
-3*(f - 1)**2/2
Let t(o) be the third derivative of 1/6*o**4 + 7/15*o**5 + 0 - 14/3*o**3 - 6*o - 1/30*o**6 - o**2. Factor t(n).
-4*(n - 7)*(n - 1)*(n + 1)
Let m(u) be the second derivative of -u**4/6 + 940*u**3 - 1988100*u**2 - 93*u - 20. Factor m(t).
-2*(t - 1410)**2
Suppose -5*m + 22 = -6*w + 4*w, -3*m - w = -11. Suppose m*z - 438 - 290 = 0. Factor -2*h**4 - 312*h**2 - 517 - 1728*h - z*h**2 - 48*h**3 - 2075 + 62*h**2.
-2*(h + 6)**4
Let a(x) = x**3 + 5*x**2 + x - 7. Let k be a(-3). Let b be 5/k*(-22)/(-55). Suppose 0 + b*s**3 - 1/2*s**2 - 3/4*s = 0. What is s?
-1, 0, 3
Let u be (-681)/(-1188) - 204/374. Let g(s) be the second derivative of 0 + 4*s + u*s**4 + 1/15*s**5 - 2/3*s**2 - 8/9*s**3. Factor g(z).
(z - 2)*(z + 2)*(4*z + 1)/3
Let q(x) be the third derivative of -2*x**7/105 - 7*x**6/40 - 3*x**5/10 + 9*x**4/8 + x**2 + 687*x. Factor q(c).
-c*(c + 3)**2*(4*c - 3)
Let k(z) be the first derivative of z**5/50 + z**4/6 + 4*z**3/15 - 263*z - 8. Let y(n) be the first derivative of k(n). Let y(i) = 0. What is i?
-4, -1, 0
Let g(w) = -w + 12. Let f be g(8). Suppose -f*s + 15 = s. Suppose 12 - 5*n - n - 6*n**2 - 3 + s*n = 0