2
Let s = 2/17178419 - -7970782726/31694183055. Let g = s + -6/205. Factor -g*k**5 + 0*k + 0 + 0*k**3 + 0*k**2 - 4/9*k**4.
-2*k**4*(k + 2)/9
Suppose 35 + 1/6*d**2 - 107/6*d = 0. Calculate d.
2, 105
Let w be (-24)/(-3) - (4 + 0). Suppose 3*x = 5*h - 30, 6*h - h = w*x + 35. What is c in 2*c**2 - h*c**3 + 0*c**2 + 25*c + 16*c**2 - 52*c = 0?
0, 3
Let r(v) be the second derivative of v**9/5040 - v**7/840 - 2*v**4/3 - 271*v. Let j(h) be the third derivative of r(h). Factor j(q).
3*q**2*(q - 1)*(q + 1)
Let w be 1*-18*3717/(-5782). Solve 45/7*h**2 - 48/7*h - 12/7 + w*h**3 = 0.
-1, -2/9, 2/3
Let h(g) = -3*g**3 + g**2 - 2. Let f be h(-1). Suppose 8 = 5*s - f. Suppose -s*r**3 - 401*r**2 + 400*r**2 + r**3 + 2*r**3 = 0. Calculate r.
0, 1
Suppose s + 2*s = 6. Let m be ((-31)/(-8))/(-1) - (-1558 - -1554). Factor -1/2*z**s - m - 5/8*z.
-(z + 1)*(4*z + 1)/8
Let p(g) be the first derivative of -176/5*g + 14/15*g**3 - 91 - 306/5*g**2. Factor p(b).
2*(b - 44)*(7*b + 2)/5
Factor 12528 + 1001*v - 946*v**2 - 123920 - 113337*v - 2*v**3.
-2*(v + 1)*(v + 236)**2
Let z(v) = 6*v**2 + 84*v - 429. Let x be z(-18). Factor 7/4*k**2 + 1/8*k**x + 2 - 31/8*k.
(k - 1)**2*(k + 16)/8
Let x(c) be the first derivative of -20/9*c + 7/9*c**2 - 2/27*c**3 - 39. Factor x(b).
-2*(b - 5)*(b - 2)/9
Suppose -2*p + 3*r - 98 = 19, -2*p + 5*r - 119 = 0. Let h = 85 + p. Find o such that 6*o**2 + 2 + 1 + h*o + 14 - 1 = 0.
-4, -2/3
Factor 89*r**2 + 19*r**2 - 365*r - 163*r - 294*r + 870 - 3*r**3 + 183*r.
-3*(r - 29)*(r - 5)*(r - 2)
Let k = 3695/10736 + 19/976. Suppose 6/11*s + k*s**2 - 2/11*s**3 + 0 = 0. Calculate s.
-1, 0, 3
Let f be 2/(-6)*((-11 - -16) + -5). Let z(b) be the third derivative of 0*b - 1/2*b**4 + f + b**2 - 3*b**3 - 1/30*b**5. Find x such that z(x) = 0.
-3
Let z(o) = 11*o**3 - 202*o**2 + 966*o + 10. Let x(a) = -17*a**3 + 304*a**2 - 1452*a - 16. Let i(w) = 5*x(w) + 8*z(w). Determine n so that i(n) = 0.
0, 6, 26
Let n(l) = l**2 + 11*l + 17. Let j be n(-10). Factor 10 + j*g**2 - 12*g - 26*g**2 + 8*g**2 + 13*g**2.
2*(g - 5)*(g - 1)
Factor 1/5*a**2 + 128*a + 20480.
(a + 320)**2/5
Let 3*i**4 + 2482*i**2 + 1706 + 6563 + 184*i**3 - 770*i**2 - 769 - 9400*i + i**4 = 0. Calculate i.
-25, 1, 3
Let d(l) = -7*l**2 - 26*l - 94. Suppose -2*o = -5*o + 6. Let c(s) = o + 2 - s - 3 - s**2. Let z(t) = 6*c(t) - d(t). Factor z(r).
(r + 10)**2
Let z be -4 - 2/((-4)/230). Suppose -t + z = -54. Determine q so that 24*q**4 + t*q**5 - 82*q**5 - 73*q**5 - 20*q**2 - 18*q - 4 + 8*q**3 = 0.
-1, -2/5, 1
Factor -51/7*i**4 - 3/7*i**5 - 45/7*i**2 + 0 + 0*i - 93/7*i**3.
-3*i**2*(i + 1)**2*(i + 15)/7
Suppose -2*c - 4*k = 38, 1243*c - 3*k - 42 = 1240*c. Factor 96/5*i + 16/5 + 152/5*i**2 + 104/5*i**c + 33/5*i**4 + 4/5*i**5.
(i + 2)**4*(4*i + 1)/5
Let a(o) = 5*o**3 - 240*o**2 - 246*o + 496. Let n(s) = s**3 + 2*s**2 + 2*s. Let p(k) = -a(k) + 3*n(k). Determine u, given that p(u) = 0.
-2, 1, 124
Let k(y) be the second derivative of 0 + 1/3*y**4 + 31*y - 28/3*y**3 + 0*y**2. Suppose k(u) = 0. What is u?
0, 14
Suppose -18*a + 241 = 5*a - 104. Let g(j) be the second derivative of -5/2*j**5 + 5/2*j**3 + 5/2*j**2 + 0 + 7/2*j**6 - 5/2*j**4 - a*j - 15/14*j**7. Factor g(m).
-5*(m - 1)**3*(3*m + 1)**2
Let x(k) be the third derivative of -k**8/112 - 4*k**7/35 - k**6/4 + 7*k**5/5 + 11*k**4/8 - 10*k**3 + k**2 + k - 322. Solve x(c) = 0.
-5, -4, -1, 1
Suppose -29*i + l - 12 = -33*i, -3*i = -2*l - 9. Let y(j) = 3*j - 3. Let w be y(2). Factor i*v - 2*v**3 - w - 2 + 6 - v**4 - v.
-(v - 1)*(v + 1)**3
Let g(l) = -15*l**3 + 2*l**2 - 3*l - 7. Let v be g(-2). Factor -4*a + 127 - 5*a**2 + a - 2*a - v.
-5*a*(a + 1)
Factor -120 - 1/3*g**4 - 127/3*g**2 - 19/3*g**3 - 119*g.
-(g + 3)**2*(g + 5)*(g + 8)/3
Let n = -49689/14 - -248529/70. Factor -9/5*h**4 + n*h**3 + 0*h + 0 + 0*h**2 + 3/5*h**5.
3*h**3*(h - 2)*(h - 1)/5
Let z(c) be the second derivative of c**4/36 - 116*c**3/9 + 77*c**2/2 + 3124*c. Factor z(r).
(r - 231)*(r - 1)/3
Factor 2/5 + 14/5*q + 7*q**3 + 5/2*q**4 + 69/10*q**2.
(q + 1)**2*(5*q + 2)**2/10
Let h be ((-2526)/(-1260) + 2/(-2)*2)/1. Let v(w) be the second derivative of 0*w**2 + 16*w - 1/63*w**4 + 0*w**3 + 0 + h*w**5. Factor v(a).
2*a**2*(a - 2)/21
Let i(o) = 7*o**3 - 19*o**2 + 17*o - 5. Let f(m) = m + 14 - m**3 - 15 + 7*m**2 + 8*m**2 - 14*m**2. Let b(x) = -24*f(x) - 3*i(x). What is s in b(s) = 0?
-13, 1
Let g(v) = 9*v**3 + 63*v**2 - 150*v + 108. Let u(t) = 16*t**3 + 122*t**2 - 299*t + 216. Let f(m) = 11*g(m) - 6*u(m). Factor f(b).
3*(b - 6)**2*(b - 1)
Let m(b) = -8*b**5 + 10*b**4 + 7*b**3 - 56*b**2 - 20*b + 10. Let s(h) = h**5 + 4*h**4 + 2. Let p(o) = 2*m(o) + 6*s(o). Solve p(k) = 0 for k.
-1, 2/5, 2, 4
Let q(l) = 4*l**3 + 2*l**2 + l - 2. Let s(i) = 48*i**3 + 28*i**2 - 116*i - 184. Let b(o) = -8*q(o) + s(o). Factor b(k).
4*(k - 3)*(k + 2)*(4*k + 7)
Factor 1/4*z**4 - 6627/4*z - 97/4*z**3 + 2491/4*z**2 + 0.
z*(z - 47)**2*(z - 3)/4
Let i be (-3*1/(-7))/3. Let w(q) = -188*q + 12787. Let b be w(68). Factor 3/7*c**2 - 3/7 + 1/7*c**b - i*c.
(c - 1)*(c + 1)*(c + 3)/7
Suppose 18*o + 5*m = 14*o + 35, 4*o - 4*m - 80 = 0. Let q = 18 - o. Factor q*w**3 - 3*w - 3/2*w**2 + 0 + 3/2*w**4.
3*w*(w - 1)*(w + 1)*(w + 2)/2
Let h(u) = 101*u + 307. Let s be h(-3). Let i(y) be the first derivative of -15/2*y**2 + 0*y + 10/3*y**3 + 8 + 5/4*y**s. Factor i(f).
5*f*(f - 1)*(f + 3)
Let l(v) = 2*v - 17. Let h be l(-6). Let n = 36 + h. Find i such that -n*i**2 + 2*i**2 + 5 + 0*i**2 - 3*i + 5*i**3 - 2*i = 0.
-1, 1
Let i(l) be the first derivative of -l**5/200 + l**4/60 + 2*l - 38. Let n(d) be the first derivative of i(d). Determine a so that n(a) = 0.
0, 2
Let y(m) be the third derivative of -76*m**2 + 1/336*m**8 - 9/40*m**6 + 0*m**3 - 1/105*m**7 + 0 - 7/6*m**4 + 0*m - 13/15*m**5. Solve y(w) = 0 for w.
-2, -1, 0, 7
Let g be 4849/(-156)*(-1 + -1). Let c = g + -54. Factor 1/6*n**2 + c - 7/3*n.
(n - 7)**2/6
Suppose 3*n - 1 = 4*n. Let u be 36*(n - (-26)/8). Factor -19 - 13 + 3*t**2 - 31*t**2 + 39*t + u*t.
-4*(t - 4)*(7*t - 2)
Let c = -1973432/5 + 394688. Solve -6/5*s**2 + 2/5*s**4 + 8/5*s + c - 4/5*s**3 = 0.
-1, 2
Suppose 2657 + 3361 = -59*d. Let t be (-120)/70 - d/35. Let -6/5*l**3 + 12/5 + 2/5*l**4 - t*l**2 + 14/5*l = 0. What is l?
-1, 2, 3
Let l = 47192 - 141574/3. Factor -2/3*g**2 + 0 + 2/3*g**4 + 2/3*g - l*g**3.
2*g*(g - 1)**2*(g + 1)/3
Let y(w) be the third derivative of -w**5/10 + 3245*w**4/12 - 2162*w**3/3 - w**2 + 35*w + 5. Determine b, given that y(b) = 0.
2/3, 1081
Let b(r) be the second derivative of -r**6/225 + 39*r**5/25 - 4483*r**4/30 - 28556*r**3/45 + 13924*r**2/5 - 18*r - 55. Determine d so that b(d) = 0.
-3, 1, 118
Let p(v) = 25*v**3 + 12*v**2 + 5*v + 6. Let y(r) = -21*r**3 - 11*r**2 - 5*r - 5. Let f be 4*2 - (-51 + 54). Let n(z) = f*p(z) + 6*y(z). What is k in n(k) = 0?
-5, -1, 0
Suppose 9*c = 40 + 5. Factor 37*g**c - 3*g**3 + 6*g**2 - 7*g**4 - 17*g**5 + g**4 - 17*g**5.
3*g**2*(g - 2)*(g - 1)*(g + 1)
Let l(o) be the second derivative of -9*o + 15/4*o**4 + 0*o**2 - 1/6*o**6 + 0*o**3 + 2*o**5 + 3. Factor l(h).
-5*h**2*(h - 9)*(h + 1)
Let s = -1837779 + 23891129/13. Let -14/13*u**2 + 12/13*u + 0 + s*u**3 = 0. Calculate u.
0, 1, 6
Let m be (11/(7084/(-174)))/((-12)/21). Let q = m + -8/23. Factor 9/8 + 3/4*p + q*p**2.
(p + 3)**2/8
Let d(v) be the third derivative of 0*v + 1/72*v**4 + 1/360*v**5 + 0*v**3 - 1/720*v**6 + 0 + 43*v**2. Find a, given that d(a) = 0.
-1, 0, 2
Let c(x) be the first derivative of 1/2*x**4 + 51 + 1/3*x**6 - 4/5*x**5 + 0*x + 0*x**2 + 0*x**3. Factor c(d).
2*d**3*(d - 1)**2
Factor -4*g**3 - g**3 - 14583664 - 2310*g**2 - 3677656 - 355740*g.
-5*(g + 154)**3
Let r(n) be the third derivative of n**7/735 - n**6/20 + 131*n**5/210 - 57*n**4/28 - 108*n**3/7 - 4*n**2 + 37. Solve r(s) = 0.
-1, 4, 9
Let w(f) be the third derivative of 8*f**6/15 + 4504*f**5/15 + 2249*f**4/6 + 562*f**3/3 - 3*f**2 - f - 60. Let w(j) = 0. What is j?
-281, -1/4
Let g(h) be the second derivative of -h**6/270 + 19*h**4/108 - h**3/9 - 4*h**2 + 2383*h. Determine p so that g(p) = 0.
-4, -2, 3
Suppose 0 = -4*d - 4*x, -5*x - 9 = -d - 3*x. Solve 3 - 11*g - 4*g - 2*g**d + 5*g + 1 + 8*g**2 = 0.
1, 2
Suppose 8 = -2*c + 3*c. Suppose -66 = -c*z + 14. Find o, given that -z*o**2 + 5*o**4 + 78*o - 78*o + 5 + 0 = 0.
-1, 1
Solve -9*z**3 + 1/3*z**5 + 0*z**2 + 2*z**4 + 0 + 0*z = 0.
-9, 0, 