y be i(7). Determine r so that -3 - 6*r**2 + 5*r - y*r - 2*r**3 + 1 = 0.
-1
Let d(x) be the second derivative of -x**5/110 - 5*x**4/22 - 14*x**3/33 + 2*x + 20. Factor d(u).
-2*u*(u + 1)*(u + 14)/11
Let q(v) be the third derivative of -v**5/180 - 43*v**4/72 - 41*v**3/9 + 4*v**2 + 41. Determine f, given that q(f) = 0.
-41, -2
Let h = 469/10180 + 2/509. Let v(x) be the third derivative of 0 + 1/14*x**7 + 0*x**5 - 3*x**2 + 0*x - h*x**6 + 0*x**4 + 0*x**3 - 3/112*x**8. Solve v(p) = 0.
0, 2/3, 1
Suppose 25/3*v**4 + 4/3*v**2 + 0*v + 0 + 20/3*v**3 = 0. Calculate v.
-2/5, 0
Let m(r) = -9*r**4 + 30*r**3 - 54*r**2 + 12*r + 15. Let x(f) = 18*f**4 - 64*f**3 + 109*f**2 - 24*f - 29. Let q(z) = 5*m(z) + 3*x(z). Solve q(i) = 0 for i.
-1/3, 1, 2
Let d(s) = 21*s**4 - 3 - 23 + 9*s**2 + 16*s + 38*s - 56*s**3. Let f(t) = -85*t**4 + 225*t**3 - 35*t**2 - 215*t + 105. Let b(y) = 25*d(y) + 6*f(y). Factor b(m).
5*(m - 2)**2*(m + 1)*(3*m - 1)
Factor 26/5*b + 1/5*b**2 - 27/5.
(b - 1)*(b + 27)/5
Let v(n) = -4*n**4 + 120*n**3 + 896*n**2 + 784*n + 4. Let l(r) = 10*r**4 - 359*r**3 - 2688*r**2 - 2352*r - 11. Let g(s) = -4*l(s) - 11*v(s). Factor g(t).
4*t*(t + 1)*(t + 14)**2
Let z(s) = -17*s - 16. Let w be z(-4). Let v = -47 + w. Factor -2/3 - 2/3*p**4 + 4/3*p**2 + 2/3*p - 4/3*p**3 + 2/3*p**v.
2*(p - 1)**3*(p + 1)**2/3
Let y be (-915)/(-1098)*3*8/15. Determine k, given that -y - 2*k - 2/3*k**2 = 0.
-2, -1
Factor -12/5 + 4/5*k - 7*k**3 + 71/5*k**2.
-(k - 2)*(5*k + 2)*(7*k - 3)/5
Solve 0 + 12*j**4 + 0*j + 30*j**3 + 0*j**2 + 2/3*j**5 = 0.
-15, -3, 0
What is w in -144313 + 740*w + 8385 - 18640 - 2*w**2 - 1852*w = 0?
-278
Determine r so that 52/5*r + 152/5*r**2 + 8*r**4 + 144/5*r**3 - 4/5*r**5 + 0 = 0.
-1, 0, 13
Let k(v) be the third derivative of v**7/315 - v**6/30 + 4*v**5/45 + 159*v**2 + v. Factor k(p).
2*p**2*(p - 4)*(p - 2)/3
Let k(y) be the second derivative of -5*y**4/48 - 65*y**3/6 - 845*y**2/2 - 157*y. Factor k(n).
-5*(n + 26)**2/4
Let z(n) = n**2 - 2*n - 37. Let g be z(-7). Let l be 1/(-3) + 4 + g/(-12). Factor -3/2*j**2 + 3/2*j - l*j**3 + 3/2.
-3*(j - 1)*(j + 1)**2/2
Let u(n) be the third derivative of n**8/336 + 2*n**7/15 + 19*n**6/10 + 48*n**5/5 - n**2 - 223*n. Factor u(l).
l**2*(l + 6)**2*(l + 16)
Factor -39/5*u + 3/5*u**2 + 36/5.
3*(u - 12)*(u - 1)/5
Let a(d) = -3*d**2 + 56*d + 1. Let p be a(23). Let j = p + 301. Factor -4/9*c + 0 + 2*c**j - 14/9*c**2.
2*c*(c - 1)*(9*c + 2)/9
Let g(m) be the first derivative of -m**5/450 - m**4/180 + 2*m**3/45 + 6*m**2 - 12. Let b(c) be the second derivative of g(c). Solve b(l) = 0 for l.
-2, 1
Let b(d) = -8*d**4 + 61*d**3 + 52*d**2 - 61*d - 59. Let r(g) = 10*g**4 - 62*g**3 - 52*g**2 + 62*g + 60. Let p(i) = 6*b(i) + 5*r(i). Factor p(u).
2*(u - 1)*(u + 1)**2*(u + 27)
Let x = -12 + 16. Suppose x*v = -2*o + 18, 2*o = -5*v + o + 15. Let 2/5*k**v + 4/5*k + 0 = 0. What is k?
-2, 0
Let y(x) be the first derivative of -x**6/72 - x**5/24 + 5*x**4/4 + 10*x**3/3 + 6. Let j(n) be the third derivative of y(n). What is g in j(g) = 0?
-3, 2
Let y(o) be the first derivative of -o**4/24 + o**3/3 - o**2 + 10*o - 4. Let a(c) be the first derivative of y(c). Suppose a(l) = 0. Calculate l.
2
Suppose 0*s = -2*s - i - 49, 3*s + 69 = -3*i. Let z be (-10)/(-780) + (-4)/s. Factor 2/3*c - 1/6*c**3 - z*c**2 + 2/3.
-(c - 2)*(c + 1)*(c + 2)/6
Let d(s) be the second derivative of s**4/6 - 30*s**3 + 2025*s**2 + 5*s + 5. Factor d(k).
2*(k - 45)**2
Suppose -4*x + 23 = 5*c, -5*c - 3*x + 2*x + 17 = 0. Factor 7*g + 2*g - 4*g**2 + 3*g - c - 5*g**2.
-3*(g - 1)*(3*g - 1)
Suppose -4*h - 342 + 344 = 3*i, 2*i - 8 = 4*h. Factor -6/19 + 2/19*k**i + 4/19*k.
2*(k - 1)*(k + 3)/19
Let q(x) be the third derivative of x**8/672 + x**7/60 + x**6/15 + x**5/10 - 271*x**2. Factor q(f).
f**2*(f + 2)**2*(f + 3)/2
Factor 0*k - 12*k - 9*k - 9*k**2 + 19 + 9*k**3 + 3*k**4 - 1.
3*(k - 1)**2*(k + 2)*(k + 3)
Solve 247*y + 56*y + 1819*y**3 - 3629*y**3 + 1807*y**3 - 300*y**2 = 0.
-101, 0, 1
Let h(z) be the first derivative of 27*z**5/160 + 11*z**4/32 + z**3/8 + 22*z - 6. Let f(o) be the first derivative of h(o). Factor f(s).
3*s*(s + 1)*(9*s + 2)/8
Let m(c) = -c**2 + 10*c - 12. Let v be m(8). Factor -6*n - 4*n**4 + 3*n**v - 2*n**4 + 3 + 0*n + 6*n**3.
-3*(n - 1)**3*(n + 1)
Let m(y) be the first derivative of 2/25*y**5 + 6 + 0*y - 2/45*y**3 + 2/15*y**4 - 2/15*y**2. Factor m(j).
2*j*(j + 1)**2*(3*j - 2)/15
Let r be (-6)/14 - 68/(-28). Factor -3*z - 5 + 1 - 8*z**2 + 5*z**r + 4*z**2.
(z - 4)*(z + 1)
Let h(t) be the first derivative of t**6/3 - 2*t**5 + 7*t**4/2 - 2*t**3 - 253. Factor h(l).
2*l**2*(l - 3)*(l - 1)**2
Suppose -59*b - 63*b - 5*b**2 - 35 + 190*b - 28*b = 0. Calculate b.
1, 7
Let j(i) be the third derivative of i**6/30 - i**5/15 - 5*i**4/6 - 2*i**3 + 79*i**2. Determine n, given that j(n) = 0.
-1, 3
Let v(k) be the third derivative of k**6/420 - k**5/105 - 2*k**4/21 - 32*k**2 - k. Determine g, given that v(g) = 0.
-2, 0, 4
Let m = -7501 - -15003/2. Find k, given that m*k**5 - k**4 + 0 + 0*k**2 + 0*k + 1/2*k**3 = 0.
0, 1
Let s(j) be the second derivative of 0*j**4 + 14*j + 0 - 1/252*j**7 + 0*j**2 - 1/180*j**6 + 0*j**3 + 0*j**5. Solve s(u) = 0.
-1, 0
Let i(b) be the second derivative of -b**6/240 - b**5/30 - 5*b**4/48 - b**3/6 + 3*b**2/2 + 2*b. Let y(g) be the first derivative of i(g). Factor y(v).
-(v + 1)**2*(v + 2)/2
Solve 6/7 + 3/7*h - 3/7*h**3 - 6/7*h**2 = 0 for h.
-2, -1, 1
Suppose 4*k - 2*d + 124 = 0, -2*d = -k - 3*d - 28. Let i be ((-56)/k + -2)/((-50)/225). Factor -6/5 + i*z**2 - 3/5*z.
3*(z - 2)*(z + 1)/5
Factor -15/2 + a**2 - 13/2*a.
(a + 1)*(2*a - 15)/2
Let i(q) = -6*q**4 - 3*q**3 - 3. Let a(r) = 7*r**3 - 12*r**2 + 4*r**4 + 11*r**2 + 4 + 1 + 9*r**4. Let j(h) = 3*a(h) + 5*i(h). Factor j(y).
3*y**2*(y + 1)*(3*y - 1)
Let o(d) be the third derivative of -d**6/150 + d**5/150 + d**4/60 + 72*d**2. Factor o(n).
-2*n*(n - 1)*(2*n + 1)/5
Let g = -5003/5 + 1001. Determine i, given that -1/5*i + 3/5*i**4 + g*i**5 - 1/5*i**3 + 0 - 3/5*i**2 = 0.
-1, -1/2, 0, 1
Let m be -3*(-10)/540*2/3. Let q(a) be the first derivative of 0*a - 1/9*a**2 - 6 - m*a**6 + 0*a**3 + 0*a**5 + 1/9*a**4. Find i such that q(i) = 0.
-1, 0, 1
Let g(a) be the third derivative of 0 + 0*a - 1/3*a**4 + 0*a**3 + 8*a**2 - 1/30*a**5. Factor g(b).
-2*b*(b + 4)
Solve -1773*r + 1194 + 4258 - 93897 - 6*r**2 + 443*r + r**2 = 0 for r.
-133
Let f(n) be the third derivative of n**6/780 - 2*n**5/195 - 29*n**4/156 - 8*n**3/13 - 13*n**2 + 1. Find l, given that f(l) = 0.
-3, -1, 8
Let f = 1116/7 + -158. Solve 0 + 10/7*g**3 - f*g**5 + 4/7*g**2 - 4/7*g**4 + 0*g = 0.
-1, -2/5, 0, 1
Let o(r) be the second derivative of -r**6/360 + r**5/120 + r**4/12 - 11*r**3/6 - 10*r. Let j(q) be the second derivative of o(q). Suppose j(t) = 0. What is t?
-1, 2
Let v(a) = 601*a + 1204. Let i be v(-2). Factor -1/3*f**4 - 3*f**i - 2/3 + 5/3*f**3 + 7/3*f.
-(f - 2)*(f - 1)**3/3
Suppose -1 = -s - 5*u - 4, u + 1 = 0. Let o be ((-2)/s)/(1*(-3)/6). Factor 2/9*r**3 + o - 10/9*r**2 + 2/3*r.
2*(r - 3)**2*(r + 1)/9
Let d(j) be the second derivative of -j**4/72 - j**3/12 - 4*j - 5. Factor d(g).
-g*(g + 3)/6
Solve 16/7*u - 2/7*u**2 - 2 = 0.
1, 7
Let r(b) = b**3 - 10*b**2 - 11*b - 2. Let z be r(11). Let j = 1 - z. Determine a, given that 11*a**5 + 2*a**3 - 6*a**4 - 4*a**4 - j*a**5 = 0.
0, 1/4, 1
Factor 2/19*j**2 - 16/19*j - 40/19.
2*(j - 10)*(j + 2)/19
Let p(i) be the first derivative of -1/5*i**2 + 0*i - 4 + 6/25*i**5 + 2/15*i**3 + 1/2*i**4. Suppose p(z) = 0. What is z?
-1, 0, 1/3
Let a be (12/(-9) + 1)/(-1). Let t = a + -1/12. Suppose -t*l**4 - l - 1/4 - 3/2*l**2 - l**3 = 0. Calculate l.
-1
Suppose 3*a + x = 5 + 50, -2*a = 5*x - 54. Factor -20*o**3 + a*o + 3*o**5 - 12*o**2 + 2*o**3 + 7*o + 3*o**4.
3*o*(o - 2)*(o - 1)*(o + 2)**2
Let x(m) be the third derivative of -5*m**8/784 - 26*m**7/245 - 33*m**6/56 - 109*m**5/70 - 31*m**4/14 - 12*m**3/7 - 9*m**2 + 7*m. Solve x(s) = 0.
-6, -2, -1, -2/5
Suppose -2*t + 187 = 173. Let p(m) be the second derivative of 0*m**4 + 0*m**2 - 1/60*m**5 + 0 + 1/18*m**3 + t*m. Let p(n) = 0. Calculate n.
-1, 0, 1
Let d(t) be the first derivative of t**4/10 - 2*t**3/15 - t**2/5 + 2*t/5 + 39. Factor d(a).
2*(a - 1)**2*(a + 1)/5
Let w be 28/16 + (-2)/(-8). Find s, given that 15 - 22 - 12*s**w - 17 + 44*s = 0.
2/3, 3
Factor -7*w - 2*w**5 + 12 + 32*w - 9*w**