). Suppose 5*i + n = 2*k - 8, 4*i = -20. Solve 2/5*m + 8/5*m**k + 0 + 7/5*m**2 + 3/5*m**4 = 0.
-1, -2/3, 0
Let o(s) = 11*s**3 - 44*s**2 + s + 56. Let n(w) = 12*w**3 - 43*w**2 + 2*w + 57. Let h(p) = -6*n(p) + 7*o(p). Solve h(l) = 0 for l.
-1, 1, 10
Let s = -1151 - -3454/3. Find u such that u - s*u**2 + 0 = 0.
0, 3
Let w be (-18)/(-6) - (-1)/(-240)*719. Let p(k) be the third derivative of w*k**6 + 1/3*k**3 + 1/24*k**5 + 0 + 0*k + 1/6*k**4 + k**2. Factor p(f).
(f + 1)*(f + 2)**2/2
Let d(n) be the third derivative of 0 - 6*n**2 + 1/9*n**3 + 0*n - 1/180*n**5 + 1/72*n**4. Factor d(j).
-(j - 2)*(j + 1)/3
Let h be ((-735)/(-54))/7 - 384/(-6912). Factor -2 + 1/3*y**h + 5/3*y.
(y - 1)*(y + 6)/3
Let g = -43 - -67. Factor -1 - g*v - 15 + 2*v**2 - 11*v**2 - v**3.
-(v + 1)*(v + 4)**2
Suppose 139*l = 90*l + 98. Factor 0 - 6/11*a**l + 0*a + 2/11*a**3.
2*a**2*(a - 3)/11
Factor -196/5 - 32/5*p**2 + 154/5*p + 2/5*p**3.
2*(p - 7)**2*(p - 2)/5
Let w(u) = -2*u**2 + 2*u. Let n = 22 + -26. Let q = n + -2. Let r(h) = 3*h**2 - h. Let b(m) = q*r(m) - 7*w(m). Determine x so that b(x) = 0.
-2, 0
Let c(k) be the first derivative of -6*k**2 - 4*k - 2*k**3 - 4*k**3 + 6*k**3 - 3*k**3 + 18. Factor c(r).
-(3*r + 2)**2
Suppose -3*w + 5 = -7. Factor -4 + 10*j - 14*j + 36*j**2 + w.
4*j*(9*j - 1)
Let s(w) be the first derivative of 5*w**6/3 + 24*w**5/5 - w**4/2 - 8*w**3 - 4*w**2 + 132. Solve s(q) = 0.
-2, -1, -2/5, 0, 1
Factor 3 + 1/9*t**2 - 28/9*t.
(t - 27)*(t - 1)/9
Let h(i) be the third derivative of i**8/2016 - i**7/1260 - i**6/120 + 10*i**2 - 1. Factor h(l).
l**3*(l - 3)*(l + 2)/6
Let n(h) = -17*h**3 + 136*h**2 - h + 10. Let k be n(8). Let g(x) be the first derivative of x**3 + 9/20*x**5 + 0*x - 2 - 3/2*x**4 + 0*x**k. Factor g(p).
3*p**2*(p - 2)*(3*p - 2)/4
Suppose -24*y + 7*y + 34 = 0. Suppose -3*t + 3*t = -y*t. Solve 1/3*q**3 + 1/3*q**4 + 0*q**2 + 0 + t*q = 0 for q.
-1, 0
Let l be ((-1)/3)/((-12)/36). Let w = l - -2. Factor -2*h**3 - 2*h**w + 3*h**5 + 3*h**3 - 2*h**3.
3*h**3*(h - 1)*(h + 1)
Let d(p) be the first derivative of p**5/25 + 37*p**4/20 + 7*p**3 + 103*p**2/10 + 34*p/5 - 147. Find i, given that d(i) = 0.
-34, -1
Let r be (4 - 0) + (-4)/2*1. Factor -54*h - 63*h**r - 3*h**4 - 24*h**3 + 1510 - 1510.
-3*h*(h + 2)*(h + 3)**2
Let f(h) be the third derivative of -h**8/560 + 3*h**7/350 - h**6/100 - h**2 + 37. Factor f(b).
-3*b**3*(b - 2)*(b - 1)/5
Let c be -2*(-4 + 1 - -1). Suppose c = 2*f - 0. Factor 6*u - 5*u**f + 0*u - 3*u + 2*u**2.
-3*u*(u - 1)
Let p(c) = 9*c**5 + 12*c**4 + 8*c**3 + 5. Let v(y) = -5*y**5 - 6*y**4 - 4*y**3 - 3. Let a(d) = -3*p(d) - 5*v(d). Let a(i) = 0. Calculate i.
-2, -1, 0
Let p(u) be the third derivative of 10*u**2 - 1/27*u**3 + 0*u + 1/270*u**5 + 0 + 1/27*u**4 - 1/135*u**6. Suppose p(j) = 0. What is j?
-1, 1/4, 1
Let b = 85 - 254/3. Let j(g) be the third derivative of 0*g - 1/6*g**4 + 4*g**2 + 0 + 1/30*g**5 + b*g**3. Factor j(i).
2*(i - 1)**2
Let v = -190 + 3041/16. Let r(k) be the second derivative of 0 + 0*k**3 + v*k**4 + 1/80*k**5 + k - 1/2*k**2. What is m in r(m) = 0?
-2, 1
Let y(r) be the second derivative of -r**6/120 + 21*r**5/80 - 33*r**4/16 - 121*r**3/24 + 22*r + 16. Find z, given that y(z) = 0.
-1, 0, 11
Let n = -97 - -680/7. Let q be -5 + (-180)/35*-1. Determine t, given that q*t**3 + 0 + 0*t + n*t**2 = 0.
-1, 0
Let s(t) = 2*t**4 + 5*t**3 - 25*t**2 + 15*t + 6. Let j(y) = -5*y**4 - 10*y**3 + 50*y**2 - 30*y - 10. Let m(r) = -3*j(r) - 5*s(r). Factor m(g).
5*g*(g - 1)**2*(g + 3)
Suppose -13 = -3*s - 7. Factor -15*z + 78*z**2 - 5*z - 73*z**s.
5*z*(z - 4)
Let b(u) be the second derivative of u**7/51 - 58*u**6/255 + 29*u**5/85 + 22*u**4/51 - 65*u**3/51 + 14*u**2/17 - 68*u + 4. Suppose b(t) = 0. What is t?
-1, 2/7, 1, 7
Let v = -4600799/720 + 6390. Let u(n) be the third derivative of 0 + 0*n + 0*n**4 - v*n**6 + 0*n**5 + 2*n**2 + 0*n**3. Solve u(f) = 0 for f.
0
Find j, given that 4624/7 - 272/7*j + 4/7*j**2 = 0.
34
Suppose k - 4 = 3*k. Let w be ((-15)/(-150))/(k/(-10)). Suppose -3/2*r + w - 2*r**2 = 0. Calculate r.
-1, 1/4
Let o(s) = s**3 + 4*s**2 - 31*s + 8. Let k be o(4). Factor k*m**2 + 0 - 3/2*m.
3*m*(8*m - 1)/2
Let o(f) be the third derivative of -f**7/210 + f**6/60 - f**5/60 + 2*f**2 - f. Suppose o(y) = 0. Calculate y.
0, 1
Let v(g) be the third derivative of g**6/30 + g**5/5 - 24*g**4 + 360*g**3 - 131*g**2. Determine q, given that v(q) = 0.
-15, 6
Factor -5/2 + y**3 - 6*y**2 + 7*y + 1/2*y**4.
(y - 1)**3*(y + 5)/2
Let c(a) be the second derivative of -a**7/3150 - 2*a**6/225 - 8*a**5/75 - 11*a**4/12 + 2*a. Let l(z) be the third derivative of c(z). Factor l(v).
-4*(v + 4)**2/5
Let n = -158/23 - -655/92. Find w such that -3/4*w - 1/2 + n*w**3 + 0*w**2 = 0.
-1, 2
Let p(o) be the third derivative of -1/3*o**3 - 1/1800*o**6 - 1/300*o**5 + 0 + 0*o + 0*o**4 - 3*o**2. Let j(m) be the first derivative of p(m). Factor j(w).
-w*(w + 2)/5
Let i be (-5)/2*(-20)/25. Factor -i*y**4 - 4*y**3 - 2*y**2 + 4*y**4 - y + 5*y.
2*y*(y - 2)*(y - 1)*(y + 1)
Let p = -159 + 166. Let d(j) be the second derivative of -p*j + 1/5*j**3 + 1/30*j**4 + 0 + 0*j**2. Find w such that d(w) = 0.
-3, 0
Let w(z) be the second derivative of -z**7/84 + 3*z**6/20 - 3*z**5/4 + 23*z**4/12 - 11*z**3/4 + 9*z**2/4 + z + 68. Factor w(r).
-(r - 3)**2*(r - 1)**3/2
Factor 576*p - 4608 - 24*p**2 + 1/3*p**3.
(p - 24)**3/3
Let f = -36 + 38. Let c(y) = y**4 + y**3 - y**2 + 1. Let t(k) = 4*k**4 - 6*k**3 + 4*k**2 + 8*k - 6. Let r(a) = f*c(a) - t(a). Factor r(z).
-2*(z - 2)**2*(z - 1)*(z + 1)
Let g = 517/1834 - -1/262. Suppose 0 + g*z + 2/7*z**2 - 2/7*z**4 - 2/7*z**3 = 0. What is z?
-1, 0, 1
Suppose 42/11*o + 30/11*o**3 - 36/11 - 350/11*o**4 + 314/11*o**2 = 0. What is o?
-3/5, 2/7, 1
Let p(w) be the first derivative of 5/6*w**2 + 2 - 1/12*w**4 + 1/9*w**3 + w. Factor p(y).
-(y - 3)*(y + 1)**2/3
Factor -56*j**2 - 297401*j + 297401*j - 4*j**3.
-4*j**2*(j + 14)
Let o(v) = 2*v**5 + 2*v**4 - 2*v**2 - 2*v. Let j = 32 - 43. Let n(i) = 10*i**5 + 9*i**4 - 9*i**2 - 10*i. Let t(x) = j*o(x) + 2*n(x). Solve t(z) = 0 for z.
-1, 0, 1
Let y(p) be the third derivative of p**6/360 + p**5/180 - p**4/18 - 2*p**3/9 - p**2 - 55*p. Suppose y(u) = 0. Calculate u.
-2, -1, 2
Let m(y) be the third derivative of y**3 + 0 + 1/20*y**5 + 3/8*y**4 - 29*y**2 + 0*y. Factor m(x).
3*(x + 1)*(x + 2)
Let n(s) = 23*s**2 + 35*s + 34. Let r(f) = 4*f**2 + 6*f + 6. Let m(q) = -6*n(q) + 34*r(q). Factor m(l).
-2*l*(l + 3)
Let -20*w**4 + 100*w + 40 - 30*w**2 + 100*w**2 + 3133*w**5 - 5*w**3 - 3138*w**5 = 0. Calculate w.
-2, -1, 2
Let z(v) = -v**3 - 11*v**2 + 2. Let p be z(-11). Suppose -5*s - k - 4 - 1 = 0, -k - 5 = p*s. Factor 0*o**4 + 0 + 1/2*o + 1/2*o**5 + s*o**2 - o**3.
o*(o - 1)**2*(o + 1)**2/2
Let r(x) = -x**2 - x. Let m(l) = 24*l**2 + 24*l - 8. Let s(d) = m(d) + 20*r(d). Factor s(f).
4*(f - 1)*(f + 2)
Let y(z) be the first derivative of z**4/16 - 3*z**2/2 - 16*z + 48. Let u(v) be the first derivative of y(v). Suppose u(c) = 0. Calculate c.
-2, 2
Let a(d) be the second derivative of -25/36*d**5 + 3/2*d**2 - 12*d + 25/12*d**4 - 5/2*d**3 + 0. Factor a(p).
-(5*p - 3)**3/9
Let z(i) be the first derivative of i**6/33 - 14*i**5/55 - 27*i**4/11 - 48*i**3/11 - 68. Suppose z(o) = 0. Calculate o.
-3, -2, 0, 12
Let c be 1/(-72)*(-6)/70. Let x(j) be the third derivative of 1/96*j**6 + 1/24*j**4 + 1/30*j**5 + 0 + 0*j**3 - j**2 + c*j**7 + 0*j. Find b such that x(b) = 0.
-2, -1, 0
Suppose -18 = 2*u - 4*b, u - 3*b = 5*u + 25. Let g be (-1 + 9)*(-7)/u. Factor 8*t + 0 + 4 + 2*t**2 + g - 4.
2*(t + 2)**2
Let p(n) be the first derivative of -1/6*n**3 + 0*n + 0*n**4 + 0*n**2 + 1/10*n**5 + 3. Determine u, given that p(u) = 0.
-1, 0, 1
Let c = -16 + 19. Solve -4 - 12 - 15*t**2 + 24*t + 3*t**3 + 1 + c = 0 for t.
1, 2
Let b(s) = 2 + 4*s**2 - 10*s**2 + 8*s**2. Let z(v) = -2 + 4 - 1. Let d(f) = b(f) - 2*z(f). Suppose d(o) = 0. Calculate o.
0
Let n(j) be the first derivative of 2*j**5/25 - 6*j**4/5 - 2*j**3/15 + 12*j**2/5 - 92. Solve n(u) = 0 for u.
-1, 0, 1, 12
Suppose 4*a - 52 = 2*d, -3*a - d - 1 + 50 = 0. Determine z, given that 3*z - 135/4*z**5 - 36*z**4 + a*z**2 + 0 + 39/4*z**3 = 0.
-1, -2/5, -1/3, 0, 2/3
Let t(j) be the third derivative of 0*j - 5/72*j**4 + 0 + 1/72*j**6 + 1/90*j**7 - 13*j**2 - 1/20*j**5 + 1/9*j**3. Solve t(r) = 0 for r.
-1, 2/7, 1
Suppose -232*