 - 5. Let d(s) = 12*s**3 + 31*s**2 + 5*s + 7. Let r(n) = 5*d(n) + 7*h(n). Solve r(j) = 0 for j.
-1, 0
Let m be (-1 - -1 - (3 + -3))/(-2). Let s = 15 - 11. Determine z, given that -4*z + 3*z**3 + s*z**2 + z**5 - 5*z**4 + m*z**3 + z**4 + 0*z**3 = 0.
-1, 0, 1, 2
Let b = 819/185 - -36/37. Factor -48/5*q**3 + 0 - 3*q**2 + 6/5*q - b*q**4.
-3*q*(q + 1)**2*(9*q - 2)/5
Factor -1/3*d**2 + 1/3 + 0*d.
-(d - 1)*(d + 1)/3
Let g(o) = -1. Let c(x) = -2*x**3 - 2*x**2 + 2*x + 14. Let k(f) = c(f) + 12*g(f). Factor k(z).
-2*(z - 1)*(z + 1)**2
Let y(w) be the second derivative of -w**7/105 - w**6/30 - w**5/30 + 5*w**2/2 - 2*w. Let b(h) be the first derivative of y(h). Factor b(g).
-2*g**2*(g + 1)**2
Let u(n) be the first derivative of n**8/840 + n**7/140 + n**6/60 + n**5/60 - n**3/3 - 3. Let f(q) be the third derivative of u(q). Factor f(v).
2*v*(v + 1)**3
Let n be 0/(((-4)/4)/1). Solve n + 1/3*d + 1/3*d**2 = 0.
-1, 0
Let 3*d**3 + 8 - 5*d**2 + 15*d - 7*d**2 - 14 = 0. Calculate d.
1, 2
Let g be (0 + -9)*1/(-3). Find d such that 3*d**2 - 3*d**g + 2*d**3 + 2 - 4*d**2 - 1 + d = 0.
-1, 1
Let b(n) be the first derivative of -n**5/150 + n**4/90 + n**3/45 - n**2/15 + n + 9. Let o(s) be the first derivative of b(s). Solve o(j) = 0.
-1, 1
Let q(h) = -4*h**5 - h**4 + h**3 - 19*h**2 + 3*h - 1. Let x(j) = 3*j**5 + j**4 - j**3 + 13*j**2 - 2*j + 1. Let t(s) = -5*q(s) - 7*x(s). Factor t(y).
-(y - 1)**2*(y + 1)**2*(y + 2)
Let x be -2 + (-4)/2*-1. Suppose x = 4*r - 16 - 4. Factor -2/7*b + 4/7*b**3 + 0*b**2 + 0 + 0*b**4 - 2/7*b**r.
-2*b*(b - 1)**2*(b + 1)**2/7
Factor -8/5 + 8/5*d - 2/5*d**2.
-2*(d - 2)**2/5
Let y = 11 + -8. Let q = -136/3 + 46. Find l such that -2/3 + 2/3*l**2 + q*l - 2/3*l**y = 0.
-1, 1
Suppose d - q = 1, 4 = 5*d - 9*q + 5*q. Solve d*j + 0 - 8/5*j**2 - 4/5*j**3 = 0 for j.
-2, 0
Let l = -4 + 8. Solve 8*b - 8*b**3 - 8*b**4 + 11*b**l + 25*b**4 - 28*b**2 = 0.
-1, 0, 2/7, 1
Let o be (0/2 - 0)*1. Factor o*g - 3*g + g + 2*g**2.
2*g*(g - 1)
Let j be (9 + -6 - 5) + 43/20. Let c(f) be the second derivative of -j*f**5 + 0 - 1/2*f**4 + 2*f + 1/2*f**3 + 3*f**2. Factor c(b).
-3*(b - 1)*(b + 1)*(b + 2)
Let l be 64/20 - (-1)/(-5). Suppose l*u - 8 = -2. Find c, given that c**2 - 3*c + 2 + c**u - 1 = 0.
1/2, 1
Let i(d) be the second derivative of 0*d**2 - 1/6*d**3 - 1/5*d**5 - 3/4*d**4 + 0 + 2*d - 1/45*d**6. Let c(l) be the second derivative of i(l). Factor c(y).
-2*(2*y + 3)**2
Factor 2*i**2 - 7 - 3*i + 7 - 5*i**2.
-3*i*(i + 1)
Let o be (-2)/8 + (-57)/(-4). Let p(q) = q - 12. Let w be p(o). Let 2 + 3*y**w - 7*y**3 - 5*y**2 + 14*y**3 - 7*y = 0. What is y?
-1, 2/7, 1
Let p = -2/75 + 502/75. Solve -p*o + 50/3*o**2 + 2/3 = 0.
1/5
Let j(t) be the third derivative of 0*t - 1/30*t**5 + 1/6*t**4 + 0 - 1/3*t**3 + 4*t**2. Factor j(u).
-2*(u - 1)**2
Let c(m) be the first derivative of -m**4/48 - m**3/8 - m**2/4 + 3*m - 1. Let n(v) be the first derivative of c(v). Factor n(i).
-(i + 1)*(i + 2)/4
Suppose -2*j = -10, 2*g + 6 = 4*j - 4. Suppose -g*n = -n - 24. Factor -4*f**5 + 8*f**2 - 12*f**3 + n*f**4 + 2*f**5 + 2*f**4 - 2*f.
-2*f*(f - 1)**4
Let i(q) be the second derivative of -q**6/165 - 3*q**5/55 - 2*q. Factor i(g).
-2*g**3*(g + 6)/11
Let j = 4/3 + -1. Factor -2/3*i + j + 1/3*i**2.
(i - 1)**2/3
Let q = 37/24 + -3/2. Let n(g) be the third derivative of -q*g**3 + 0 - 1/48*g**4 - g**2 + 0*g + 1/80*g**5. Factor n(c).
(c - 1)*(3*c + 1)/4
Let l(c) be the third derivative of -c**5/240 - c**4/48 - 9*c**2. Let l(a) = 0. What is a?
-2, 0
Suppose 2*j + 2*j = 0. Let x(c) be the first derivative of -1/7*c**2 - 2 + 2/21*c**3 + j*c. Solve x(u) = 0.
0, 1
Let f(j) be the first derivative of 2*j**3/9 - j**2/6 - 4. Find h, given that f(h) = 0.
0, 1/2
Let y(t) be the first derivative of -1/21*t**6 + 0*t**3 + 0*t**4 + 1 + 0*t + 0*t**2 - 2/35*t**5. Factor y(c).
-2*c**4*(c + 1)/7
Let k(x) be the first derivative of 0*x - 5/3*x**3 - 2 - 3/4*x**4 + 1/6*x**6 - x**2 + 1/5*x**5. Find u, given that k(u) = 0.
-1, 0, 2
Factor -2/3*y - 2/3*y**3 - 4/3*y**2 + 0.
-2*y*(y + 1)**2/3
Let a be (2/8*2/(-12))/(-15). Let c(z) be the third derivative of -2*z**2 - 1/630*z**7 + 0*z + 0*z**5 + 0*z**4 + a*z**6 + 0*z**3 + 0. Let c(t) = 0. Calculate t.
0, 1
Let n(c) = c**4 - 16*c**3 + 5*c**2 - 5*c. Let h(p) = p**4 + p**2 - p. Let t(y) = 5*h(y) - n(y). Factor t(o).
4*o**3*(o + 4)
Let z(k) be the second derivative of -5*k**4/12 + 5*k**3/2 - 5*k**2 + 34*k. Solve z(r) = 0.
1, 2
Let t = -24 + 74/3. Let 2/3 + 20/3*i**3 + 10/3*i**4 + t*i**5 + 20/3*i**2 + 10/3*i = 0. Calculate i.
-1
Let t(z) be the third derivative of z**8/112 - z**7/70 - z**6/40 + z**5/20 - 7*z**2. Factor t(g).
3*g**2*(g - 1)**2*(g + 1)
Let g(q) = -45*q**4 + 100*q**3 + 90*q**2. Let o(b) = -5*b**4 + 11*b**3 + 10*b**2. Let j(h) = 6*g(h) - 55*o(h). What is v in j(v) = 0?
-1, 0, 2
Let b(a) = a**3 + 5*a**2 + 7*a + 5. Let u be b(-4). Let z be (-2)/6 + u/(-21). Find o, given that 1/3*o**3 + 0 + 0*o**2 - 1/3*o**4 + z*o = 0.
0, 1
Let k(i) be the third derivative of -i**7/945 + i**5/135 - i**3/27 - i**2. Suppose k(l) = 0. What is l?
-1, 1
Suppose 4*y + 7*y - 5*y**3 - 11*y + 5*y**4 = 0. What is y?
0, 1
Factor -4*d**3 - 2*d**4 + 4*d**3 - d**2 + 3*d**3.
-d**2*(d - 1)*(2*d - 1)
Suppose 70*l**2 + 1536 - 143*l + 35*l**2 + 179 + 878*l + 5*l**3 = 0. Calculate l.
-7
Suppose 5*d - 7 + 2 = 0. Suppose d - 9*v**4 - 6*v + 2*v**3 + 7*v**2 + 5*v**5 + v**2 - v**5 = 0. What is v?
-1, 1/4, 1
Let i(q) be the first derivative of 1/30*q**4 - q + 1 + 1/5*q**2 + 2/15*q**3. Let j(o) be the first derivative of i(o). Suppose j(k) = 0. What is k?
-1
Suppose -6*r + 11*r - 25 = 0. Let n(q) be the first derivative of 1 + 0*q + 0*q**2 - 119/10*q**r - 245/24*q**6 - 19/4*q**4 - 2/3*q**3. Factor n(z).
-z**2*(5*z + 2)*(7*z + 2)**2/4
Suppose 2 = c - 0. Factor l**c + 3*l**2 - 2*l**2 + 0*l**2.
2*l**2
Let l(x) be the third derivative of 0*x**4 + 1/140*x**7 - 1/40*x**5 + 0*x + 5*x**2 + 0*x**6 + 0*x**3 + 0. Factor l(t).
3*t**2*(t - 1)*(t + 1)/2
Solve -3*a - 63*a**3 + 147*a**4 - 72*a**2 + a - 10*a = 0 for a.
-2/7, 0, 1
Let i(v) = v**5 - v**4 - v**2 + 1. Let j(z) = -30*z**5 + 70*z**4 - 46*z**3 + 3*z**2 + 7*z - 4. Let y(f) = -20*i(f) - 4*j(f). Let y(d) = 0. Calculate d.
-1/5, 1
Let d(n) be the first derivative of -n**4/13 + 58*n**3/39 - 112*n**2/13 + 98*n/13 - 43. Solve d(c) = 0.
1/2, 7
Factor 8/9*n**2 + 2/9*n**4 + 0 + 0*n - 8/9*n**3.
2*n**2*(n - 2)**2/9
Let -6/5*y**3 + 4/5 - 2/5*y**4 - 2/5*y**2 + 6/5*y = 0. Calculate y.
-2, -1, 1
Let b(y) be the first derivative of 4 - y - 11/4*y**2 - 3/2*y**3. Find m, given that b(m) = 0.
-1, -2/9
Suppose 4*c = -c + 10. Suppose -20 = v - 6*v. Suppose -n**c + 0 + n**2 - 2 - v*n - 2*n**2 = 0. What is n?
-1
Suppose -5*x = -x + 36. Let q(b) = -2*b**2 + 6*b - 10. Let n(s) = -8*s**2 + 23*s - 41. Let t(i) = x*q(i) + 2*n(i). Factor t(l).
2*(l - 2)**2
Let a(m) be the third derivative of -m**8/2520 - m**7/2520 + m**5/60 - 2*m**2. Let g(f) be the third derivative of a(f). Factor g(j).
-2*j*(4*j + 1)
Let s(d) = -d**5 + d**3 + d**2 - d. Let k(g) = 11*g**5 - 8*g**4 - 6*g**3 - 2*g**2 + 6*g - 1. Let n(h) = 3*k(h) + 21*s(h). Determine w so that n(w) = 0.
-1/2, 1
Let j(v) = v - 6. Let h(q) = q - 1. Let p(r) = 6*h(r) - j(r). Let y be p(1). Factor 1/3*x**3 + 0*x**2 + 0*x + 2/3*x**4 + 0 + 1/3*x**y.
x**3*(x + 1)**2/3
Let g(u) be the third derivative of 11/105*u**5 + 1/294*u**8 + 0*u + 1/21*u**3 + 1/15*u**6 + 0 + 2/21*u**4 + 17/735*u**7 + 6*u**2. Determine i so that g(i) = 0.
-1, -1/4
Let q(o) be the second derivative of -o**8/3360 + o**7/560 - o**6/240 + o**5/240 - o**3/6 - o. Let c(i) be the second derivative of q(i). Factor c(h).
-h*(h - 1)**3/2
Determine s so that -3/2*s + 2*s**2 - 1/2 = 0.
-1/4, 1
Let l(x) be the second derivative of x**7/13860 - x**5/660 - x**4/12 - 2*x. Let d(t) be the third derivative of l(t). Let d(g) = 0. What is g?
-1, 1
Factor -48/5*i**4 + 0 + 36/5*i**3 + 0*i - 8/5*i**2 + 4*i**5.
4*i**2*(i - 1)**2*(5*i - 2)/5
Let a = -2024/15 + 135. Let d(v) be the third derivative of 0*v**5 - v**2 + 1/525*v**7 + 0*v - a*v**3 + 0 + 1/30*v**4 - 1/150*v**6. Factor d(q).
2*(q - 1)**3*(q + 1)/5
Let t(d) = -d**4 - 2*d**3 + 3*d**2 - 2*d. Let g(u) = u**3. Let i(n) = 2*g(n) + t(n). Determine w, given that i(w) = 0.
-2, 0, 1
Let f(p) be the third derivative of p**7/525 + p**6/75 - p**5/25 - p**4/15 + p**3/3 - 35*p