980 - 4*x**3/3 - 10. Let m(z) be the third derivative of k(z). Let m(n) = 0. What is n?
-1, -1/2, 0
Let t(p) = -p**2 - 6*p - 4. Let w be t(-4). Factor j**2 + 3*j + w*j - 2*j**3 - 1 - 6*j + j**3.
-(j - 1)**2*(j + 1)
Let i = -28/19 + 346/209. Find b, given that -2/11 - i*b**2 + 4/11*b = 0.
1
Let u(f) be the first derivative of f**3/6 + f**2/4 - 3*f + 58. Factor u(m).
(m - 2)*(m + 3)/2
Factor 22/21*v**2 + 2/3*v**3 + 2/21*v**4 + 0 + 10/21*v.
2*v*(v + 1)**2*(v + 5)/21
Suppose -36/7*t**3 - 20/7 - 124/7*t - 204/7*t**2 = 0. Calculate t.
-5, -1/3
Let v be 5*4/(-2)*-1. Let n be 32/v*(-2 - -7). Solve n*h**2 - h - h + 32*h**3 + 4*h = 0.
-1/4, 0
Let m = -13 + 15. Let q(v) be the first derivative of -3 - m*v - 2/3*v**3 + 2*v**2. Determine t so that q(t) = 0.
1
Let q(m) = 9*m**4 + 20*m**3 - 36*m**2 - 36*m + 11. Let c(f) = -3*f**4 - 7*f**3 + 12*f**2 + 12*f - 4. Let k(n) = 11*c(n) + 4*q(n). Let k(i) = 0. What is i?
-2, -1, 0, 2
Factor 1/3*k**4 + 1/6*k**3 + 0*k + 1/6*k**5 + 0 + 0*k**2.
k**3*(k + 1)**2/6
Suppose 5*w = 2*w + 6. Suppose 0*d - d**3 - 6*d**w + 2*d**2 - 4*d = 0. Calculate d.
-2, 0
Let w(r) = -r**3 + 8*r**2 + 9*r + 1. Let i be w(9). Solve 31*m - m**2 + i - 31*m = 0.
-1, 1
Let r(m) = -2*m**2 + 2*m - 3. Let j(u) = -5*u**2 + 5*u - 5. Let f(i) = 3*j(i) - 5*r(i). Determine g, given that f(g) = 0.
0, 1
Let l be -3 + 2 + (0 - -3). Suppose -s + l = -0*s. Solve -s*x**4 + 13*x**2 - x + x**3 - 2*x**4 - 9*x**2 = 0 for x.
-1, 0, 1/4, 1
Let g(x) = -24*x**3 + 14*x**2 - 4*x + 14. Let m be (-3 + -2)*28/10. Let a(l) = 5*l**3 - 3*l**2 + l - 3. Let i(j) = m*a(j) - 3*g(j). Factor i(q).
2*q*(q - 1)*(q + 1)
Let i(c) be the third derivative of c**7/735 + c**6/140 + c**5/105 + 19*c**2. Factor i(w).
2*w**2*(w + 1)*(w + 2)/7
Factor 0*p - 1/9*p**2 + 0 - 1/9*p**5 - 1/3*p**3 - 1/3*p**4.
-p**2*(p + 1)**3/9
Let b = -124/3 - -42. Factor 0 - 2/3*w**2 + b*w.
-2*w*(w - 1)/3
Solve -4/7*d**4 - 36/7*d**2 - 8/7 - 4*d - 20/7*d**3 = 0 for d.
-2, -1
Let -o**2 - 3/2*o - 1/2 = 0. What is o?
-1, -1/2
Let w be 1/(-1) + (-1 - -6 - 4). Factor w*y + 0 + 2/5*y**2 - 2/5*y**3.
-2*y**2*(y - 1)/5
Let x(l) be the first derivative of 4/15*l**6 + 2/15*l**3 + 16/25*l**5 - 3 + 1/2*l**4 + 0*l + 0*l**2. Find j, given that x(j) = 0.
-1, -1/2, 0
Find g such that -g**3 - g - 1/4*g**4 - 1/4 - 3/2*g**2 = 0.
-1
Let r(w) be the second derivative of -11*w**5/70 - 2*w**4/3 - 23*w**3/21 - 6*w**2/7 - 19*w. Let r(g) = 0. Calculate g.
-1, -6/11
Let h(i) = -i**3 + i**2 + 1. Let w(a) = 2*a**3 + 2*a**2 - 4*a - 4. Let q(j) = -4*h(j) - w(j). Factor q(n).
2*n*(n - 2)*(n - 1)
Suppose -4*k - 4*b + 32 = -0*b, -2*k - 5*b = -25. Factor -k*z - 8 - 11*z - z**2 + 24 + 5*z**2.
4*(z - 2)**2
Let l = 186 - 183. Let x(z) be the first derivative of -1 + 0*z**3 + l*z - 3/5*z**5 - 3*z**2 + 3/2*z**4. Factor x(a).
-3*(a - 1)**3*(a + 1)
Let c be 204/3*-5 - -4. Let r be (-1)/7 + (-7216)/c. Determine w, given that 30*w**4 - r*w - 72*w**3 + 182/3*w**2 + 8/3 = 0.
1/3, 2/5, 2/3, 1
Factor 2/3*l**2 - 2/9*l**3 + 32/9*l + 8/3.
-2*(l - 6)*(l + 1)*(l + 2)/9
Solve 4/5*q**3 - 64/15*q + 64/15*q**2 - 14/15*q**4 + 0 + 2/15*q**5 = 0 for q.
-2, 0, 1, 4
Suppose 2*d - 6 = -d. Factor 2*l**4 + l**5 + 3*l**d + 2*l**5 - 2*l - 7*l**4 + 3*l**3 - 2*l**4.
l*(l - 1)**3*(3*l + 2)
Let m = 73 - 73. Let -2/5*v**2 - 4/5*v + m = 0. What is v?
-2, 0
Let v(h) = -h - 3. Let g be v(0). Let d(k) = -2*k**3 + 2*k. Let x(i) = 10*i**3 - 10*i. Let a(b) = g*x(b) - 14*d(b). Factor a(j).
-2*j*(j - 1)*(j + 1)
Solve -11/6*a**3 + 1/6*a**4 + 1/6*a**5 - 29/6*a**2 - 4/3 - 13/3*a = 0 for a.
-2, -1, 4
Let i(b) be the first derivative of 2*b**6/3 + 88*b**5/25 + 38*b**4/5 + 128*b**3/15 + 26*b**2/5 + 8*b/5 + 3. Let i(d) = 0. What is d?
-1, -2/5
Let b(w) = -3*w**4 + 3*w**2 - 6. Let l(j) = -6*j**4 + 5*j**2 - 13. Let v = 1 - 8. Let u(c) = v*b(c) + 3*l(c). Solve u(h) = 0 for h.
-1, 1
Let w = 959/2360 - 3/472. What is a in -3/5*a - 2/5 + w*a**2 = 0?
-1/2, 2
Let z(i) be the third derivative of -i**5/180 - i**4/72 + i**3/9 - 3*i**2. Factor z(v).
-(v - 1)*(v + 2)/3
Let g = 55/114 + -6/19. Let w(y) be the second derivative of -g*y**4 + 0*y**3 + 0 + 2*y + 1/2*y**2 + 0*y**5 + 1/30*y**6. What is x in w(x) = 0?
-1, 1
Suppose 0 = p + t + 12, 3*t - 3 = -4*p - 51. Let m be (45/p - -3)*-4. Factor -3/2*x**m + x**4 + 1/2*x + 0*x**2 + 0.
x*(x - 1)**2*(2*x + 1)/2
Factor -5 + 0 + 3 + 3 - w**2.
-(w - 1)*(w + 1)
Let i = 21 - 19. Let r(n) be the second derivative of 1/48*n**4 - 1/60*n**6 + 0*n**3 + i*n + 0 + 1/80*n**5 + 0*n**2. Factor r(u).
-u**2*(u - 1)*(2*u + 1)/4
Factor -4/3*z**2 - 4/3*z + 0.
-4*z*(z + 1)/3
Factor -4/3 + 6*s**3 + 32/3*s**2 + 10/3*s.
2*(s + 1)**2*(9*s - 2)/3
Suppose -5*l + 19 = -31. Let b = l + -6. Suppose -3*t**2 + 4*t**2 + 2*t**3 - t**b - 2*t**2 = 0. Calculate t.
0, 1
Let j(o) be the first derivative of 4*o**5/15 + 2*o**4/3 + 4*o**3/9 + 22. Suppose j(f) = 0. What is f?
-1, 0
Let r be 9 + 2 - (-1)/(-1). Suppose -4*n = -r - 2. Solve 3*x**3 + 2*x**5 + 2*x**2 - 2*x**4 - 4*x**n - x**3 = 0 for x.
-1, 0, 1
Let i(b) = 5*b**3 + 5*b**2 + b + 1. Let s(h) = h**3 + h**2 + h + 1. Let z = 1 - 2. Let j(p) = z*i(p) + 3*s(p). Find v such that j(v) = 0.
-1, 1
Let c(h) be the first derivative of -3*h**5/20 - 21*h**4/8 - 18*h**3 - 60*h**2 - 96*h - 27. Find z, given that c(z) = 0.
-4, -2
Let 16/7*d + 32/7 - 2*d**2 + 2/7*d**3 = 0. Calculate d.
-1, 4
Suppose -5 + 64*m**2 + 15*m - 5 - 49*m**2 - 10*m**3 = 0. Calculate m.
-1, 1/2, 2
Let j(p) be the second derivative of 1/2*p**4 + 1/3*p**3 + 0*p**2 - 4*p - 1/40*p**5 + 0 - 1/4*p**6. Let j(f) = 0. What is f?
-2/3, -2/5, 0, 1
Let b = 16 + -14. Suppose 12*g**2 - 23*g**2 + 4*g + 9*g**b = 0. What is g?
0, 2
Let c(z) = 4*z**4 + 6*z**4 + 4 - z**4 + 22*z**3 + z**4 + 20*z + 28*z**2. Let n(x) = -x**4 + x**2. Let r(t) = -c(t) - 5*n(t). Factor r(i).
-(i + 1)**2*(i + 2)*(5*i + 2)
Solve 1/7*s + 1/7 - 1/7*s**2 - 1/7*s**3 = 0 for s.
-1, 1
Factor 93 + 33 - 18 + 44*p + 3*p**2 - 8*p.
3*(p + 6)**2
Let u(s) be the second derivative of -3*s - 1/8*s**3 - 1/8*s**4 + 0 + 0*s**2 - 3/80*s**5. Factor u(l).
-3*l*(l + 1)**2/4
Let f(w) be the first derivative of w**6/8 - 3*w**4/8 + 3*w**2/8 - 8. Solve f(c) = 0 for c.
-1, 0, 1
Let l(b) be the second derivative of 0*b**2 - 4*b**4 + 5*b - b**5 + 0 - 8/3*b**3. Factor l(z).
-4*z*(z + 2)*(5*z + 2)
Let d be 20/(-15) + 24/(-9) - -6. Solve -2/9*q**5 + 0 - 4/9*q**d + 0*q**3 + 2/9*q + 4/9*q**4 = 0.
-1, 0, 1
Suppose 0 = -l - 2*l + d + 11, -3*l = -2*d - 10. Suppose 2 = 5*v - l*v. Let -2*s**v + 2/7 + 8/7*s**3 + 4/7*s = 0. Calculate s.
-1/4, 1
Let n(b) be the first derivative of 1/18*b**4 + 3*b + 0*b**3 - 1 - 1/3*b**2. Let l(t) be the first derivative of n(t). Factor l(j).
2*(j - 1)*(j + 1)/3
Let n(i) be the second derivative of 0 - 2*i + 0*i**2 + 0*i**6 + 0*i**4 + 0*i**3 + 1/42*i**7 - 1/20*i**5. Factor n(q).
q**3*(q - 1)*(q + 1)
Suppose 3*n + 4 + 8 = 0. Let y(g) = g**3 - g**2 + 12*g - 3. Let x(j) = -j**2 - 1. Let r(k) = n*y(k) - 20*x(k). Determine w so that r(w) = 0.
2
Let n = -59 - -61. What is d in d + 1/4*d**n + 1 = 0?
-2
Let k be (1*(-4 - -2))/(-1). Let i(p) be the second derivative of -k*p + 0 - 1/30*p**4 - 2/15*p**3 + 0*p**2. Factor i(b).
-2*b*(b + 2)/5
Suppose -3*l + x + 20 = l, 12 = 2*l - x. Factor -8*t**3 + l*t**4 + 16/3*t**2 - 2/3*t**5 + 0*t + 0.
-2*t**2*(t - 2)**3/3
Suppose 21*j - 18*j = 0. Let q(m) be the third derivative of 0*m**4 - 1/120*m**6 + 3*m**2 + 0*m + 0*m**3 + j - 1/60*m**5. Determine o so that q(o) = 0.
-1, 0
Let l = 2 - 0. Let x(o) = 28*o**4 - 20*o**3 - 45*o**2 + 29*o + 8. Let d(y) = 7*y**4 - 5*y**3 - 11*y**2 + 7*y + 2. Let q(n) = l*x(n) - 9*d(n). Factor q(w).
-(w - 1)**2*(w + 1)*(7*w + 2)
Let r(j) be the third derivative of j**5/390 + 5*j**4/78 + 3*j**3/13 - 61*j**2. Let r(w) = 0. What is w?
-9, -1
Let s(g) be the first derivative of -g**3 - 54*g**2 - 972*g + 47. Solve s(y) = 0 for y.
-18
Let b(z) be the third derivative of -z**8/2352 - z**7/735 + z**5/210 + z**4/168 + 6*z**2. Factor b(i).
-i*(i - 1)*(i + 1)**3/7
Let p(g) = -g**3 + 6*g**2 + 2*g - 9. Let z be p(6). Factor b**2 + 3*b - z*b.
b**2
Let r(t) be the third derivative of t**8/840 + t**7/525 - t**2. Factor r(o).
2*o**4*(o + 1)/5
Let v(a) be the first derivative of a**4/6 - a**2/3 + 3. Factor v(l).
2*l*(l - 1)*(l + 1)/3
Suppose -4*z + 5 = -4*t + 1, 0 = -3*t + 4*z - 7. Determine g so that -7*g + 24*