 Let f(y) = -1. Let p(u) = -6. Let m(r) = 5*f(r) - p(r). Let n(d) = -6*m(d) - z(d). Factor n(i).
2*i*(i - 2)
Let c = 5 + 0. Suppose -3*d + c*f + 24 = 0, 2*f + 24 = 4*d - 2*f. Factor 2/7 - 2/7*z**d + 6/7*z**2 - 6/7*z.
-2*(z - 1)**3/7
Let c(b) be the first derivative of 0*b + 7/6*b**3 + 1/4*b**2 + 13/10*b**5 + 1 + 15/8*b**4 + 1/3*b**6. Factor c(n).
n*(n + 1)**3*(4*n + 1)/2
Let c = -29 + 29. Factor 2/3*q**5 + q**4 + c + 0*q + 0*q**3 - 1/3*q**2.
q**2*(q + 1)**2*(2*q - 1)/3
Let p(m) be the third derivative of -m**8/84 + 2*m**7/105 + m**6/30 - m**5/15 - 3*m**2. Find f such that p(f) = 0.
-1, 0, 1
Let k be 12/(-10)*90/(-27). Let 4*s + s**4 + 4 + k*s**3 + s**3 - 7*s**3 - 3*s**2 = 0. What is s?
-1, 2
Let l = 3631/3948 - 1/329. Let b(p) be the third derivative of -1/3*p**3 + 64/105*p**7 + 4/15*p**6 + l*p**4 + 2*p**2 + 0*p - 6/5*p**5 + 0. Factor b(w).
2*(w + 1)*(4*w - 1)**3
Let c(k) be the third derivative of -k**6/60 + k**5/6 - k**4/2 + 26*k**2. Factor c(f).
-2*f*(f - 3)*(f - 2)
Let l be (-4)/14 + (-161)/(-49). Let p be (-2 - 57/(-27))*6. Factor -2/3*y**4 - 4*y**2 + 8/3*y + 8/3*y**l - p.
-2*(y - 1)**4/3
Suppose 3*b = -2*b + 20. Let 0 + 2/5*t**3 - 2/5*t + 6/5*t**2 - 6/5*t**b = 0. Calculate t.
-1, 0, 1/3, 1
Factor 0 - 3/5*n**2 + 39/5*n.
-3*n*(n - 13)/5
Suppose -3*z = 25 - 16. Let t be 12/(-28) - z/7. Factor 0*n - 1/3*n**2 + t.
-n**2/3
Let v be (6/(-8))/(-4*(-35)/(-336)). What is z in v*z**3 + 0*z + 0*z**2 + 3/5*z**4 + 0 = 0?
-3, 0
Let m = -96 - -98. Let n(h) be the second derivative of 0*h**m - 3*h + 1/5*h**6 + 1/6*h**4 - 2/5*h**5 + 0*h**3 + 0. Find c such that n(c) = 0.
0, 1/3, 1
Suppose -l - 1 = -3. Factor 19*n**l - 4*n**4 - 19*n**2.
-4*n**4
Let d be (-2)/12*0/(-4). Solve d - 1/5*f**2 + 1/5*f = 0.
0, 1
Factor -5*j**2 - 4 + 10*j + 3 - 4.
-5*(j - 1)**2
Let n(t) be the first derivative of -1/24*t**4 + 1/6*t**3 - 4 + 0*t**2 + 4*t. Let h(i) be the first derivative of n(i). Solve h(y) = 0.
0, 2
Solve 2 + 5 + 2*r - 9 + 6 - 2*r**2 = 0.
-1, 2
Let c(z) be the third derivative of -z**5/90 - z**4/12 + 4*z**3/9 - z**2 - 3*z. Solve c(y) = 0 for y.
-4, 1
Let n be 8 + 3/(-2)*2. Let y = n + -1. Solve -5*g**2 + 2*g - 7 + 3 + 3*g**2 + y*g**2 = 0 for g.
-2, 1
Let t(w) be the first derivative of -7 + 1/24*w**4 + 0*w**2 + 1/9*w**3 + 0*w. Let t(h) = 0. Calculate h.
-2, 0
Let s(k) = 3*k**4 - 3*k**3 + 15*k**2 + 3*k. Let g(b) = 8*b**4 - 9*b**3 + 44*b**2 + 9*b - 1. Let j(c) = 6*g(c) - 17*s(c). Factor j(o).
-3*(o - 1)**2*(o + 1)*(o + 2)
Solve 12/5*f - 4/5*f**2 + 0 = 0 for f.
0, 3
Solve -1 + 4*u**5 + 3*u**5 - u**4 - 4*u**5 + 2*u**2 - 2*u**3 - 2*u**5 + u = 0 for u.
-1, 1
Let r(c) be the third derivative of -c**8/224 + c**6/40 - c**4/16 + c**2. Factor r(u).
-3*u*(u - 1)**2*(u + 1)**2/2
Let c(t) be the second derivative of 25*t**4/3 - 20*t**3 + 18*t**2 - 22*t. Factor c(s).
4*(5*s - 3)**2
Let a(x) = x**2 + 6*x + 6. Let w(p) = -1 + 0*p + 0 + 2 + p. Let d(o) = a(o) - 6*w(o). Suppose d(k) = 0. What is k?
0
Let s(p) be the first derivative of 3*p**4/20 + p**3/5 - 3. Factor s(u).
3*u**2*(u + 1)/5
Let y(m) = 3*m**4 - 3*m**3 - 9*m**2 + 6*m + 9. Let z(s) = 6*s**4 - 6*s**3 - 18*s**2 + 11*s + 17. Let i(h) = 5*y(h) - 3*z(h). Factor i(r).
-3*(r - 2)*(r - 1)*(r + 1)**2
Let -14/5*f - 26/5*f**2 + 4/5 + 36/5*f**3 = 0. Calculate f.
-1/2, 2/9, 1
Let t be -3*(-3)/18 - (1 - 1). Determine m, given that 1/2*m**3 + t*m**2 - m + 0 = 0.
-2, 0, 1
Factor 18/5*f**2 + 3/5*f**3 + 27/5*f + 0.
3*f*(f + 3)**2/5
Let q(u) be the third derivative of u**7/315 - u**6/180 - u**5/30 - 7*u**4/24 - 4*u**2. Let b(y) be the second derivative of q(y). Let b(d) = 0. Calculate d.
-1/2, 1
Let v(l) be the third derivative of l**5/360 - l**3/36 - 3*l**2. Factor v(c).
(c - 1)*(c + 1)/6
Let p be (-4 - 0)/(1 + -3). Determine y, given that 26*y**2 - 8 - 38*y**2 - 7*y**4 - 22*y**p + 44*y + 37*y**3 - 32*y**2 = 0.
2/7, 1, 2
Let o be 51/15 + 10/(-25). Let l be 0/(6/(12/4)). Determine z, given that -1/2*z**o - z**2 - 1/2*z + l = 0.
-1, 0
Let g(k) be the second derivative of -k**8/4704 + k**7/5880 + k**6/840 + k**5/840 - k**4/12 + 3*k. Let m(u) be the third derivative of g(u). Factor m(a).
-(a - 1)*(2*a + 1)*(5*a + 1)/7
Find b, given that -b + b + 2*b**3 + 3*b**4 + 2*b - 4*b - 3*b**2 = 0.
-1, -2/3, 0, 1
Suppose 24 = 4*o + 8. Let a be (-207)/(-252) - 1/o. Factor a - 2/7*q**2 - 2/7*q.
-2*(q - 1)*(q + 2)/7
Let m = 3 - 1. Let k be 2 - 0/(-2 - -1). Factor l**3 + k + 1 - 3 + l - 2*l**m.
l*(l - 1)**2
Let x(j) be the third derivative of -j**9/8640 + j**8/4032 + j**7/2520 - 7*j**5/60 + 5*j**2. Let g(o) be the third derivative of x(o). Factor g(y).
-y*(y - 1)*(7*y + 2)
Suppose -q - 5 = n, -5*n + 29 - 9 = -4*q. Factor 0*g - 1/4*g**3 + n + 1/2*g**2.
-g**2*(g - 2)/4
Let t = -152/3 + 766/15. Factor -2*s**3 + 0 - t*s**4 - 16/5*s**2 - 8/5*s.
-2*s*(s + 1)*(s + 2)**2/5
Let o = 31/22 + -10/11. Let -1/2*d**3 - o*d + 4/3*d**2 - 1/3 = 0. What is d?
-1/3, 1, 2
Let x(t) be the first derivative of -t**3/3 - t**2 + 20. Factor x(m).
-m*(m + 2)
What is z in 9/4 - 5/4*z**2 + 3/4*z + 1/4*z**3 = 0?
-1, 3
Let k(v) be the first derivative of 0*v + 1/16*v**4 + 0*v**2 + 1/12*v**3 + 1. Suppose k(m) = 0. What is m?
-1, 0
Factor -2 + 5/2*l - 1/2*l**2.
-(l - 4)*(l - 1)/2
Let i be 6/8*72/(-33) - -2. Let r(f) be the second derivative of 2*f + 0 + 1/110*f**5 - i*f**2 + 8/33*f**3 - 5/66*f**4. Factor r(q).
2*(q - 2)**2*(q - 1)/11
Let t(q) = 3*q**5 + 7*q**4 + q**3 - 7*q**2 + 10*q. Let v = 9 - 5. Let h(d) = -d**5 - 2*d**4 + 2*d**2 - 3*d. Let l(o) = v*t(o) + 14*h(o). Factor l(g).
-2*g*(g - 1)**2*(g + 1)**2
Let p(y) be the first derivative of y**4/7 - 4*y**3/21 - 2*y**2/7 + 4*y/7 + 9. Factor p(u).
4*(u - 1)**2*(u + 1)/7
Let h(z) = 4*z**4 - 31*z**3 + 36*z**2. Let p(l) = 2*l**4 - 15*l**3 + 18*l**2. Let i(v) = 3*h(v) - 7*p(v). Factor i(f).
-2*f**2*(f - 3)**2
Suppose -4*c = -5*n - 170, -5*n + 110 = 7*c - 4*c. Suppose -y**2 + 3 + 9 + c*y**3 - 5*y**2 - 19*y - 15*y = 0. Calculate y.
-1, 2/5, 3/4
Let g be 1/2*0/2. Find z, given that -1/5*z**4 + 0*z**3 + g + 0*z + 0*z**2 = 0.
0
Suppose 2*w - 12 = -4. Let k(u) be the third derivative of 13/84*u**w + u**2 + 0 + 0*u - 1/15*u**6 - 13/210*u**5 - 2/21*u**3. Solve k(z) = 0.
-1, 1/4, 2/7
Let f = -23 - -25. Suppose -f*y**2 + 3*y**5 + 2*y**3 - 4*y**2 + 13*y**3 - 12*y**4 + 0*y**3 = 0. Calculate y.
0, 1, 2
Let i = -273 - -821/3. Determine d so that -4/3*d - 2/3*d**2 + i*d**4 + 4/3*d**3 + 0 = 0.
-2, -1, 0, 1
Factor 8*k**2 - 6*k**2 + 0*k - k**3 - k + 0*k.
-k*(k - 1)**2
Let d(b) = 5*b**2 - 4*b + 11. Let u(v) = 5*v**2 - 5*v + 10. Let c(x) = -5*d(x) + 6*u(x). Factor c(n).
5*(n - 1)**2
Find l such that 3/7*l**3 + 3/7*l**5 - 6/7*l + 0 - 9/7*l**4 + 9/7*l**2 = 0.
-1, 0, 1, 2
Let d(w) be the first derivative of 7*w**6/24 - 19*w**5/20 - 41*w**4/16 + 11*w**3/12 + 17*w**2/4 + 2*w + 62. Determine s, given that d(s) = 0.
-1, -2/7, 1, 4
Let j be (-9 + 9)/(2*1). Let q(v) be the third derivative of 0*v**5 + j*v**3 + 0*v + v**2 + 0 + 1/1176*v**8 + 1/84*v**4 + 0*v**7 - 1/210*v**6. Factor q(c).
2*c*(c - 1)**2*(c + 1)**2/7
Suppose -8 = -4*o - 0*o. Let 0*s**3 - s + 3*s**2 + s**o + s**3 - 1 - 3*s**2 = 0. Calculate s.
-1, 1
Suppose -2*l + 4 = 0, -l = -d + 3*l - 1. Find m such that -d*m**4 + 5 + 44*m**2 + 11 - 53*m**4 + 72*m - 14*m**5 - 58*m**3 = 0.
-2, -1, -2/7, 1
Let z(a) = -a**3 - 9*a**2 + 10*a + 2. Let q be z(-10). Factor 0*b**q + 4 + 12*b - 5*b**2 + 10*b**2.
(b + 2)*(5*b + 2)
Let c(k) = -k**5 - k**4 - k**3 - k**2 + 1. Let o(i) = -12*i**5 - 15*i**4 - 9*i**3 - 3*i**2 + 3*i + 9. Let h = -9 - -18. Let a(b) = h*c(b) - o(b). Factor a(q).
3*q*(q - 1)*(q + 1)**3
Let k(x) be the second derivative of 0*x**2 + 1/2*x**5 + 2/21*x**4 + 3*x - 4/21*x**3 + 0. Solve k(n) = 0.
-2/5, 0, 2/7
Suppose 10*l - 78 = -16*l. Factor 3/2*y**l + 0*y + 0 - 3/2*y**2.
3*y**2*(y - 1)/2
Let 384*g**2 - 56*g**3 + 29*g**4 + 32 - 37*g - 127*g**4 + 261*g = 0. What is g?
-2, -2/7, 2
Let j(s) be the first derivative of -6/7*s**3 - 3/7*s**4 - 4/7*s**2 - 2/35*s**5 + 0*s - 6. Solve j(i) = 0 for i.
-4, -1, 0
Let k = 876/4697 + -2/427. Factor 2/11*y**3 - k*y + 0 - 2/11*y**4 + 2/11*y**2.
-2*y*(y - 1)**2*(y + 1)/11
Let m(d) be the second derivative of d**7/315 - d**6/180 + 2*d**2 + 9*d. Let l(f) be the first derivative of m(f). Let l(v) = 0. Calculate v.
0, 1
Solve -2 - 2*d - 2*d**4 + 3*d**5 - 5*d**5 + 0*d**4 + 4*d**2 + 7*d**3