Let z be (-127)/(-99) - (-22)/(-99). Let k = -8/11 + z. Suppose -1/3 - k*p**2 + 2/3*p = 0. Calculate p.
1
Let o(a) be the first derivative of -a**3 + 3*a**2/2 + 6*a - 16. Find z such that o(z) = 0.
-1, 2
Factor -2*x**3 - 2*x + 2*x**3 + 0*x**2 + 6*x**2 - 8*x**4.
-2*x*(x + 1)*(2*x - 1)**2
Let w(n) = n**3 - n**2 + n + 1. Let f(z) = 2*z**4 - 2*z**3 - 2*z - 2. Let i(h) = -f(h) - 2*w(h). Factor i(j).
-2*j**2*(j - 1)*(j + 1)
Let v be (-4)/(-10) + (-64)/(-40). Determine c, given that -4*c + 0*c + c + 3*c**v = 0.
0, 1
Let u(k) = k**2 + 12*k + 16. Let m be u(-13). Suppose 20 = 4*v, -5*v - 4 + m = -t. Factor t*j - 1/4*j**2 + 0.
-j**2/4
Find z such that -z**4 + 7*z**2 - 6*z**3 + 11*z - 31*z + 20*z = 0.
-7, 0, 1
Suppose -4*r + 3*m = -80, -2*m = -r - r + 40. Let n = 81/4 - r. Determine o, given that 1/4 + n*o**2 - 1/2*o = 0.
1
Let h(v) be the third derivative of v**8/168 + 11*v**7/315 + v**6/12 + v**5/10 + v**4/18 + 6*v**2. Factor h(o).
2*o*(o + 1)**3*(3*o + 2)/3
Let z(w) be the second derivative of 2/5*w**5 + 4/3*w**3 - w**2 - w**4 + 0 - 2*w - 1/15*w**6. Factor z(y).
-2*(y - 1)**4
Let c(y) be the third derivative of y**6/480 + y**5/48 + y**4/32 - 3*y**3/8 - 2*y**2. Find u such that c(u) = 0.
-3, 1
Let x(n) = 10*n**2 + 2*n - 8. Let p(t) = 11*t**2 + 3*t - 9. Let s(y) = 4*p(y) - 3*x(y). Let m(d) = -d**2 - d + 1. Let j(z) = 8*m(z) + s(z). Factor j(f).
2*(f - 1)*(3*f + 2)
Let w(a) be the second derivative of -a**4/42 + 2*a**3/7 - 5*a**2/7 + 34*a. Factor w(j).
-2*(j - 5)*(j - 1)/7
Let v be ((-6)/(-12))/(2/16). Suppose -2*z**3 + z**2 + 5*z**3 - v*z**3 + 0*z**2 = 0. What is z?
0, 1
Let v(u) = u + 7. Let z be v(-5). Let t(a) be the second derivative of 4*a**2 + 0 + 13/6*a**4 + 1/15*a**6 - 4*a**3 - 3/5*a**5 - z*a. Factor t(b).
2*(b - 2)**2*(b - 1)**2
Let l(m) be the first derivative of m**4/14 + 8*m**3/21 + 5*m**2/7 + 4*m/7 + 12. Solve l(o) = 0 for o.
-2, -1
Factor -2/3 - 8/3*t - 5/6*t**2 + 25/6*t**3.
(t - 1)*(5*t + 2)**2/6
Let n(y) = -y**3 - y**2 + 1. Let i(g) = -18*g**3 + 2*g**2 + 2*g - 3. Let w(j) = i(j) + 3*n(j). Suppose w(l) = 0. Calculate l.
-1/3, 0, 2/7
Suppose k = 2*k. Let i(d) be the third derivative of 0*d - 2/735*d**7 + k*d**3 + 0 + 0*d**4 + 3*d**2 - 1/140*d**6 - 1/210*d**5. Factor i(r).
-2*r**2*(r + 1)*(2*r + 1)/7
Let x(h) be the first derivative of -2*h**3/9 - 2*h**2/3 - 2*h/3 + 7. Factor x(y).
-2*(y + 1)**2/3
Let b(a) be the first derivative of -a**7/21 + a**6/15 - 2*a + 2. Let l(i) be the first derivative of b(i). Factor l(z).
-2*z**4*(z - 1)
Suppose -43*a - 205 = -38*a. Let d = a + 83/2. Solve m**3 - 3/4*m**5 + 3/2*m**2 - 1/4*m - d - m**4 = 0 for m.
-1, 2/3, 1
Let -8/7*c**4 + 0 - 4/7*c**5 + 0*c + 0*c**2 - 4/7*c**3 = 0. What is c?
-1, 0
Suppose 5*c - c = 2*p - 14, 12 = -4*c. Factor u - 5*u**2 + u + p + 6*u**2.
(u + 1)**2
Let g be -2 - -7 - 2 - 1. Let q be 4/(2 + 2 + -2). What is t in -2*t**q + 0*t**4 + t**g + t**4 = 0?
-1, 0, 1
Determine r, given that -2/7*r**3 + 8/7*r**2 + 0 - 8/7*r = 0.
0, 2
Suppose -3*i = -0*i. Factor -2 + d**5 - 3*d**4 + d - 2*d**3 + i*d**5 + 4*d**2 - d**4 + 2*d**4.
(d - 2)*(d - 1)**2*(d + 1)**2
Let k(r) be the second derivative of r**4/12 - r**3/6 - r**2 + 16*r. Factor k(c).
(c - 2)*(c + 1)
Let c be 5/(225/(-44)) - -2. Let h = -2/9 + c. Determine a, given that -h*a - 2/5*a**2 - 2/5 = 0.
-1
Let a(h) be the first derivative of -h**8/112 + 3*h**7/70 - 3*h**6/40 + h**5/20 - h**2/2 - 9. Let p(b) be the second derivative of a(b). Factor p(q).
-3*q**2*(q - 1)**3
Let o(c) be the third derivative of c**6/660 - c**4/44 + 2*c**3/33 + 13*c**2. Factor o(w).
2*(w - 1)**2*(w + 2)/11
Let k(h) be the second derivative of 0 + 1/15*h**6 + 5*h - 1/3*h**3 - 1/2*h**4 + 1/10*h**5 + 2*h**2. Factor k(c).
2*(c - 1)**2*(c + 1)*(c + 2)
Find u, given that 3*u + 4*u**5 - 6*u**3 - u**5 - 12 + 12 = 0.
-1, 0, 1
Suppose 5*q = -25, -7*m = -2*m - 4*q - 40. Factor -4/3*y - m*y**2 - 2*y**4 - 13/3*y**3 - 1/3*y**5 + 0.
-y*(y + 1)**2*(y + 2)**2/3
Suppose -53 - 76 = 3*f. Let a = f + 303/7. Find l, given that -a*l**2 + 0 - 2/7*l = 0.
-1, 0
Let x(c) be the first derivative of -3/4*c**4 + 2*c**3 + 0*c - 3/2*c**2 - 2. Suppose x(n) = 0. What is n?
0, 1
Let i(g) be the third derivative of 1/72*g**5 + 13/144*g**4 - 4*g**2 - 1/6*g**3 + 0 + 0*g. Factor i(f).
(f + 3)*(5*f - 2)/6
Factor -12*v**2 + 0 - 8*v**3 - 4/3*v**4 - 16/3*v.
-4*v*(v + 1)**2*(v + 4)/3
Let p(y) be the third derivative of 11/300*y**6 + 0 - 1/175*y**7 - 1/10*y**5 - 2/15*y**3 + 2*y**2 + 3/20*y**4 + 0*y. Factor p(v).
-2*(v - 1)**3*(3*v - 2)/5
Let k be (-8)/(-30) - 76/(-228). Factor 1/5 + 3/5*i**2 + 1/5*i**3 + k*i.
(i + 1)**3/5
Let g = -13 - -19. Let n(m) be the second derivative of 0*m**2 + 2/21*m**4 - 3/35*m**5 + 0 - 1/147*m**7 - 1/21*m**3 - m + 4/105*m**g. Let n(i) = 0. What is i?
0, 1
Let v(s) = 3*s**2 + 23. Let m(a) = -a**2 - 11. Let d(l) = 13*m(l) + 6*v(l). Factor d(b).
5*(b - 1)*(b + 1)
Let u(n) be the third derivative of n**8/26880 - n**6/960 + n**5/240 + n**4/12 + 3*n**2. Let t(b) be the second derivative of u(b). Solve t(a) = 0.
-2, 1
Let a be ((-2)/5)/((-3)/15). Factor 4 + w - 4 - w**a.
-w*(w - 1)
Let s = 3 - 0. Let o(j) be the first derivative of 0*j + 2 + 1/12*j**s + 0*j**2 + 0*j**4 - 1/20*j**5. Factor o(k).
-k**2*(k - 1)*(k + 1)/4
Let b(v) = v**3 - 10*v**2 + 11*v - 16. Let s be b(9). Let 2/3*y**s + 4/3 + 2*y = 0. Calculate y.
-2, -1
Let a(h) be the second derivative of -h**6/30 + h**4/12 - 35*h. Factor a(m).
-m**2*(m - 1)*(m + 1)
Let d(q) be the third derivative of 49*q**8/24 - 182*q**7/15 + 371*q**6/12 - 662*q**5/15 + 116*q**4/3 - 64*q**3/3 - 17*q**2. Solve d(b) = 0 for b.
4/7, 1
Let i(t) be the second derivative of t**7/42 - t**5/20 - t. Factor i(m).
m**3*(m - 1)*(m + 1)
Factor -3*o + 0 + 3/7*o**3 + 18/7*o**2.
3*o*(o - 1)*(o + 7)/7
Let s(h) be the third derivative of -h**9/302400 - h**8/33600 + h**7/6300 - h**5/15 + 6*h**2. Let w(v) be the third derivative of s(v). Factor w(l).
-l*(l - 1)*(l + 4)/5
Let n(w) be the third derivative of 0 + 1/270*w**5 + 7*w**2 + 1/945*w**7 - 1/270*w**6 + 0*w**3 + 0*w**4 + 0*w. Find g, given that n(g) = 0.
0, 1
Let l(p) be the second derivative of -p**6/15 + 3*p**5/10 - p**4/2 + p**3/3 + 13*p. Factor l(i).
-2*i*(i - 1)**3
Let a(h) be the second derivative of -h**4/12 + h**3 - 9*h**2/2 + 4*h. Let b(n) = -n**2 + 6*n - 9. Let z(y) = 2*a(y) - 3*b(y). Factor z(u).
(u - 3)**2
Let o(s) be the second derivative of s**5/50 - 2*s**4/15 + s**3/3 - 2*s**2/5 + 5*s. Factor o(j).
2*(j - 2)*(j - 1)**2/5
Let y(q) be the third derivative of q**6/160 - 11*q**5/240 - q**4/24 + 26*q**2. Factor y(v).
v*(v - 4)*(3*v + 1)/4
Let k be (-6)/24 + (-238)/40. Let r = -29/5 - k. Let -r - 8/5*n**3 - 18/5*n**2 - 12/5*n = 0. What is n?
-1, -1/4
Let c(v) = -v**5 - 3*v**3 + 2*v**2 - 3*v - 3. Let u(k) = -k**4 - k**2 + k + 1. Let l(q) = -2*c(q) - 6*u(q). Factor l(j).
2*j**2*(j + 1)**3
Let t(l) be the third derivative of l**7/1470 - l**6/140 + 11*l**5/420 - l**4/28 + 41*l**2. Find y, given that t(y) = 0.
0, 1, 2, 3
Let q(b) = 6*b**4 + 9*b**3 + 12*b**2 + 3. Let c(x) = -7*x**4 - 9*x**3 - 13*x**2 + x - 4. Let r(y) = 3*c(y) + 4*q(y). Factor r(u).
3*u*(u + 1)**3
Determine n so that -12*n**4 - 4 - 4*n**5 - 12 + 317*n**2 + 4*n**3 - 289*n**2 = 0.
-2, -1, 1
Let u(j) be the second derivative of -1/54*j**4 - j**2 + 0 + 4*j + 2/9*j**3. Factor u(q).
-2*(q - 3)**2/9
Let b(i) = -20*i**3 - 96*i**2 + 84*i - 16. Let w(c) = -4*c**3 - 19*c**2 + 17*c - 3. Let s(p) = -3*b(p) + 16*w(p). Suppose s(y) = 0. Calculate y.
-5, 0, 1
Let d(w) be the second derivative of -w**5/20 - w**4/12 + w**3/6 + w**2/2 + 5*w. Solve d(h) = 0.
-1, 1
Let x(k) be the first derivative of -k**5/180 - k**4/24 - k**3/9 + 2*k**2 - 1. Let h(f) be the second derivative of x(f). Let h(i) = 0. Calculate i.
-2, -1
Let y be 2/(-5) - (-2)/5. Let n = y + 3. Find d such that d**3 - 4*d**3 - n*d**2 + d**3 - d = 0.
-1, -1/2, 0
Let q(h) be the third derivative of h**6/360 + h**5/60 - 3*h**2. Determine v so that q(v) = 0.
-3, 0
Let l(o) be the third derivative of 4394*o**7/45 + 5746*o**6/45 + 208*o**5/3 + 184*o**4/9 + 32*o**3/9 - 35*o**2. Factor l(r).
4*(7*r + 2)*(13*r + 2)**3/3
Let u = -938/6789 + 2/219. Let q = 15/124 - u. Suppose -1/4*k**3 + 1/4*k**2 + 1/4*k - q = 0. Calculate k.
-1, 1
Factor -2/5*g**2 + 6/5*g + 8/5.
-2*(g - 4)*(g + 1)/5
Suppose -u = 5*g - 74, -12 = -