Let a(i) = i**5 - 13*i**4 + 23*i**3 - 28*i**2 + 17. Let z(n) = 6*a(n) - 34*m(n). Factor z(y).
2*y**2*(y - 1)**2*(3*y + 1)
Let h = -16 + 19. Suppose -h*j = -6 - 12. Determine i so that -2*i**2 + j - i**2 + 0*i**2 + 3*i = 0.
-1, 2
Let z = 635 - 635. Let t(f) be the third derivative of f**2 + 0 + 1/224*f**8 + 0*f + 1/16*f**4 + 0*f**3 + z*f**7 + 0*f**5 - 1/40*f**6. Factor t(y).
3*y*(y - 1)**2*(y + 1)**2/2
Let k(t) = t**3 + 22*t**2 + 83*t - 94. Let r(c) = c**2 + c + 2. Let p(n) = k(n) - 3*r(n). Factor p(z).
(z - 1)*(z + 10)**2
Let b = -10 - -16. Factor 4*l**3 + b*l - 21*l**2 + 21*l**3 - 15*l**4 - 3*l**3 + 5*l**3 + 3*l**5.
3*l*(l - 2)*(l - 1)**3
Suppose -2*r = 5*f + 52, 17 = -f + 4*r - 11. Let n be ((-2)/(-16))/((6/(-1))/f). What is t in -3/4*t**2 + 3/4*t + 1/4*t**3 - n = 0?
1
Let x(d) = -51*d**3 + 279*d**2 - 291*d + 21. Let z(f) = 5*f**3 - 28*f**2 + 29*f - 2. Let u(h) = 2*x(h) + 21*z(h). Factor u(l).
3*l*(l - 9)*(l - 1)
Let o(b) = 6*b**3 - 31*b - 25. Let u(h) = -h**3 + 5*h + 4. Let g = 50 + -89. Let w(v) = g*u(v) - 6*o(v). Factor w(f).
3*(f - 2)*(f + 1)**2
Let q = -1944 + 25274/13. Let d be 5*-2*(-2)/10. What is k in -2/13*k**3 - q*k + 0 - 4/13*k**d = 0?
-1, 0
Let i(d) = -d**3 + 9*d**2 - 13*d - 4. Let m be i(7). Let g(v) be the first derivative of -3/5*v**5 + m*v**2 + 0*v**3 - 2 - 3/2*v**4 + 3*v. Factor g(z).
-3*(z - 1)*(z + 1)**3
Solve -78*x - 1/2*x**2 + 5*x**3 + 144 - 1/2*x**4 = 0 for x.
-4, 3, 8
Let r(g) be the first derivative of -7*g**3/8 - 255*g**2/8 - 18*g - 13. Factor r(u).
-3*(u + 24)*(7*u + 2)/8
Let r be (26/(-6))/((-284)/20). Let i = r - -2/71. Factor -1/3*g**2 - 1/3*g**3 + 1/3*g**4 + 0 + i*g**5 + 0*g.
g**2*(g - 1)*(g + 1)**2/3
Let b(q) be the first derivative of q**5/10 - 113*q**4/4 + 2128*q**3 + 113*q**2/2 - 12769*q/2 + 659. Factor b(x).
(x - 113)**2*(x - 1)*(x + 1)/2
Suppose -2*w + 10 = -2*b, -w - 2*b + b - 5 = 0. Let l(d) be the third derivative of w + 0*d**3 + 0*d + 0*d**4 - 1/660*d**6 + 0*d**5 - 3*d**2. Factor l(u).
-2*u**3/11
Let r(o) be the first derivative of -o**4 + 292*o**3/3 - 2736*o**2 + 5184*o + 309. Let r(j) = 0. Calculate j.
1, 36
Factor 39/7*x**2 - 6/7 + 33/7*x.
3*(x + 1)*(13*x - 2)/7
Let m be 12/50*655/262. Determine y so that -1/5*y**3 - 3/5 + m*y**2 + 1/5*y = 0.
-1, 1, 3
Let c(j) be the first derivative of j**4/3 - 40*j**3/9 - 16*j**2 + 96. Factor c(h).
4*h*(h - 12)*(h + 2)/3
Let z(r) be the first derivative of r**4/14 + 6*r**3/7 + 23*r**2/7 + 30*r/7 - 60. Factor z(m).
2*(m + 1)*(m + 3)*(m + 5)/7
Factor -64/5*d + 22/5*d**2 - 2/5*d**3 + 56/5.
-2*(d - 7)*(d - 2)**2/5
Let n(y) = 4*y. Let w be n(1). Let q = w - 1. Factor -6*x**2 + 1 + 3*x**q - 7*x**3 - 4*x + x**4 + 12*x**2.
(x - 1)**4
Let u be ((-26)/10 - 2/(-10)) + 2 + 1. Factor 42/5*x**3 - 18/5*x**4 - 48/5*x**2 + u*x**5 + 27/5*x - 6/5.
3*(x - 2)*(x - 1)**4/5
Suppose 8/9 + 94/9*g**2 - 20/9*g**5 - 2*g**4 + 16/3*g + 56/9*g**3 = 0. What is g?
-1, -1/2, -2/5, 2
Let a(b) be the third derivative of -b**8/168 + 17*b**7/105 + 19*b**6/30 + b**5/15 - 37*b**4/12 - 19*b**3/3 + 12*b**2 + 2. Let a(k) = 0. Calculate k.
-1, 1, 19
Let c(w) be the third derivative of 1/360*w**6 + 0 + 0*w**3 + 0*w**4 + 0*w**5 + 0*w + 3*w**2. Factor c(n).
n**3/3
Let g(n) be the third derivative of -n**7/70 - n**6/10 - n**5/10 + n**4/2 + 3*n**3/2 + 152*n**2. Find h such that g(h) = 0.
-3, -1, 1
Let p(a) be the second derivative of -4*a + 1/21*a**3 + 0 - 1/28*a**4 + 1/140*a**5 + 0*a**2. Factor p(g).
g*(g - 2)*(g - 1)/7
Let l(p) be the first derivative of p**6/15 - p**5/5 + 2*p**3/3 - p**2 + 17*p - 15. Let y(z) be the first derivative of l(z). Let y(r) = 0. What is r?
-1, 1
Suppose -24*d + 21*d = -15. What is f in d*f**2 + 4*f - 197*f**4 - 8 + 7*f**2 - 4*f**3 + 193*f**4 = 0?
-2, -1, 1
Let z(d) be the second derivative of -d**5/110 - 5*d**4/22 + d**3 + 77*d**2 + 43*d + 2. Suppose z(t) = 0. What is t?
-11, 7
Let a = -11 - -4. Let u = -2 - a. Determine c so that -3*c + 4*c**2 - u*c + 0*c**2 = 0.
0, 2
Let x(o) be the first derivative of 4*o**5/5 + 16*o**4 + 256*o**3/3 - 87. Factor x(z).
4*z**2*(z + 8)**2
Let p(q) be the third derivative of -q**7/630 - q**6/180 - q**4/4 + 3*q**2. Let o(v) be the second derivative of p(v). Factor o(u).
-4*u*(u + 1)
Suppose 31 = t + 25. Let f(d) be the third derivative of 0*d + 0*d**5 + 1/336*d**8 - 1/120*d**t + 0*d**4 + 0*d**3 + 0 - 4*d**2 + 0*d**7. Factor f(y).
y**3*(y - 1)*(y + 1)
Let b = 220/27 - 8. Let d(z) be the first derivative of 0*z - b*z**3 - 1/9*z**2 + 1 - 1/18*z**4. Find f such that d(f) = 0.
-1, 0
Let m(s) = -23*s**3 - 12*s**2 + 11*s. Let a(k) = 3*k**3 + 5*k**3 - 4*k - 3*k**2 + 12*k**2 - 5*k**2. Let o(p) = -17*a(p) - 6*m(p). Let o(f) = 0. Calculate f.
-1, 0
Let z(v) = 8*v**4 - v**3 + 7*v**2 + 7*v. Let w(c) be the second derivative of -c**6/30 - c**4/12 - c**3/6 + 8*c. Let s(j) = 28*w(j) + 4*z(j). Factor s(g).
4*g**3*(g - 1)
Let v = -13775 - -96465/7. What is m in -4*m**2 + v*m + 6/7*m**3 - 16/7 = 0?
2/3, 2
Let u(q) = -13*q - 17. Let y be u(9). Let l = y + 136. Factor 8/13*x**l - 10/13*x - 2/13*x**3 + 4/13.
-2*(x - 2)*(x - 1)**2/13
Let i be 102/20*400/(-5280) - (-3)/4. Solve -i*u + 2/11*u**2 + 2/11 = 0 for u.
1
Let x(v) be the first derivative of 1/2*v**4 - 41 - 8/3*v**3 + 3*v**2 + 0*v. Factor x(n).
2*n*(n - 3)*(n - 1)
Factor 44 + 24 + 4*f**2 - 8*f**2 + 200*f - 86 - 178.
-4*(f - 49)*(f - 1)
Let q(h) be the third derivative of -h**6/60 - h**5/2 - 11*h**4/3 - 3*h**2 - 41. Suppose q(o) = 0. What is o?
-11, -4, 0
Suppose -3*n = 2*n + n. Let r(i) be the third derivative of 0*i + i**2 + n + 1/20*i**5 + 1/6*i**3 + 1/120*i**6 + 1/8*i**4. Factor r(o).
(o + 1)**3
Let m(n) = -4*n. Let r be m(1). Let c be 69/12 + 3/r. Factor 0*g**2 - 9*g + 1 - 6*g**2 + c.
-3*(g + 2)*(2*g - 1)
Let p(h) be the third derivative of 0*h + 0*h**3 + 1/30*h**5 + 0 + 1/504*h**8 + 1/180*h**6 - 1/18*h**4 - 9*h**2 - 1/105*h**7. Suppose p(w) = 0. What is w?
-1, 0, 1, 2
Let d(p) be the third derivative of 2*p + 0*p**3 - 16*p**2 + 0 + 1/6*p**4 - 17/30*p**5. Let d(u) = 0. Calculate u.
0, 2/17
Suppose 43*i + 53 = 139. Factor -4/11*o**4 - 6/11*o**3 - 1/11*o**5 - 1/11*o + 0 - 4/11*o**i.
-o*(o + 1)**4/11
Let z(a) be the second derivative of -a**10/75600 + a**9/37800 + a**8/16800 - a**7/6300 + a**4/12 - 15*a. Let r(n) be the third derivative of z(n). Factor r(w).
-2*w**2*(w - 1)**2*(w + 1)/5
Let r(l) be the second derivative of -l**6/30 - l**5/80 + 3*l**4/8 - 36*l + 1. Find z, given that r(z) = 0.
-9/4, 0, 2
Let i = -738 + 743. Let c(l) be the third derivative of 0 + 0*l**3 + 1/45*l**i + 1/90*l**6 + 0*l - 6*l**2 + 0*l**4. Find b such that c(b) = 0.
-1, 0
Let 8/7*h**3 - 18/7*h**2 - 6/7*h + 20/7 = 0. Calculate h.
-1, 5/4, 2
Let f be 240/(-216)*3/(-15). Let 8/9 + 4/9*v**3 - f*v**4 - 16/9*v + 2/3*v**2 = 0. What is v?
-2, 1, 2
Let j = -7/44 - -197/132. Let s(z) be the first derivative of -12/5*z**5 + j*z**3 + 0*z**2 - 2*z**4 + 3 + 0*z. Suppose s(o) = 0. Calculate o.
-1, 0, 1/3
Let k(y) be the second derivative of -1/40*y**5 + 0 + 1/12*y**3 + 0*y**2 + 1/180*y**6 - 15*y - 1/72*y**4. Factor k(g).
g*(g - 3)*(g - 1)*(g + 1)/6
Let h be 2 - (246/36 - 5). Let j(z) be the second derivative of -h*z**4 - 2/3*z**3 + 0 + 3*z**2 + 5*z. Find d such that j(d) = 0.
-3, 1
Find g, given that 44 + 45 - 65 - g**2 + 28*g + g**2 - 4*g**3 = 0.
-2, -1, 3
Let i(s) = 4*s + 12. Let k be i(-4). Let h = -4 - k. Factor 0 + h*p + 1/4*p**2 - 1/4*p**3.
-p**2*(p - 1)/4
Let q(h) = 14*h**2 - 50*h + 100. Let x(c) = -c**2 - 3*c - 4. Let g(u) = -u**2 - 2*u - 3. Let i(a) = -4*g(a) + 3*x(a). Let s(l) = 10*i(l) - q(l). Factor s(w).
-4*(w - 5)**2
Let g = 10/179 - -159/358. Factor 2/5*x + g - 1/10*x**2.
-(x - 5)*(x + 1)/10
Let s = -43 - -60. Let s + 2*d**2 + 2*d**2 - 8 - 24*d + 23 = 0. Calculate d.
2, 4
Let a(u) be the first derivative of 7*u**6/24 - u**5/6 - 35*u**4/6 + 20*u**3/3 + 2*u**2 - 16. Let c(z) be the second derivative of a(z). Solve c(v) = 0.
-2, 2/7, 2
Factor 207*l**2 - 567/2*l - 1/6*l**5 + 29/6*l**4 + 243/2 - 149/3*l**3.
-(l - 9)**3*(l - 1)**2/6
Let a(z) be the third derivative of 0 - 3/50*z**6 + 17/50*z**5 + z**3 + 0*z + 9*z**2 - 4/5*z**4. Factor a(q).
-6*(q - 1)**2*(6*q - 5)/5
Suppose 23*g = 26*g. Let k be -4 - g - 114/(-24). Factor -k*i + 0 - 3/4*i**3 - 3/2*i**2.
-3*i*(i + 1)**2/4
Let h be (-5)/6*88/11110. Let b = 616/1515 + h. Find q such that 6/5