Let v(u) be the third derivative of 5/77*u**7 - 3/11*u**4 + 0 - 30*u**2 + 23/55*u**5 + 0*u - 3/11*u**6 + 1/11*u**3. Factor v(a).
6*(a - 1)**2*(5*a - 1)**2/11
Let x(g) be the first derivative of -g**5/30 - 11*g**4/24 - 2*g**3 - 4*g**2/3 + 32*g/3 - 142. Factor x(m).
-(m - 1)*(m + 4)**3/6
Determine k so that 47/3*k**3 - 140/9*k**4 + 0*k - 2*k**2 - 196/3*k**5 + 0 = 0.
-2/3, 0, 3/14
What is r in -5*r**2 + 20/3 - 25/3*r - 5/3*r**4 + 25/3*r**3 = 0?
-1, 1, 4
Factor 28*t - 503*t**2 + 467*t**2 + 4*t**4 - 8*t**3 + 44*t.
4*t*(t - 3)*(t - 2)*(t + 3)
Let s(l) be the second derivative of l**6/10 + l**5/2 - 11*l**4/9 - 44*l**3/9 - 16*l**2/3 + 3*l + 1. Find t, given that s(t) = 0.
-4, -2/3, 2
Let x(r) be the second derivative of r**9/37800 + r**8/5600 + r**7/2100 + r**6/1800 + 3*r**4/4 + 12*r. Let g(j) be the third derivative of x(j). Factor g(o).
2*o*(o + 1)**3/5
Let h(j) = -j**2 - 5*j + 4. Let o be h(-5). Suppose 4*z - 3*i - o = 0, -i + 12 = z + z. Factor 5*w**2 - 5*w**z + 2*w**3 + 14 - 2*w - 14.
-w*(w - 1)*(w + 1)*(5*w - 2)
Let v(p) be the second derivative of -p**5/120 - p**4/12 - p**3/4 + 11*p**2/2 + 26*p. Let d(l) be the first derivative of v(l). Find t, given that d(t) = 0.
-3, -1
Let k(b) = 9*b**4 + 297*b**3 + 291*b**2 - 309*b - 264. Let d(j) = -8*j**4 - 298*j**3 - 292*j**2 + 308*j + 270. Let n(r) = -6*d(r) - 5*k(r). Factor n(l).
3*(l - 1)*(l + 1)**2*(l + 100)
Let j(w) be the second derivative of -w**5/20 + w**4/6 + w**3/2 + 7*w. Factor j(f).
-f*(f - 3)*(f + 1)
Let y(z) be the second derivative of -z**5/150 - z**4/45 - 85*z - 1. Factor y(g).
-2*g**2*(g + 2)/15
Let s = -180 - -192. Let b be 5/s - (-5)/(-30). Factor b*z**2 + 1/4*z**3 + 0 + 0*z.
z**2*(z + 1)/4
Let c(z) be the first derivative of z**7/98 + z**6/280 - z**5/35 + 3*z**2 + 23. Let k(h) be the second derivative of c(h). Factor k(q).
3*q**2*(q + 1)*(5*q - 4)/7
Let j = 1043 - 1041. Suppose -6/17*k**j + 16/17*k - 8/17 = 0. Calculate k.
2/3, 2
Let i(p) be the second derivative of p**8/10080 + p**7/1260 - p**4/6 - 17*p. Let b(s) be the third derivative of i(s). Solve b(k) = 0.
-3, 0
Find q such that 2250*q + 5*q**5 + 43 + 592*q**2 - 335*q**3 + 5*q**4 - 63 - 117*q**2 + 20 = 0.
-9, -2, 0, 5
Let o be ((-374)/55 + 8)*(-9)/(-6). Factor -9/5*n**4 + 9/5*n + 6/5 - o*n**2 - 21/5*n**3.
-3*(n + 1)**3*(3*n - 2)/5
Solve -1/6*m**2 - 9075/2 + 55*m = 0 for m.
165
Let u = -86 - -199. Let z = u - 110. Factor 0*x + 0*x**2 + 0 + 2/7*x**z.
2*x**3/7
Let j(w) be the second derivative of -w**4/4 - 4*w**3 + 27*w**2/2 - 2*w + 1. Solve j(c) = 0 for c.
-9, 1
Factor -49/3 - 1/3*b**2 + 50/3*b.
-(b - 49)*(b - 1)/3
Let c be 1/(-2*(-2)/(-12)). Let q be c - 2*(-7)/2. Solve 3*m**2 - 12*m**4 + 6*m**q + 3*m**2 + 21*m**5 - 21*m**3 = 0.
-1, 0, 2/7, 1
Let k be ((-12)/9)/(-2*21/9). Suppose -5 = -4*q + 3. Determine i, given that -k*i**3 - 2/7*i + 4/7*i**q + 0 = 0.
0, 1
Let d(c) = -2*c**2 + c - 1. Let r(l) = l**2 + 5*l - 12. Let p(w) = -12*d(w) + 4*r(w). Let p(n) = 0. Calculate n.
-9/7, 1
Let k(q) be the third derivative of -7/330*q**5 - 11*q**2 - 1/132*q**6 + 1/66*q**4 + 0 + 0*q + 4/1155*q**7 + 0*q**3. What is o in k(o) = 0?
-1, 0, 1/4, 2
Let z(a) be the second derivative of -a**7/420 + a**6/60 - a**5/20 + a**4/12 + 7*a**3/6 - 12*a. Let o(n) be the second derivative of z(n). Factor o(u).
-2*(u - 1)**3
Let z(c) be the first derivative of 2/9*c**3 + 0*c - 35 + 7/3*c**2. Let z(h) = 0. Calculate h.
-7, 0
Let p be ((-8)/(-14))/(-5 - 742/(-98)). Solve 14/9 + p*k**3 + 2*k**2 + 10/3*k = 0 for k.
-7, -1
Let b(j) = -j**2 - 3*j. Suppose -12 = -o + 2*y, 4*o - 13 = -2*y + 5. Let t(z) = -8*z**2 - 24*z + 1. Let q(g) = o*t(g) - 51*b(g). Factor q(m).
3*(m + 1)*(m + 2)
Let y(w) be the first derivative of -w**7/70 - w**6/60 + w**5/60 + w**2 - 1. Let a(h) be the second derivative of y(h). Suppose a(m) = 0. What is m?
-1, 0, 1/3
Let h(a) = 1. Let p(l) be the second derivative of 20*l**4/3 - 20*l**3/3 + l**2/2 - 11*l. Let s(b) = 4*h(b) + p(b). Factor s(x).
5*(4*x - 1)**2
Suppose 3*a = -4*m + 169, -5*a = -5*m + 289 - 34. Suppose m*x = 33*x. Determine l, given that -5/3*l**4 + 5/3*l**2 + x*l**3 + 0*l + 0 = 0.
-1, 0, 1
Let z(b) = -2*b**2 - 244*b. Let v(w) = w**2 + 2*w. Let h(a) = 6*v(a) + z(a). Factor h(d).
4*d*(d - 58)
Let k(w) be the first derivative of 1/18*w**4 - 2/27*w**3 + 0*w**2 + 0*w + 15. Factor k(x).
2*x**2*(x - 1)/9
Let j(p) = -16*p**2 + 20*p. Let r(c) = c**3 + 2*c**2 - 2*c. Let l(b) = -2*j(b) - 4*r(b). Find a such that l(a) = 0.
0, 2, 4
Let j = 9231 - 36921/4. Find p, given that j*p**3 + 9/4*p**2 - 3/4*p**4 + 3/2 - 15/4*p = 0.
-2, 1
Factor -c**5 + 100*c**2 + 994*c - 6*c**4 + 19*c**3 - 4*c**3 - 994*c.
-c**2*(c - 4)*(c + 5)**2
Let h be -1 - (-931)/(-95) - -12. Suppose 4/5*v - h + 2/5*v**2 = 0. Calculate v.
-3, 1
Let p(c) be the first derivative of 4*c**3/3 + 22*c**2 + 40*c - 339. Factor p(z).
4*(z + 1)*(z + 10)
Factor -15/8 - 1/8*f**2 - 2*f.
-(f + 1)*(f + 15)/8
Let o(q) be the first derivative of q**6/120 - q**5/40 - q**4/4 + 10*q**3/3 - 20. Let l(p) be the third derivative of o(p). Let l(n) = 0. What is n?
-1, 2
Let p(b) be the third derivative of b**6/60 - b**4/4 - 2*b**3/3 + 540*b**2. Solve p(k) = 0 for k.
-1, 2
Let r(i) be the third derivative of -i**5/20 - 55*i**4/8 - 53*i**3 + 74*i**2. Determine q, given that r(q) = 0.
-53, -2
Let v = 244/3 + -730/9. Factor -4/9*b**2 - 2/9*b + v*b**4 - 2/9*b**5 + 4/9*b**3 + 2/9.
-2*(b - 1)**3*(b + 1)**2/9
Suppose 61*q + 40 = 57*q + 12*h, 6 = -q + 2*h. What is j in q*j**2 + 0 - 2/5*j**3 + 12/5*j = 0?
-1, 0, 6
Let h(m) = 2*m**3 + 12*m**2 + 19*m + 4. Let u(w) = w**3 + 6*w**2 + 9*w + 2. Let a(y) = 3*h(y) - 5*u(y). Let t(g) be the first derivative of a(g). Factor t(r).
3*(r + 2)**2
Factor 3*p**2 + 15 + 10 - 40 - 12*p.
3*(p - 5)*(p + 1)
Let g be (-8)/(-76) - (-279)/57. Let q(i) be the first derivative of -3/2*i**2 - 9/4*i**4 + 7 + 0*i + 3/5*i**g + 3*i**3. Factor q(u).
3*u*(u - 1)**3
Let o be ((-56)/98 - 32/(-7))/2. Let 95/4*q**3 + 13*q - 57/2*q**2 - o - 25/4*q**4 = 0. What is q?
2/5, 1, 2
Let s = -3080 - -3080. What is u in 3/5*u**2 + 12/5*u**3 + s - 12/5*u - 3/5*u**4 = 0?
-1, 0, 1, 4
Determine d, given that -7*d**2 + 9/2*d**4 + 4 + d**5 + 7/2*d**3 - 6*d = 0.
-2, 1/2, 1
Let t = 86 - 112. Let h be (-18)/27*54/t. Let 32/13*c + h*c**3 + 8/13 + 42/13*c**2 = 0. What is c?
-1, -2/3
Solve -20*o**3 + 30*o**3 - 2890 + 233*o - 1338*o - 15*o**3 + 160*o**2 = 0 for o.
-2, 17
Let g(i) be the first derivative of -3*i**3 + 63*i**2/20 + i - 78. Determine v so that g(v) = 0.
-2/15, 5/6
Let n(s) = 3*s**4 + 2*s**3 - 6*s - 1. Let b(d) = -7*d**4 - 4*d**3 + 14*d + 2. Let p(l) = -2*b(l) - 5*n(l). Factor p(c).
-(c - 1)*(c + 1)**3
Factor 159 - 4*g**2 + 17 + 180*g - 4*g**2 + 12*g**2.
4*(g + 1)*(g + 44)
Let p(f) be the third derivative of f**6/180 - f**5/10 - 7*f**4/12 - 11*f**3/9 - 37*f**2 + f. Suppose p(d) = 0. Calculate d.
-1, 11
Let w(y) = 9*y - 33*y + 16*y + 9*y - 2. Let z(h) = -h**2 - 8*h - 1. Let v(i) = 2*w(i) + z(i). Let v(q) = 0. Calculate q.
-5, -1
Let c(g) be the second derivative of 0 + 3*g + 3/8*g**2 + 5/48*g**4 - 3/80*g**5 + 11/24*g**3. Factor c(r).
-(r - 3)*(r + 1)*(3*r + 1)/4
Determine c so that -104/7*c**2 - 64 - 440/7*c + 2/7*c**3 = 0.
-2, 56
Let q(h) be the second derivative of h**8/84 - 8*h**7/105 + h**6/5 - 4*h**5/15 + h**4/6 - 7*h**2/2 - 3*h. Let z(c) be the first derivative of q(c). Factor z(s).
4*s*(s - 1)**4
Let y(j) be the third derivative of 1/15*j**6 + 0 + 2/15*j**5 - 13*j**2 - 1/12*j**3 + 0*j - 1/48*j**4. Solve y(k) = 0 for k.
-1, -1/4, 1/4
Let o be 6/(-45) + (-48)/(-10). Let -8/15 - 118/15*c**2 - 56/15*c - o*c**3 = 0. What is c?
-1, -2/5, -2/7
Let w = -227 + 232. Let y(x) be the second derivative of 0*x**2 + 1/70*x**w + 5*x + 0 + 1/21*x**3 - 1/21*x**4. Suppose y(v) = 0. What is v?
0, 1
Let k be -1 - -9 - (-5)/((-50)/30). Let l(f) be the third derivative of -1/180*f**k + 0 - 1/6*f**3 + 0*f + 2*f**2 - 1/18*f**4. Let l(c) = 0. What is c?
-3, -1
Let y be (-40)/(-14) + -3*4/(-84). Factor 77*q - 8*q**y + 0*q**2 + 0 - 85*q - 12*q**2 - 2*q**4 - 2.
-2*(q + 1)**4
Suppose 13*q - 29 = -4*c + 10*q, 5*c + q = 17. Factor -56/15*h - 4/5*h**3 + 8/15 + 10/3*h**c.
-2*(h - 2)**2*(6*h - 1)/15
Let n(j) be the third derivative of j**7/70 + j**6/15 - 2*j**5/45 - 4*j**4/9 + 8*j**3/9 + 48*j**2. Factor n(z).
(z + 2)**2*(3*z - 2)**2/3
Let h =