Let c(n) be the second derivative of 3*n**5/4 + 5*n**4/12 - 20*n**3/3 + 10*n**2 - 105*n. Factor c(l).
5*(l - 1)*(l + 2)*(3*l - 2)
Let i(c) be the third derivative of -1/20*c**6 + 0*c + 31*c**2 - 17/20*c**5 - c**4 + 0*c**3 + 0. What is k in i(k) = 0?
-8, -1/2, 0
Factor -368*i**2 - i**3 + 2*i**3 - 14*i + 381*i**2.
i*(i - 1)*(i + 14)
Let p(c) be the first derivative of -c**4/28 - 19*c**3/21 - 115*c**2/14 - 225*c/7 + 1040. Solve p(f) = 0 for f.
-9, -5
Let v = 2187/29525 + 7/1181. Determine x, given that -2/25*x + 2/25 + v*x**4 - 2/25*x**5 + 4/25*x**3 - 4/25*x**2 = 0.
-1, 1
Let m = -70 - -70. Let p(r) = 3*r**2 - 21*r + 2. Let c be p(7). Find u, given that -4/7*u - 2/7*u**c + m = 0.
-2, 0
Let z(r) be the second derivative of 3*r**3 + 0 - 2*r**4 - 2*r**2 + 2*r + 1/2*r**5. Suppose z(w) = 0. What is w?
2/5, 1
Let z(k) be the third derivative of -k**5/240 + 19*k**4/96 - 17*k**3/12 - 31*k**2 + 2. Suppose z(j) = 0. What is j?
2, 17
Suppose 6*w - 2958 = -2940. Factor 3*s**2 + 1/3*s**w + 0*s + 0.
s**2*(s + 9)/3
Let h(b) be the first derivative of -4/5*b**5 + 0*b**2 + 0*b - 5/3*b**6 + 4/3*b**3 + 5/2*b**4 + 10. What is r in h(r) = 0?
-1, -2/5, 0, 1
Find z such that 128/3 - 352/3*z + 28/3*z**4 - 146/3*z**3 + 344/3*z**2 - 2/3*z**5 = 0.
1, 4
Let s = 25/183 + -1/305. Let l(j) be the second derivative of 2/3*j**4 + 0*j**5 + 0 + 0*j**3 - s*j**6 - 2*j**2 - 10*j. Suppose l(d) = 0. Calculate d.
-1, 1
Let z(v) = -72*v - 212. Let l be z(-3). Let 2/3*k + 0 + 4/9*k**l - 2/3*k**3 - 4/9*k**2 = 0. What is k?
-1, 0, 1, 3/2
Let x = 17118/5 + -3423. Suppose 3 = l - 0. Factor x*u - 6/5*u**2 + 3/5*u**l + 0.
3*u*(u - 1)**2/5
Let d be (6/(-14))/(28/((-7448)/171)). Solve 10/3*t**2 + 16/3*t + d*t**3 + 8/3 = 0.
-2, -1
Factor 7/8*q**4 - 1/8*q**2 + 3/4*q**3 + 0 + 0*q.
q**2*(q + 1)*(7*q - 1)/8
Factor -15/8*m**3 + 71/8*m**2 - 1/8*m**4 + 19/4 - 93/8*m.
-(m - 2)*(m - 1)**2*(m + 19)/8
Suppose -5*o + 10 = p, -2 - 6 = -o + p. Suppose 21 = o*l + 3*f, 4*f - 26 = 4*l - 7*l. Factor -2*c + 1/4*c**l + 4.
(c - 4)**2/4
Let g be 2*(-1)/4*-2 - -2. Suppose -g*x + 0 = -0. Factor x*q + 1/2*q**3 + 0 + 1/2*q**2.
q**2*(q + 1)/2
Let i be (1 + 4/(-6))*0. Factor 4/3*a**4 - 14/3*a**5 + 0*a**3 + 0*a + i*a**2 + 0.
-2*a**4*(7*a - 2)/3
Let h = -130 + 135. Suppose h*r - 17 = -k, -k + 3 = 1. Find f such that 16/9*f - 2*f**r + 2/3*f**2 - 8/9 = 0.
-1, 2/3
Let c(u) = -u**2 + 4*u - 38. Let i(d) = 2*d - 20. Let o(w) = 2*c(w) - 5*i(w). Factor o(k).
-2*(k - 3)*(k + 4)
Solve 9/2*y + 3/2*y**2 - 6 = 0 for y.
-4, 1
Let g(i) = -i**4 - 2*i**3 + 4*i**2 + 5*i + 5. Let b(t) = -t**4 - 2*t**3 + 5*t**2 + 6*t + 6. Let v(f) = 5*b(f) - 6*g(f). Find l, given that v(l) = 0.
-1, 0
Find z such that 9/4 - 1/2*z**4 + 9/4*z**3 - 7/4*z**2 - 9/4*z = 0.
-1, 1, 3/2, 3
Let q(p) be the third derivative of -41*p**2 + 0*p**4 + 0*p**3 + 1/105*p**7 + 1/10*p**5 + 0*p + 0 - 1/15*p**6. Factor q(l).
2*l**2*(l - 3)*(l - 1)
Let v(y) be the third derivative of -y**6/960 - y**5/60 - 3*y**4/64 + 3*y**3/8 - 50*y**2 - y. Let v(t) = 0. What is t?
-6, -3, 1
Let n(g) = -4*g**3 + 5*g - 5. Let z(r) = -4*r + 7 - r + 6*r**3 - 2*r. Let w(o) = 7*n(o) + 5*z(o). Suppose w(f) = 0. Calculate f.
0
Suppose -b + 9 = -4*b. Let h be (-16)/4 - b - 10. Let a(o) = -8*o**4 - 4*o + 4. Let m(y) = -23*y**4 + y**2 - 11*y + 11. Let k(c) = h*a(c) + 4*m(c). Factor k(j).
-4*j**2*(j - 1)*(j + 1)
Let n = 106 + -115. Let a be 7/(-39) - n/27. Factor 2/13*v**2 + 0*v + 0 + 2/13*v**5 - a*v**3 - 2/13*v**4.
2*v**2*(v - 1)**2*(v + 1)/13
Factor -56307/7*m**2 - 27/7 - 2466/7*m.
-3*(137*m + 3)**2/7
Let w be 12/66 + (-97)/594. Let f(u) be the second derivative of w*u**4 + 12*u + 0 - 1/9*u**2 + 1/6*u**3 - 1/20*u**5. Factor f(c).
-(c - 1)*(c + 1)*(9*c - 2)/9
Suppose -3*d = -4*b + 14, 3*b - 8*b + 6 = 2*d. Suppose -2*j - 18 = -5*j. Factor -2*w - j - 2*w**b + 15 + 6*w - 11.
-2*(w - 1)**2
Solve -2/13*h - 2/13*h**4 - 6/13*h**3 - 6/13*h**2 + 0 = 0.
-1, 0
Let k(y) be the second derivative of -y**6/135 + y**5/15 - y**4/6 + 4*y**3/27 + 86*y - 2. Suppose k(f) = 0. What is f?
0, 1, 4
Let l(i) = 4*i**5 + 16*i**4 - 88*i**2 - 76*i + 4. Let g(y) = y**4 + y**3 + y**2 + y - 1. Let p(t) = 4*g(t) + l(t). Factor p(w).
4*w*(w - 2)*(w + 1)*(w + 3)**2
Suppose -15 = 53*a - 50*a. Let n be 39/(-24) - (a + 3). Find y such that -n*y**2 + 3/8 + 0*y = 0.
-1, 1
Factor 28*x - 88*x + 25*x**3 + 2065*x**2 + 20 - 2050*x**2.
5*(x - 1)*(x + 2)*(5*x - 2)
Let t(j) = j**3 + 15*j**2 + 54*j + 112. Let h be t(-11). Factor 4/5 + 1/5*f**h - 4/5*f.
(f - 2)**2/5
Suppose -12*h + 28 = 2*h. Let k(i) be the third derivative of 1/20*i**5 - h*i**3 + 0*i**4 + i**2 + 0 + 0*i. Determine p so that k(p) = 0.
-2, 2
Let u(j) = 0 + 2 - j**2 - 8*j + j**2 + 4*j**2. Let n(r) = -r**3 - 7*r**2 + 17*r - 4. Let m = -14 - -9. Let f(d) = m*u(d) - 2*n(d). Factor f(v).
2*(v - 1)**3
Let k be 2/7 - 32/112. Suppose k = -30*f + 18*f + 24. Factor 0 - 2/5*c**5 + 6/5*c**3 - f*c**2 + 2/5*c**4 + 4/5*c.
-2*c*(c - 1)**3*(c + 2)/5
Suppose -5*j + 0*k + 2*k = -54, 5*j + 5*k = 75. Let b be (8/6)/(8/j). Solve -3*t**2 + 7*t**2 - 2*t**b = 0.
0
Factor 1/2*x**3 - 15/2*x**2 - 33/2*x - 17/2.
(x - 17)*(x + 1)**2/2
Suppose 150*a = 1021*a - 2613. Solve -2/7*c - 2/7*c**a + 0 - 4/7*c**2 = 0 for c.
-1, 0
Let l(o) be the third derivative of -o**6/60 - 19*o**5/2 - 9025*o**4/4 - 857375*o**3/3 - o**2 - 89. Let l(u) = 0. Calculate u.
-95
Let p(v) = -v. Let z(o) = 5*o - 7. Let q(d) = 4*p(d) + z(d). Let k be q(7). Factor k + 0*f**2 + 0*f**4 + 2/13*f**5 + 2/13*f - 4/13*f**3.
2*f*(f - 1)**2*(f + 1)**2/13
Let f(o) be the third derivative of -4*o**2 + 0*o - 1/112*o**8 + 1/8*o**4 + 0 - 1/35*o**7 + 1/10*o**5 + 0*o**3 + 0*o**6. Factor f(c).
-3*c*(c - 1)*(c + 1)**3
Suppose y + 5*u = 4, -3*y + 5*u = -2*y - 4. Factor 2*c**4 + 3*c**4 + 48*c**2 + 16*c**3 + 26 + 64*c - 3*c**y + 6.
2*(c + 2)**4
Suppose -179*y + 78 + 93 + 187 = 0. Factor 1/3*d**3 - 2/3*d - 1/2*d**y + 2/3 + 1/6*d**4.
(d - 1)**2*(d + 2)**2/6
Suppose -9*n + 560 = 2036. Let c = -490/3 - n. Factor -c*y + 2 - 8/3*y**2.
-2*(y + 1)*(4*y - 3)/3
Let w(m) = -29*m**3 + 11*m**2 + 4*m - 3. Let h(x) = -88*x**3 + 32*x**2 + 12*x - 8. Let t = 25 + -28. Let u(z) = t*h(z) + 8*w(z). Let u(l) = 0. What is l?
-1/4, 0, 1/2
Suppose 243 = -2*g + 5*g. Factor -g - 5*z**3 + 15*z + 71 + 0*z**3.
-5*(z - 1)**2*(z + 2)
Let c(i) be the second derivative of i**4/20 - i**3/2 - 36*i - 1. Solve c(a) = 0 for a.
0, 5
Suppose 12/5*z**2 - 354/5*z - 36 = 0. What is z?
-1/2, 30
Let c be 1 + (2 - 0) - (-12)/(-27). Let g = c + -125/63. Factor 2/7*o**2 + 2/7 - g*o.
2*(o - 1)**2/7
Let s(r) be the third derivative of 0 - 1/8*r**4 + 1/40*r**6 - 1/20*r**5 + 0*r + 10*r**2 + 1/2*r**3. Factor s(k).
3*(k - 1)**2*(k + 1)
Let j be 93/(-124) + (-9)/4 - -6. Suppose j*q**3 + 0 - 27/4*q**2 + 3/2*q = 0. Calculate q.
0, 1/4, 2
Let z(r) be the first derivative of r**3/12 - r**2/4 + r/4 - 21. Factor z(k).
(k - 1)**2/4
Let z = -23/770 + 377/2310. Factor -2/15*h**2 + 0 - 8/15*h**3 + 8/15*h + z*h**4.
2*h*(h - 4)*(h - 1)*(h + 1)/15
Suppose 0 = 5*g - v - 29, 5*g - 1 - 36 = 3*v. Factor 10 + 5*z**3 - 40*z**2 + 9*z**2 - g*z + 21*z**2.
5*(z - 2)*(z - 1)*(z + 1)
Let s(w) = w - 7. Let c be s(-5). Let m be c/9 - 4/6. Let b(q) = 7*q**3 + 11*q**2 - 2. Let a(k) = k**2 - k - 1. Let n(o) = m*a(o) + b(o). Factor n(y).
y*(y + 1)*(7*y + 2)
Suppose -2 + 0 = j + a, 3*a = -6. Suppose -8*w - 3*p = -3*w - 10, 0 = 2*w + 4*p - 4. Let j - 2*g + 1/2*g**w = 0. What is g?
0, 4
Let q(x) be the first derivative of -x**5/35 - 3*x**4/14 + x**3/3 + 89. Factor q(i).
-i**2*(i - 1)*(i + 7)/7
Let c(l) = 13*l - 154. Let a be c(12). Solve -2/5*s + 2/5*s**4 + 6/5*s**a - 6/5*s**3 + 0 = 0.
0, 1
Let f be (40/(-105))/(100/(-70)). What is b in 2/15*b**4 - 2/5*b**2 - 2/3*b - f + 2/15*b**3 = 0?
-1, 2
Let k(c) be the second derivative of 1/36*c**4 - 7/9*c**3 + 49/6*c**2 + 5*c + 0. Factor k(d).
(d - 7)**2/3
Let v(q) = -24*q**2 + 7*q. Let m(k) = -50*k**2 + 13*k. Let u(x) = -3*m(x) + 5*v(x). Solve u(f) = 0 for f.
0, 2/15
Let i be (-48)/640*-8 - (0 - 0). Let 0 - 3/5*x + i*x**3 + 0*x**2 = 0. Calculate x.
-1, 0, 1
Let c = 143 - 139. Suppose -34*v**3 + 74*v**3 + c - 3*v**2 - 39*v**3 = 0. Calculate v.
-1, 2
Let h(p) be the second derivative of 5*p + 1/65*p**5 - 8/39*p**3 + 1/195*p**6 + 0 - 1/26*p**4 - 4/13*p**2. What is q in h(q) = 0?
-2, -1, 2
Suppose 0 = 5*m - 4*a - 0 + 2, 0 = a - 