 Let v(j) = 12*j**3 - 8*j**2 + 6*j + 10. Let o(k) = c*n(k) - 3*v(k). Factor o(r).
2*r*(r - 1)*(2*r - 1)
Let s(b) be the second derivative of b**4/4 + 47*b**3 + 6627*b**2/2 + 44*b. Factor s(o).
3*(o + 47)**2
Determine q, given that 67*q**3 + 41*q**3 - 48*q + 22*q**2 - 110*q**3 = 0.
0, 3, 8
Suppose 93*b = 98*b. Let f(x) be the second derivative of -1/42*x**4 + 1/105*x**6 + 4*x + 0*x**3 + b*x**2 + 1/70*x**5 + 0 - 1/147*x**7. Factor f(v).
-2*v**2*(v - 1)**2*(v + 1)/7
Let m(c) = 11*c**3 - c**2 - c + 1. Let n be m(1). Let x = 14 - n. Factor 2*i**5 - i**5 + 0*i**5 + i**x.
i**4*(i + 1)
Let i be (-18)/(-42) + 2*330/28. Solve 24*g**2 - 17*g**3 - 26*g**3 - i + 40*g**3 + 3*g = 0.
-1, 1, 8
Let q(c) be the second derivative of 32/11*c**2 + 35*c + 5/33*c**4 - 32/33*c**3 - 1/110*c**5 + 0. Factor q(a).
-2*(a - 4)**2*(a - 2)/11
Let k(i) = 2*i**2 + 10*i + 2. Let l be k(-5). Factor 2*n + 179 - 2*n**l + n - 177.
-(n - 2)*(2*n + 1)
Suppose 109 = 10*l - 51. Suppose -l*c + 19*c - 6 = 0. Factor 0 - 1/3*k**3 + 4/3*k + 0*k**c.
-k*(k - 2)*(k + 2)/3
Let c be 6 - ((-35)/(-21) + -1). Factor -16/3*o - c + 4/3*o**3 + 4/3*o**2.
4*(o - 2)*(o + 1)*(o + 2)/3
Let u(t) = t - 28. Let v be u(9). Let c = v + 23. Factor -27*l**c - 4/3*l - 15*l**3 + 32/3*l**2 + 0.
-l*(l + 1)*(9*l - 2)**2/3
Let j(y) be the first derivative of y**8/420 + y**7/210 - y**3 + 1. Let m(n) be the third derivative of j(n). What is t in m(t) = 0?
-1, 0
Let b be (2 + -1)/((-29)/(696/(-120))). Factor -b*q**2 + 7/5 - 6/5*q.
-(q - 1)*(q + 7)/5
Let h = 234 + -222. Suppose -h*d + 5 = -55. Suppose 0*a + 192/7*a**4 + 4/7*a**2 - 48/7*a**3 - 256/7*a**d + 0 = 0. Calculate a.
0, 1/4
Let r(c) = -11*c**3 + 67*c**2 - 10*c - 5. Let l(b) = -39*b**3 + 234*b**2 - 36*b - 18. Let p(w) = 5*l(w) - 18*r(w). What is i in p(i) = 0?
0, 12
Let -392/9*k**3 - 4 - 616/9*k**2 + 106/3*k = 0. Calculate k.
-2, 3/14
Let o(f) be the first derivative of -2*f**3 + 0*f + 0*f**4 + 2/5*f**5 - 40 - 2*f**2. What is c in o(c) = 0?
-1, 0, 2
Suppose -46611*t + 92 = -46588*t. Solve -5/4*f + f**3 - 1/2*f**2 + f**t - 1/2 + 1/4*f**5 = 0 for f.
-2, -1, 1
Determine h so that -2/7*h**3 - 4/7*h**4 + 0*h**2 + 0 + 0*h - 2/7*h**5 = 0.
-1, 0
Determine g so that 34*g + 8*g**5 - 9 + 240*g**4 - 84*g**3 - 6*g - 4*g**2 - 284*g**4 + 9 = 0.
-1, 0, 1/2, 7
Let i(g) be the first derivative of -21*g**4/4 + 152*g**3 - 354*g**2 - 240*g - 81. Let i(u) = 0. What is u?
-2/7, 2, 20
Find x, given that 140 - 1695*x**2 - x**3 - 120*x + 1710*x**2 + 6*x**3 = 0.
-7, 2
Let n be 36/(-162) + (-677)/(-9). Find z, given that -73*z + n*z + 2*z**2 + 0*z**2 = 0.
-1, 0
Let w(i) be the third derivative of 1/4032*i**8 - 1/504*i**7 + 0*i + 7/1440*i**6 + 1/720*i**5 + 1/18*i**3 - 1/36*i**4 + 0 - 5*i**2. Solve w(p) = 0.
-1, 1, 2
Let v(u) = u**3 + 11*u**2 - u - 9. Let w be v(-11). What is d in -5*d**5 - 8*d**2 + 3*d**3 + 3*d**4 + 5*d**w + 2*d**5 = 0?
-1, 0, 1
Let s(x) be the third derivative of 7*x**6/30 - x**5/3 - 7*x**4/6 + 10*x**3/3 + 19*x**2 + 4. Factor s(r).
4*(r - 1)*(r + 1)*(7*r - 5)
Let c(x) be the second derivative of x - 1/40*x**5 + 1/4*x**4 - 2*x**2 - x**3 + 0. Let t(s) be the first derivative of c(s). Determine d so that t(d) = 0.
2
Let r(m) be the first derivative of 8*m**6/3 + 2*m**5/35 + 415. Find c such that r(c) = 0.
-1/56, 0
Let v(q) = 7*q**4 + q**3 - 3*q**2 - q + 8. Let d(r) = 6*r**4 + r**3 - 4*r**2 - r + 7. Let j(l) = 4*d(l) - 3*v(l). What is a in j(a) = 0?
-4/3, -1, 1
Factor 25*a**2 + 8*a**2 + 12*a - 41*a**2 - 4*a**3.
-4*a*(a - 1)*(a + 3)
Suppose f - 2*v = 4*f - 4, -5*v + 10 = -2*f. Let p = f + 5. Factor -u**4 + 5*u**3 + 3*u**4 - 7*u**3 + 2*u**p - 2*u**2.
2*u**2*(u - 1)*(u + 1)**2
Let s(d) be the third derivative of 0 + 1/504*d**8 + 4/27*d**3 - 1/90*d**5 - 1/945*d**7 + 2/27*d**4 + 0*d + 28*d**2 - 11/540*d**6. Find j, given that s(j) = 0.
-1, -2/3, 1, 2
Let b(r) be the first derivative of -2*r**3/11 - 26*r**2/11 + 18*r/11 - 237. Factor b(w).
-2*(w + 9)*(3*w - 1)/11
Factor 25*s + 13*s**3 - 18*s**2 - 46*s - 12*s**3 + 38.
(s - 19)*(s - 1)*(s + 2)
Suppose 3*b + u = -6 - 36, -4*b = -u + 56. Let t = 14 + b. What is h in t + 2*h - h - h**3 + 5 - 6 + h**2 = 0?
-1, 1
Suppose r - o + 4*o = -7, -2*o - 6 = 0. Let f(h) be the first derivative of 3 + 0*h**2 + 0*h + r*h**3 + 5/2*h**4. Find m, given that f(m) = 0.
-3/5, 0
Suppose 0*k + 49 = 2*k - j, 5*j + 113 = 4*k. Suppose 5*n + 5 = -15, 0 = -p + 5*n + k. Find f, given that -10 - 9*f - 6 + 3*f**p + 9*f**3 + 13 = 0.
-1, -1/3, 1
Let o(a) be the first derivative of 3/4*a**6 + 45/8*a**4 - 9/2*a**3 + 3/2*a**2 + 0*a + 6 - 33/10*a**5. Solve o(t) = 0.
0, 2/3, 1
Let -25/2*d**4 + 0 - 255/2*d**2 - 35*d - 105*d**3 = 0. What is d?
-7, -1, -2/5, 0
Factor 150/7 + 62/21*a**2 - 170/7*a - 2/21*a**3.
-2*(a - 15)**2*(a - 1)/21
Let p(m) be the first derivative of m**4/42 + 4*m**3/21 - 10*m + 16. Let x(n) be the first derivative of p(n). Factor x(s).
2*s*(s + 4)/7
Let r = -254 + 254. Let c(a) be the third derivative of 4/3*a**3 - 7/30*a**5 + 0*a - 3*a**2 - 1/12*a**6 + 2/3*a**4 + r. Factor c(s).
-2*(s - 1)*(s + 2)*(5*s + 2)
Let f(m) be the third derivative of 3*m**6/70 - 289*m**5/420 + m**4/28 + 8*m**3/21 + 5*m**2 - 4*m. Find q such that f(q) = 0.
-2/9, 1/4, 8
Suppose 3*u = -2*a + 5, -25 = -a - 4*a + 5*u. Let t(s) be the third derivative of 0*s + 1/6*s**3 + 1/240*s**5 + 1/24*s**a + 0 - 3*s**2. Let t(g) = 0. What is g?
-2
Suppose -1 + 22 = 7*g. Determine m so that 16 + 2*m**g - 16 - 16*m**2 = 0.
0, 8
Let b(x) = -x**2 + 11*x - 21. Let k be b(5). Factor -3*l**3 + l**4 - 3*l**4 + 5*l**3 + k*l**2 - 8*l + 3*l**2 - 16.
-2*(l - 2)**2*(l + 1)*(l + 2)
Suppose -2*m + 2*d + 210 = 4*d, -4*m - 2*d + 420 = 0. Solve -3*u**3 - 3*u**5 + m - 105 + 6*u**4 = 0.
0, 1
Let n be (0/2)/(34/(-17)). Determine o so that 0*o**2 + n + 2/7*o**3 - 2/7*o = 0.
-1, 0, 1
Solve 3/4*s**2 + 0 + 1/4*s**5 + 5/2*s - 11/4*s**3 - 3/4*s**4 = 0.
-2, -1, 0, 1, 5
Let r = 153 - 149. Let a(i) be the first derivative of 4/5*i**5 + 0*i + 1/6*i**6 + 4 + 4/3*i**3 + 1/2*i**2 + 3/2*i**r. Determine b, given that a(b) = 0.
-1, 0
Let l(m) be the third derivative of m**9/362880 - m**8/120960 - m**5/30 + 33*m**2. Let q(g) be the third derivative of l(g). Determine y so that q(y) = 0.
0, 1
Suppose 0 = 2*t + 2*h + h - 1, 5*t + 5*h - 5 = 0. Suppose q = 3*x + 16, 5*q - 5*x - 32 = -t*x. Factor -3*a + 1 + 10*a**3 - 11*a**3 + q*a - a**2.
-(a - 1)*(a + 1)**2
Let i(s) = 3*s**2 - 16*s + 19. Let u(t) = -9*t**2 + 47*t - 59. Let x(z) = -7*i(z) - 2*u(z). Factor x(o).
-3*(o - 5)*(o - 1)
Let d = -603 + 607. Let 3*p**2 + 1/7*p**d + 12/7*p**3 + 0 + 10/7*p = 0. Calculate p.
-10, -1, 0
Let t = 324 - 324. Solve t - 1/3*p + 2/3*p**2 - 1/3*p**3 = 0 for p.
0, 1
Let h(x) = -x**2 - 7*x - 7. Let m be h(-6). Let g be m/4 - 70/(-40). Suppose -t**3 + t**2 - 1/2*t**5 - 3/2*t**4 + 1/2 + g*t = 0. Calculate t.
-1, 1
Let w = 44 + -42. Let i be (2 - w)/(4 + -2). Factor 3/2*p**5 - 3*p**3 + 3/2*p + 0*p**4 + i*p**2 + 0.
3*p*(p - 1)**2*(p + 1)**2/2
Solve -24*n + 12 + 59*n + 40*n**2 + 21*n + 24*n**5 - 80*n**3 - 52*n**4 = 0.
-1, -1/2, -1/3, 1, 3
Let j = -118/5 + 424/15. Let w(h) be the second derivative of -1/15*h**6 - 5*h + 0 - 13/20*h**5 - j*h**3 - 5/2*h**4 - 4*h**2. Suppose w(g) = 0. Calculate g.
-2, -1/2
Suppose -5*g = -c + 1 - 10, g = 2*c. Let a be -6 - ((-322)/49)/c. Factor a*p**5 + 4/7*p + 4/7 - 8/7*p**3 - 8/7*p**2 + 4/7*p**4.
4*(p - 1)**2*(p + 1)**3/7
Let h(j) be the second derivative of j**4/24 - 19*j**3/12 + 17*j**2/2 - 45*j. Find w, given that h(w) = 0.
2, 17
Suppose -4*k - 8 = -2*k, -5*y + 4*k = -8336. Let o = -6617/4 + y. Factor 3 - o*b + 9/4*b**2.
3*(b - 4)*(3*b - 1)/4
Let j = 2818/9 + -313. Let p(l) be the third derivative of -1/60*l**6 + 2/9*l**3 - 1/4*l**4 + 0 + 0*l + j*l**5 - 6*l**2. Find m such that p(m) = 0.
1/3, 1, 2
Solve 0*p - 12/5*p**4 + 0*p**3 + 0 + 64/5*p**2 - 2/5*p**5 = 0 for p.
-4, 0, 2
Let m(n) = -15*n**4 - 137*n**3 - 113*n**2 + 15*n. Let b(t) = -2*t**4 - 17*t**3 - 14*t**2 + 2*t. Let g(y) = -51*b(y) + 6*m(y). Factor g(i).
3*i*(i + 2)**2*(4*i - 1)
Let i = 904/31 + -7640/279. Determine z, given that 4/9 + i*z**2 + 20/9*z = 0.
-1, -1/4
Let u(j) = 5*j**3 + 12*j**2 + 5*j - 2. Let f(i) = -25*i**3 - 61*i**2 - 25*i + 11. Let t(s) = 2*f(s) + 11*u(s). Suppose t(z) = 0. Calculate z.
-1, 0
Let q be 6 - 105/(-65) - (-10 + 17). Factor -8/13*d + q + 2/13*d**2.