ppose -4*a - 18 - 7 = -3*k, -4*k = 3*a. Let v be p(a). Factor -4*l**3 + 3 + 2*l + 0 - l**2 - 1 + 2*l**4 + 2*l**v - 3*l**2.
2*(l - 1)**2*(l + 1)**3
Let k(g) be the second derivative of 20*g + 0 + 5/12*g**4 + 20/3*g**3 + 40*g**2. Factor k(h).
5*(h + 4)**2
Let n(r) be the third derivative of r**5/30 - 4*r**4/3 + 64*r**3/3 - 44*r**2. Find u such that n(u) = 0.
8
Let l(o) = 50*o**2 - 28*o**2 + 13*o + 12 - 21*o**2. Let f be l(-12). Factor 0*b + 2/3*b**4 + 4/3*b**2 - 2*b**3 + f.
2*b**2*(b - 2)*(b - 1)/3
Let j(g) = 5*g**3 - 6*g**2 - 8*g + 24. Let o(p) = -9*p**3 + 12*p**2 + 16*p - 48. Let f(u) = -5*j(u) - 3*o(u). Find h, given that f(h) = 0.
-2, 2, 3
Let j(z) = z**5 - z**3 - z**2 - z. Let n(d) = -d**5 + 2*d**3 + 2*d - 6*d**2 + 3*d**2 + 5*d**2. Let k(y) = 4*j(y) + 2*n(y). Find a such that k(a) = 0.
0
Let c be 9/(-2)*(-8)/6. Let a be 30/14 + (-9)/63. Factor -n**a + c*n**5 + n**4 - n**3 + 0*n**4 - 5*n**5.
n**2*(n - 1)*(n + 1)**2
Let q(k) = -56*k + 954. Let s be q(17). What is y in -16/3 - 8/3*y - 1/3*y**s = 0?
-4
Let j(u) be the third derivative of -u**7/1365 + u**6/780 + 7*u**2 - 2. Find v, given that j(v) = 0.
0, 1
Let b(v) be the second derivative of v**4/12 + 7*v**3/6 + 4*v**2 - 9*v. Let y be b(-8). Determine s, given that 4 + y*s - 4 + 54*s**2 - 58*s**2 = 0.
0, 4
Let z(k) be the third derivative of -1/63*k**7 - 1/504*k**8 - 2/45*k**6 + 0*k**4 - 30*k**2 + 0*k + 0 - 2/45*k**5 + 0*k**3. Factor z(x).
-2*x**2*(x + 1)*(x + 2)**2/3
Let t(r) be the first derivative of 0*r + 40/3*r**3 + 39 + 5/4*r**4 - 30*r**2 - r**5. Find n, given that t(n) = 0.
-3, 0, 2
Suppose -36 + 15*l - 3/2*l**3 + 9/2*l**2 = 0. Calculate l.
-3, 2, 4
Let u = 93 + 2. Let j = u + -95. Factor 3/2*o**3 + 0*o**2 - 3/4*o**4 + 0 + j*o.
-3*o**3*(o - 2)/4
Let m(x) be the first derivative of -2*x**3/45 - 56*x**2/15 + 38*x/5 - 1004. Factor m(o).
-2*(o - 1)*(o + 57)/15
Let h = 3920 + -3918. Determine w so that 46/9*w**h - 4/9 - 14/3*w**4 - 2/9*w + 2/9*w**3 = 0.
-1, -2/7, 1/3, 1
Let 1/4*k**3 + 7/4*k + 0 + 2*k**2 = 0. Calculate k.
-7, -1, 0
Let b(a) = -a**3 - a + 1. Let s(m) = 9*m**3 + 30*m**2 + 54*m - 6. Let y(g) = -6*b(g) - s(g). Factor y(k).
-3*k*(k + 2)*(k + 8)
Factor 8*b**2 + 2*b**4 - 18*b**2 + 8*b**3 + 4*b**2 - 36*b.
2*b*(b - 2)*(b + 3)**2
Find r such that 26244/5 - 28*r**4 + 360*r**3 + 4/5*r**5 + 2916*r - 1944*r**2 = 0.
-1, 9
Let m(u) = -u - 25. Let a be m(-21). Let o = -7/2 - a. Suppose -1/2*h + 0 + h**2 - o*h**3 = 0. Calculate h.
0, 1
Suppose x - 18 + 6 = 0. Factor 5*h**2 - 7*h**2 - x - 2*h**2 - 12*h + h**2.
-3*(h + 2)**2
Let u(r) be the first derivative of -r**6/2 + 9*r**5/5 + 33*r**4/4 - 3*r**3 - 15*r**2 - 32. Let u(s) = 0. Calculate s.
-2, -1, 0, 1, 5
Let b(g) be the first derivative of -3*g**5/20 - 21*g**4/16 - 11*g**3/4 - 15*g**2/8 + 92. Factor b(p).
-3*p*(p + 1)**2*(p + 5)/4
Suppose -43*u - 78*u = 0. Factor 1/6*b**2 - 1/2*b + u.
b*(b - 3)/6
Let z(k) = -k + 11. Let g be z(8). Suppose 0 = n + g*n - 12. Solve -12 + 12 - 2*b**4 + 2*b**n = 0.
0, 1
Let b(t) be the first derivative of 0*t - 3/2*t**2 + 24 + t**3. Determine h so that b(h) = 0.
0, 1
Factor -3*f - 8/5 + 59/5*f**2 - 36/5*f**3.
-(f - 1)*(4*f + 1)*(9*f - 8)/5
Let d(c) be the third derivative of c**6/1440 + c**5/160 + c**4/48 + 4*c**3/3 + 8*c**2. Let g(p) be the first derivative of d(p). Factor g(a).
(a + 1)*(a + 2)/4
Suppose 2*m + 7*m - 45 = 0. Let j = -3/196 + 407/980. Factor -j*x**m + 4/5*x**4 + 2/5*x + 0*x**3 - 4/5*x**2 + 0.
-2*x*(x - 1)**3*(x + 1)/5
Let x = 150 - 157. Let d be x/4 + 2 - (-18)/(-72). Solve -3*h**2 + 0*h + 6*h**4 + d + 21/2*h**3 = 0 for h.
-2, 0, 1/4
Suppose 5*h - 10 = -5*a, -9*h - 2*a - 4 = -11*h. Suppose 0 = 2*b - 4*g, -3*g + 8*g = h*b. Solve -2/7*p**2 + 0 - 6/7*p**4 + 6/7*p**3 + b*p + 2/7*p**5 = 0 for p.
0, 1
Let w be 1*(6 + -6 + 4). Let s(y) be the first derivative of 3*y**2 + 2/3*y**3 - 3/2*y**w + 2/5*y**5 - 4*y + 5. Factor s(h).
2*(h - 2)*(h - 1)**2*(h + 1)
Let x be (-224)/(-1) + -1 - 240/60. Let g = 223 - x. Factor 8/5*z**3 + 2/5*z**g + 2/5 + 12/5*z**2 + 8/5*z.
2*(z + 1)**4/5
Let c(a) be the first derivative of -2*a**5/35 + a**4/14 + 4*a**3/7 - 96. Factor c(d).
-2*d**2*(d - 3)*(d + 2)/7
Let y(s) be the first derivative of -s**6/6 - 6*s**5/5 + 25*s**4/4 - 6*s**3 + 65. Factor y(h).
-h**2*(h - 2)*(h - 1)*(h + 9)
Let k(z) be the second derivative of 16*z + 2/3*z**3 + 0*z**2 + 0 + 1/10*z**5 - 1/2*z**4. Suppose k(d) = 0. Calculate d.
0, 1, 2
Let c be (41/39 - 1)/(8/30). Let f = c + 4/13. Factor 0*q + 1/2*q**2 + 0 - f*q**4 + 0*q**3.
-q**2*(q - 1)*(q + 1)/2
Let y(w) = 2*w**2 + 8. Let g(d) = 15*d**2 + 556*d + 77340. Let z(v) = 2*g(v) - 14*y(v). Factor z(h).
2*(h + 278)**2
Let a(f) be the third derivative of f**5/40 + 2*f**4 + 31*f**3/4 + 67*f**2 - 2*f. What is d in a(d) = 0?
-31, -1
Let n = 13 - 15. Let v be 4 + (-2 - 2) - n. Find g such that -5 + 6*g + 5*g - 9*g**2 + v + 3*g**3 - 2*g = 0.
1
Let o(x) be the second derivative of x**6/15 - 19*x**5/10 + 25*x**4/3 - 32*x**3/3 + 571*x. Factor o(m).
2*m*(m - 16)*(m - 2)*(m - 1)
Let s = -365 - -3653/10. Let j(q) be the first derivative of s*q**2 - 21/25*q**5 + 6/5*q - 2 - 3*q**3 + 57/20*q**4. Factor j(f).
-3*(f - 1)**3*(7*f + 2)/5
Let s(n) be the first derivative of n**6/120 + 3*n**5/40 - 3*n**3 + 6. Let p(t) be the third derivative of s(t). Let p(f) = 0. Calculate f.
-3, 0
Solve -4/5*a**3 - 228/5*a + 288/5 + 56/5*a**2 = 0 for a.
3, 8
Let -80/9*a - 800/9 - 2/9*a**2 = 0. Calculate a.
-20
Let a(b) be the first derivative of -b**6/6 + 4*b**5 - 145*b**4/4 + 150*b**3 - 270*b**2 + 216*b + 127. Factor a(t).
-(t - 6)**3*(t - 1)**2
Factor 100*r - 105 - 6*r + r - 55*r**2 + 60*r + 5*r**3.
5*(r - 7)*(r - 3)*(r - 1)
Let y = -34 + 18. Let d be (-50)/y - (-13)/(-104). Solve -2*z**2 + 5*z**2 + 7*z**3 - 25*z**3 - 3*z**5 + 9*z**4 + 9*z**d = 0.
0, 1
Let i(k) be the third derivative of -2*k**7/525 - k**6/30 - 3*k**5/25 - 7*k**4/30 - 4*k**3/15 - 86*k**2. Suppose i(w) = 0. What is w?
-2, -1
Let k = 20 - 27. Let d(m) = -19*m**4 - 11*m**3 + 2*m**2 + 3*m. Let s(i) = -39*i**4 - 23*i**3 + 5*i**2 + 7*i. Let z(g) = k*d(g) + 3*s(g). Factor z(v).
v**2*(4*v + 1)**2
Let b(l) = -2*l**2 - 9*l. Let z(a) be the second derivative of a**4/4 + 13*a**3/6 + 3*a. Let t(n) = 7*b(n) + 5*z(n). Suppose t(h) = 0. Calculate h.
-2, 0
Suppose 0 = 4*t - 2*o - 26, -3*o - 14 = -t - 0*o. Let x(i) be the third derivative of 0 + 1/144*i**6 + 0*i - 5*i**2 + 0*i**4 + 0*i**3 + 1/180*i**t. Factor x(m).
m**2*(5*m + 2)/6
Let m(a) = 3*a**4 + 3*a**3 - 6*a**2. Let l(t) = 3*t**4 + 3*t**3 - 5*t**2. Let i be 3 + 1 + (-18 - -19). Let w(o) = i*m(o) - 6*l(o). Suppose w(y) = 0. What is y?
-1, 0
Let n(l) be the second derivative of -1/24*l**4 + 1/24*l**3 + 1/4*l**2 + 0 + 5*l - 1/80*l**5. Suppose n(i) = 0. Calculate i.
-2, -1, 1
Suppose -54*j + 108 + 9*j**2 - 1/2*j**3 = 0. What is j?
6
Let p(w) be the first derivative of -1/21*w**6 - 2/35*w**5 + 1/7*w**4 + 0*w**3 + 26 + 0*w + 0*w**2. Factor p(v).
-2*v**3*(v - 1)*(v + 2)/7
Let o = -24 - -65. Let a = 61 - o. Factor -26 + 9*q + 40 + 6*q**2 - a.
3*(q + 2)*(2*q - 1)
Factor 0 + 2/15*r**2 + 26/5*r.
2*r*(r + 39)/15
Let y = 7 + -7. Suppose f + 2*f - 5*f = y. Find z, given that -1/2*z**4 + f + 1/2*z**2 - 1/2*z**3 + 1/2*z = 0.
-1, 0, 1
Let f(z) be the first derivative of 6/7*z + 1/7*z**3 - 9/14*z**2 - 6. Factor f(u).
3*(u - 2)*(u - 1)/7
Let y = 46/137 + 547/411. Find m such that 0*m + 0 - y*m**3 + 10/3*m**2 = 0.
0, 2
Let d(c) be the first derivative of -2 - 5/9*c**3 - 1/3*c**2 + 2*c - 2/15*c**5 - 4/9*c**4. Let q(x) be the first derivative of d(x). Factor q(f).
-2*(f + 1)*(2*f + 1)**2/3
Let p(i) be the third derivative of 5*i**8/168 + 128*i**7/105 + 773*i**6/60 - 85*i**5/3 - 793*i**4/3 + 1352*i**3/3 - 284*i**2. Let p(q) = 0. Calculate q.
-13, -2, 2/5, 2
Let n(h) be the first derivative of -1/6*h**5 + 0*h**2 - 1/3*h**4 + 0*h - 31 - 1/36*h**6 - 2/9*h**3. Factor n(z).
-z**2*(z + 1)*(z + 2)**2/6
Let j be 10/7*38/95. Factor 0 + 2/7*d + 1/7*d**4 + j*d**3 + 5/7*d**2.
d*(d + 1)**2*(d + 2)/7
Let r be (-832)/65*(-5)/2. Find q such that -6 - 2 - 4 + r*q**2 - 10*q - 34*q**2 = 0.
-3, -2
Find y, given that 9*y**3 - 135/2*y + 21/4*y**2 + 54 - 3/4*y**4 = 0.
-3, 1, 2, 12
Let k(g) be the third derivative of g**8/112 - 53*g**7/70 + 153*g**6/40 - 151*g**5/20 + 25*g**4/4 + 36*g**2 - g. Find p, given that k(p) = 0.
0, 1, 50
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