*k**3. Suppose l(i) = 0. Calculate i.
-2, -1
Let l(h) be the first derivative of 3*h**4/16 + 27*h**3/4 + 729*h**2/8 + 2187*h/4 - 75. Factor l(v).
3*(v + 9)**3/4
Let w = -8180 - -8181. Factor w + 2/3*s - 1/3*s**2.
-(s - 3)*(s + 1)/3
Let h(s) be the first derivative of s**4/54 - 8*s**3/27 + 16*s**2/9 - 51*s + 17. Let y(z) be the first derivative of h(z). Let y(c) = 0. Calculate c.
4
Suppose 0 = 4*l - g - 12, 4*l = -7*g + 3*g - 8. Solve 8*s**2 - 6*s**3 - 426 + s**l + 426 - 3*s**4 = 0.
-3, 0, 1
Let o(j) = j**3 + 14*j**2 + 51*j + 16. Let t be o(-7). Factor -20 - 8*w - 4/5*w**t.
-4*(w + 5)**2/5
Let a = 73 + -66. Let l(f) = 2*f**3 + 2*f**2 + 5*f. Let k(c) = -5*c**3 - 5*c**2 - 11*c. Let u(x) = a*l(x) + 3*k(x). Let u(r) = 0. What is r?
-2, 0, 1
Suppose 0 = 2*j, -6*d = -d - 3*j + 5. Let z(p) = p**4 + p + 1. Let h(w) = -3*w**4 + 27*w**3 + 18*w**2 - 12*w - 15. Let a(r) = d*h(r) - 15*z(r). Factor a(c).
-3*c*(c + 1)**2*(4*c + 1)
Let l(j) be the second derivative of j**6/150 - j**5/50 - 7*j**4/60 - 2*j**3/15 + j + 8. Factor l(q).
q*(q - 4)*(q + 1)**2/5
Let p(l) be the third derivative of l**6/240 + 19*l**5/120 - 7*l**4/8 + 3*l**2 + 56. Let p(g) = 0. Calculate g.
-21, 0, 2
Let i(q) be the first derivative of 3/5*q**5 + 3 + 0*q + 3*q**2 - 3/4*q**4 - 7/3*q**3 + 1/6*q**6. Find r, given that i(r) = 0.
-3, -2, 0, 1
Let p(n) = -n**2 + 3*n + 507. Let q be p(-21). Solve 3/7*c**q - 18/7 + 18/7*c**2 - 3/7*c = 0 for c.
-6, -1, 1
Let u(z) = -3*z**2 + 6*z - 9. Let p(b) = b**2 - b + 1. Let x be 3/18 - (-222)/(-36). Let o(y) = x*p(y) - u(y). Suppose o(k) = 0. What is k?
-1, 1
Suppose -4*i + 74 = 2*j, -4*j - 2*i + 142 + 30 = 0. Factor j*s**3 + 5 - s**2 + 10*s**2 + 0 + 6*s**2 - 25*s.
5*(s + 1)*(3*s - 1)**2
Let r = -61 - -46. Let i be -3 - 100/r - 3*1. Factor i*h**4 + 6*h**2 + 4/3 - 14/3*h - 10/3*h**3.
2*(h - 2)*(h - 1)**3/3
Let c(g) be the second derivative of 0 + 5*g**2 + 12*g + 1/40*g**6 - 1/2*g**3 - 1/8*g**4 + 1/20*g**5. Let f(j) be the first derivative of c(j). Solve f(a) = 0.
-1, 1
Let l = -1 + 10. Suppose l*a**2 - 10*a**2 + 6*a**2 + 15 + 20*a = 0. Calculate a.
-3, -1
Let y be (-4)/(-12) + (-22)/(-6) + 1. Find w such that y - 24 + 1 + 3*w**2 - 2*w + 5*w = 0.
-3, 2
Find i such that -i**2 + 4*i**2 - i**2 - 4*i - 21334 - 10*i + 21346 = 0.
1, 6
Let b(t) = -t**3 + t**2 + t - 1. Let m(o) = -4*o**3 + 5 - 20*o**2 - 19*o - 4*o + 2*o**3 + 4*o**3. Let q(d) = 5*b(d) + m(d). Factor q(r).
-3*r*(r + 2)*(r + 3)
Let v = -2704 - -2707. Factor 1/3*g**4 + 0 + g**v + g**2 + 1/3*g.
g*(g + 1)**3/3
Let i be (-121)/(-66) - 2/(-12). Determine l, given that -9*l**3 + 39*l**2 - 138*l**i + 1664 + 1089*l - 5657 + 12*l**3 = 0.
11
Factor -21/4*z**3 + 0 - 3/2*z + 9/4*z**4 + 19/4*z**2 - 1/4*z**5.
-z*(z - 6)*(z - 1)**3/4
Suppose -66 - 69 = -27*l. Let a(b) be the third derivative of 0*b**3 + 0*b - 1/28*b**4 + 1/280*b**6 + 1/140*b**l + 0 - b**2. Let a(t) = 0. Calculate t.
-2, 0, 1
Let q(x) = -3*x**2 - 4*x + 3. Let u(t) = -1 + 545*t - 2 - 541*t + 2*t**2. Let l(j) = 3*q(j) + 4*u(j). Factor l(v).
-(v - 3)*(v - 1)
Let r(h) be the first derivative of -2/33*h**3 - 14 + 0*h + 1/11*h**2. Let r(y) = 0. Calculate y.
0, 1
Let r(h) = -7*h**2 + 12*h - 1. Let v be r(1). Let w(p) be the first derivative of -7 - 2/55*p**5 + 4/11*p**3 + 0*p**v - 8/11*p**2 + 6/11*p. Factor w(c).
-2*(c - 1)**3*(c + 3)/11
Suppose -15*m + 30*m - 90 = 0. Let z(g) be the second derivative of -3/20*g**5 + 0 - 6*g + 1/2*g**4 + 0*g**3 - 1/10*g**m + 0*g**2. Let z(a) = 0. What is a?
-2, 0, 1
Let m(g) be the first derivative of 0*g**2 + 8/3*g + 1/6*g**4 + 3 - 2/3*g**3. Find q such that m(q) = 0.
-1, 2
Let f(q) be the first derivative of 2*q**3/15 - 4*q**2 - 88*q/5 - 159. Determine s, given that f(s) = 0.
-2, 22
Let u = 7346/385 - 636/35. Factor -8/11*y**3 + 0 - 2/11*y**4 - 4/11*y - u*y**2.
-2*y*(y + 1)**2*(y + 2)/11
Let y(p) be the first derivative of 2*p**5/45 - p**4/12 - p**3/3 - p**2/18 + p/3 + 137. Factor y(c).
(c - 3)*(c + 1)**2*(2*c - 1)/9
Suppose -4*d + 32 = 5*w, -5*d + 0*w - w = -19. Factor -22*s**2 + 11*s**2 - 6*s + 8*s**2 + 3*s**d.
3*s*(s - 2)*(s + 1)
Let r = 3/305 - -119/305. Determine g so that r*g**3 + 0*g + 2/5*g**4 + 0 + 0*g**2 = 0.
-1, 0
Let v(y) be the second derivative of y**5/16 - 95*y**4/16 - 145*y**3/12 - 21*y. Factor v(l).
5*l*(l - 58)*(l + 1)/4
Let c(l) = -21*l**2 + 20*l. Let m be ((-8)/(-12))/(((-1)/(-6))/(-1)). Let g(a) = 43*a**2 - 40*a + 1. Let z(n) = m*g(n) - 7*c(n). Solve z(w) = 0 for w.
2/5
Let c(v) be the third derivative of -v**5/20 - 5*v**4/24 - 2*v**3/3 - v**2. Let z(a) = a**2 + a + 1. Let k(t) = -3*c(t) - 6*z(t). Factor k(h).
3*(h + 1)*(h + 2)
Let j(c) be the first derivative of 1/6*c**5 - 12 + 10/3*c**3 + 0*c**2 + 0*c - 5/8*c**4 - 1/72*c**6. Let y(w) be the third derivative of j(w). Factor y(i).
-5*(i - 3)*(i - 1)
Let r(t) = -44*t + 1454. Let x be r(33). Factor 2/5 - 9/5*b + 3/5*b**x + 4/5*b**3.
(b - 1)*(b + 2)*(4*b - 1)/5
Let g(r) be the third derivative of 1/945*r**7 + 1/270*r**5 + 0*r + 0 + 11*r**2 + 1/270*r**6 + 0*r**4 + 0*r**3. Find v, given that g(v) = 0.
-1, 0
Let z = -43 - -47. Factor 98 + 4*v**2 - z*v**3 - 106 + 4*v - 4*v**4 + 8*v**2.
-4*(v - 1)**2*(v + 1)*(v + 2)
Let g = -55 - -61. Let x be (-2 - 58/(-20))*10/g. Factor -2 + 3*q - x*q**2 + 1/4*q**3.
(q - 2)**3/4
Let k be ((-12)/(-10))/1*800/240. Suppose -w = 4*h - 2 + 3, -k*w - 2*h = -10. Solve 0*n**2 + 0 + 2/3*n**4 + 0*n**w + 0*n = 0 for n.
0
Let i = 1184 + -1179. Let r(c) be the first derivative of 6 - 3/2*c**2 - 8/5*c**i - 1/2*c + 3*c**4 - 1/6*c**3. Find h, given that r(h) = 0.
-1/4, 1
Let h(w) be the first derivative of -5*w**6/6 + 27*w**5 - 245*w**4/2 + 710*w**3/3 - 465*w**2/2 + 115*w - 474. Determine l, given that h(l) = 0.
1, 23
Let z(n) = n**2 - 11*n - 20. Let v be z(14). Suppose v = 10*u - 8. Solve 4/7*k**u - 2/7*k**4 + 6/7*k**2 - 8/7 - 8/7*k = 0 for k.
-1, 2
Let c(q) be the first derivative of 1/3*q**3 + 3 + 1/24*q**4 + q**2 + 4*q. Let u(f) be the first derivative of c(f). Factor u(t).
(t + 2)**2/2
Let w(x) = 3*x**4 + 15*x**3 + 6*x**2 - 3*x - 3. Let d = 90 - 87. Let v(z) = -3*z**4 - 16*z**3 - 5*z**2 + 4*z + 4. Let i(o) = d*v(o) + 4*w(o). Factor i(y).
3*y**2*(y + 1)*(y + 3)
Let g(l) be the third derivative of -l**5/60 - l**4/24 + l**3/6 - l**2. Let c = 184 - 183. Let j(o) = -2*o**2 - o + 4. Let p(r) = c*j(r) - 3*g(r). Factor p(a).
(a + 1)**2
Factor 258/7*l + 3/7*l**2 + 5547/7.
3*(l + 43)**2/7
Let c(l) be the third derivative of -l**10/30240 + l**9/6048 - l**7/504 + l**6/144 + 2*l**5/5 - 34*l**2. Let b(x) be the third derivative of c(x). Factor b(m).
-5*(m - 1)**3*(m + 1)
Let j(o) be the second derivative of o**5/50 - 49*o**4/30 - 101*o**3/15 - 51*o**2/5 - 12*o. Find b, given that j(b) = 0.
-1, 51
Let k(y) be the second derivative of -4/165*y**6 - 1/33*y**3 + 0*y**5 + 0 - 8*y + 1/22*y**4 + 0*y**2. Find u, given that k(u) = 0.
-1, 0, 1/2
Let c(l) = -l**3 - 2*l**2 + 37*l + 16. Let u be c(-7). Solve 0*w**u - 1/2*w + 0 + 1/2*w**3 = 0.
-1, 0, 1
Let i(u) = u**5. Let q(p) = -p**5 + 3*p**4 - 18*p**3 - 42*p**2 - 33*p - 9. Let w(m) = 4*i(m) + q(m). Factor w(g).
3*(g - 3)*(g + 1)**4
Let n be 9/21*2/3. Let t = 16 + -11. Factor -n*z**4 + 0*z**3 + 2/7*z**2 + 0 - 1/7*z**t + 1/7*z.
-z*(z - 1)*(z + 1)**3/7
Suppose -21*f - 1541 = 1126. Let n = -123 - f. Factor 4*g**n - 32/5*g**3 + 0*g + 16/5*g**2 - 4/5*g**5 + 0.
-4*g**2*(g - 2)**2*(g - 1)/5
Let u(n) = 6*n + 6. Let p(o) = o**3 - 11*o**2 + 16*o + 17. Let k be p(9). Let y(b) = -b**2 - b. Let s(f) = k*u(f) - 2*y(f). Factor s(q).
2*(q - 3)*(q + 1)
Let q(d) be the third derivative of -d**9/504 + d**8/210 - d**7/420 - 2*d**3 - 3*d**2. Let a(h) be the first derivative of q(h). Determine j so that a(j) = 0.
0, 1/3, 1
Let f be 40/(-14)*(-7)/2. Suppose b - 6*b + f = 0. Suppose 2*y**2 - y**2 - b*y + 8*y - 3*y + 2 = 0. What is y?
-2, -1
Let m(x) be the third derivative of x**5/150 - x**4/15 + 4*x**3/15 - 96*x**2. Solve m(j) = 0 for j.
2
Let l(k) be the second derivative of k**4/18 - 35*k**3/9 + 32*k**2 - 27*k - 14. Factor l(o).
2*(o - 32)*(o - 3)/3
Determine z so that 4994/3*z**2 - 68*z**3 + 5408/3 + 3536*z + 2/3*z**4 = 0.
-1, 52
Solve 28/5*t**4 + 0*t + 24/5*t**2 + 92/5*t**3 + 0 = 0.
-3, -2/7, 0
Let x(h) = 4*h**2 + 40*h + 64. Let u be x(-2). Suppose 0 - 1/7*t**3 + u*t + 1/7*t**5 + 1/7*t**2 - 1/7*t**4 = 0. What is t?
-1, 0, 1
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