 2)**3
Let i(z) = z**3 + z**2 - z - 1. Let q(f) = 16*f**3 - 72*f**2 + 16*f + 40. Let j(m) = -4*i(m) - q(m). Find p such that j(p) = 0.
-3/5, 1, 3
Let u(m) be the second derivative of 3*m**5/20 + 83*m**4/4 + 41*m**3 - 9*m - 11. Find d such that u(d) = 0.
-82, -1, 0
Let u(p) be the first derivative of -p**8/2310 - 3*p**7/1540 - p**6/990 + 14*p**3/3 + 15. Let y(j) be the third derivative of u(j). Factor y(o).
-2*o**2*(o + 2)*(4*o + 1)/11
Suppose 0 = -24*k - 227*k + 7 - 7. Factor 8/3*x**3 + 0 - 8/3*x**2 - 2/3*x**4 + k*x.
-2*x**2*(x - 2)**2/3
Let s(q) = -q - 17*q + 6*q**4 + 3*q**3 + 4*q**2 + 18 - 22*q**2 + 0*q**3 - 15*q**5. Let f(t) = -t**5 - t**2 - t + 1. Let r(g) = 18*f(g) - s(g). Factor r(v).
-3*v**3*(v + 1)**2
Suppose -6*x + 12*x - 72 = 0. Suppose 0 = x*p - p - 22. Let 2/13*k**p + 0*k - 2/13 = 0. What is k?
-1, 1
Suppose 18 = 4*h - 2. Factor h*f**2 - 6*f**2 - 2*f**2 - 6*f - 3.
-3*(f + 1)**2
Suppose -8 = -10*u + 12. Let v(y) = 2*y**3 - 14*y**2 + 10*y - 6. Let r(l) = -l**3 + 15*l**2 - 9*l + 7. Let f(h) = u*r(h) + 3*v(h). Factor f(i).
4*(i - 1)**3
Let y(x) be the second derivative of -x**7/10 + 13*x**6/25 + 69*x**5/25 + 6*x**4/5 + x + 29. Solve y(w) = 0.
-2, -2/7, 0, 6
Let s(g) be the first derivative of -g**6/160 + g**5/40 - g**4/24 + 6*g**3 + 3. Let y(u) be the third derivative of s(u). Solve y(v) = 0.
2/3
Suppose -55 - 41 = -2*p. Let h be (-2)/8 + (-3)/p*-4. Find u, given that h*u - 8/5*u**2 + 4/5*u**4 - 4/5*u**3 + 0 = 0.
-1, 0, 2
Let u = -5746 + 5746. Solve 3/4*b**3 + 0*b - 3/4*b**5 + 3/2*b**4 - 3/2*b**2 + u = 0.
-1, 0, 1, 2
Factor o**3 - 1393*o - 18*o**2 + 5*o**2 + 1433*o.
o*(o - 8)*(o - 5)
Let p(u) = -10*u - 64. Let j(x) = x + 1. Let d(n) = 3*j(n) - p(n). Let y be d(-5). Find h such that -4/11*h**3 + 0 + 2/11*h**5 + 0*h**y + 0*h**4 + 2/11*h = 0.
-1, 0, 1
Let d(b) be the third derivative of 0 + 0*b - 1/45*b**5 + 20*b**2 + 2/9*b**4 - 2/3*b**3. Factor d(t).
-4*(t - 3)*(t - 1)/3
Suppose 0 = -5237*h + 5244*h - 21. Factor -1/3*w**4 + 1/3*w**h + 11/3*w + 3*w**2 + 4/3.
-(w - 4)*(w + 1)**3/3
Let j(z) be the first derivative of 1/2*z + 1/2*z**2 + 1/6*z**3 - 6. Factor j(q).
(q + 1)**2/2
Let a(h) be the second derivative of 49/5*h**3 - 23*h + 0 - 343/5*h**2 - 7/10*h**4 + 1/50*h**5. Factor a(m).
2*(m - 7)**3/5
Find l such that -10*l**3 + 34*l**2 - 523*l - 48*l**2 - 162*l**2 + 324 - 474*l + 259*l = 0.
-9, 2/5
Let f(g) be the first derivative of g**5/20 + 5*g**4/12 + 7*g**3/6 + 3*g**2/2 - 12*g + 22. Let v(b) be the first derivative of f(b). Factor v(p).
(p + 1)**2*(p + 3)
Suppose -10*c + 5*c - d + 2 = 0, 0 = -d + 2. Let 4/3*v**2 + 2*v**3 + 0*v + c*v**4 + 0 - 2/3*v**5 = 0. Calculate v.
-1, 0, 2
Let p = -7 - 2. Let c = p - -15. Factor 4 - 11*q**2 + 6*q - 5 + 8*q**2 + 4 - c*q**3.
-3*(q - 1)*(q + 1)*(2*q + 1)
Suppose -249*f = -256*f + 14. Let t(a) be the first derivative of 0*a**3 + 0*a**4 + 0*a**5 + 0*a**f + 6 - 1/18*a**6 + 0*a. Let t(c) = 0. Calculate c.
0
Suppose -r - h - 1 = 0, -3*r + 5*h + 37 = 8. Factor 2*x**2 - r*x - 2 + 2*x + 2*x - x**2.
(x - 1)*(x + 2)
Let h(v) = v**3 + 28*v**2 + 14*v + 3. Let g be h(0). Solve -8/7*p + 0*p**2 + 2/7*p**g + 0 = 0.
-2, 0, 2
Let p(y) = 5*y**3 + 95*y**2 - 15*y - 75. Let m(f) = -7*f**3 - 145*f**2 + 23*f + 113. Let d(s) = -5*m(s) - 8*p(s). Determine h so that d(h) = 0.
-7, -1, 1
Let a(w) = 6*w + 82. Let u be a(-13). Let d(b) be the third derivative of 1/240*b**6 + 1/120*b**5 + 0*b**3 + 0 + 0*b - 1/24*b**u + 2*b**2. Factor d(k).
k*(k - 1)*(k + 2)/2
Let p be -10 - (3 + -4)*3. Let a be 4 + -1 - (7 + p). Factor 1/3 + 1/6*o**4 + 7/6*o + 5/6*o**a + 3/2*o**2.
(o + 1)**3*(o + 2)/6
Let x(v) be the third derivative of -v**7/1050 - v**6/150 - v**5/75 - 95*v**2 - 3. Factor x(i).
-i**2*(i + 2)**2/5
Let g(u) be the first derivative of -u**6/6 + 9*u**5/5 - 7*u**4/2 - 2*u**3/3 + 15*u**2/2 - 7*u - 148. Find k, given that g(k) = 0.
-1, 1, 7
Suppose -2*i + 21 - 13 = 0. Let t(n) = 3*n - 3. Let b be t(1). Factor 1/2*h**2 - 3/2*h**3 - 1/2*h**5 + 3/2*h**i + 0*h + b.
-h**2*(h - 1)**3/2
Let v(i) = i**3 - 3*i**2 + 4*i - 2. Let w be v(2). Let k(r) = -7*r**3 - r**2. Let l be k(-1). Factor 0*q**4 + 0*q**4 - l*q**3 - 7*q**4 - 3*q**w + 4*q**4.
-3*q**2*(q + 1)**2
Let l(p) be the third derivative of 0 - 1/448*p**8 + 1/140*p**7 + 12*p**2 - 1/160*p**6 + 0*p**5 + 0*p**4 + 0*p + 0*p**3. Find g, given that l(g) = 0.
0, 1
Suppose 0 = g - 3, 5*b = -g - 0*g + 158. Let 12 + 70*y**2 - b*y**2 + 20*y + y - 33*y**2 - 3*y**3 = 0. What is y?
-1, 4
Let p(w) be the first derivative of 5*w**3/6 + 245*w**2/4 - 125*w + 382. Solve p(u) = 0 for u.
-50, 1
Determine d so that -540*d + d**2 + 63 + 0*d**2 + 556*d = 0.
-9, -7
Let t = 128 - 383/3. Let z(n) be the third derivative of 2*n**2 - t*n**3 + 1/5*n**6 - 1/2*n**4 + 0 + 0*n - 1/6*n**5. Factor z(a).
2*(a - 1)*(3*a + 1)*(4*a + 1)
Let z(g) be the second derivative of -g**4/4 + 2*g**3 + 18*g**2 - 3*g + 12. Let z(r) = 0. Calculate r.
-2, 6
Let c be 5/(-6)*9/(-45). Let j = 692 - 1383/2. Factor 1/6*v**4 + j*v**2 + 0 - 1/2*v**3 - c*v.
v*(v - 1)**3/6
Let u be ((40/36)/2)/((-60)/(-72)). Factor 2/3*q**3 + 0 + 2/3*q**4 - u*q**2 - 2/3*q.
2*q*(q - 1)*(q + 1)**2/3
Let y(g) be the second derivative of 7/4*g**5 + 0 + 5/3*g**4 - 11*g + 0*g**2 - 5/2*g**3. Solve y(b) = 0 for b.
-1, 0, 3/7
Let s(z) be the second derivative of 3*z**2 - 13/2*z**3 + 0 - 30*z + 11/4*z**4. Factor s(g).
3*(g - 1)*(11*g - 2)
Let y(p) = -2*p**2 + 66*p + 65. Let j(c) = -5*c**2 + 130*c + 130. Let t(a) = 3*j(a) - 5*y(a). Factor t(g).
-5*(g - 13)*(g + 1)
Let w = 262/2415 - -4/161. Let t(v) be the first derivative of -1 + w*v**5 + 1/6*v**4 - 1/3*v**2 + 0*v - 2/9*v**3. Suppose t(c) = 0. Calculate c.
-1, 0, 1
Let b(f) be the third derivative of -1/15*f**5 + 1/3*f**4 - 1/15*f**6 + 0*f - 1/105*f**7 + f**3 + 18*f**2 + 0. Factor b(k).
-2*(k - 1)*(k + 1)**2*(k + 3)
Let k(l) be the first derivative of -l**3 + 81*l**2 - 2187*l - 68. Factor k(b).
-3*(b - 27)**2
Let h(o) be the first derivative of 7*o**6/10 + 69*o**5/20 + 5*o**4 + 2*o**3 + 12*o - 3. Let r(l) be the first derivative of h(l). Factor r(z).
3*z*(z + 1)*(z + 2)*(7*z + 2)
Let h = 120 + -188. Let f = h - -68. Let 0*l**2 - 3/2*l**5 + 0*l**4 + 0 + f*l + 3/2*l**3 = 0. What is l?
-1, 0, 1
Factor -3224 + 216*z**2 - 44*z**2 - 116*z**2 + 8029 - 5115*z - 5*z**3 + 259*z**2.
-5*(z - 31)**2*(z - 1)
Let k(o) = -o**3 - 27*o**2 - 136*o + 95. Let c be k(-20). Let 75/7*t + 0 + 108/7*t**4 - c*t**2 - 72/7*t**3 = 0. What is t?
-1, 0, 5/6
Let i(r) be the third derivative of r**8/112 + r**7/5 + 11*r**6/40 - 13*r**5/10 - 7*r**2 - 20*r. Let i(y) = 0. What is y?
-13, -2, 0, 1
Let x(t) = t - t**2 + 17 + 7*t - 5 - 3. Let y be x(9). Determine l so that -2/7*l**5 - 4/7*l**3 + 0*l + 0*l**2 + y + 6/7*l**4 = 0.
0, 1, 2
Let w = 21 + -17. Let m be 0 + w/2 + 3. Let -10 + 2*g**5 - 5*g**5 - 3*g**5 + 10*g**2 + g**m - 15*g + 20*g**3 = 0. Calculate g.
-1, 1, 2
Let r(c) be the second derivative of -c**3 - 5*c**2 + 4*c. Let t be r(-3). Factor -3*z**2 - 3*z**2 - 6*z**2 - t*z + 4.
-4*(z + 1)*(3*z - 1)
Factor 575*m**2 + 30417500/3 + 132250*m + 5/6*m**3.
5*(m + 230)**3/6
Let p = 223/3 + -865/12. What is k in -p + 9/4*k**2 + 6*k = 0?
-3, 1/3
Let v(c) be the third derivative of 21*c**2 + 0*c**4 + 0 + 3/80*c**5 - 1/2*c**3 + 0*c - 1/160*c**6. What is j in v(j) = 0?
-1, 2
Let p(j) be the first derivative of 1/18*j**3 + 9 + 0*j + 0*j**4 - 5/2*j**2 - 1/180*j**5. Let z(s) be the second derivative of p(s). Factor z(x).
-(x - 1)*(x + 1)/3
Let z = -47/3 - -16. Let q be (-20)/(-75)*(-15)/(-2). Factor 0*c**3 - 1/3 - z*c**4 + 2/3*c**q + 0*c.
-(c - 1)**2*(c + 1)**2/3
Let o(x) be the second derivative of 0 + 3/16*x**3 + 0*x**4 + 3/8*x**2 - 3/160*x**5 + 12*x. Determine a so that o(a) = 0.
-1, 2
Let s be -22 + 70/3 - 2/(-3). Factor -4/11*v**s + 6/11*v - 2/11*v**5 - 4/11*v**3 + 6/11*v**4 - 2/11.
-2*(v - 1)**4*(v + 1)/11
Factor 900/11 - 56/11*z**2 + 2/11*z**3 + 30*z.
2*(z - 15)**2*(z + 2)/11
Let u = 196253/1587 + 2/529. Let j = 124 - u. Let 2/3*g - 2/3*g**3 - 1/3*g**4 + j*g**2 + 0 = 0. Calculate g.
-2, -1, 0, 1
Let o = -912 - -914. Let g(c) be the second derivative of 2/15*c**6 + 2*c**o - 2/21*c**7 + 2/5*c**5 - 2/3*c**3 + 0 - c - 2/3*c**4. Solve g(m) = 0 for m.
-1, 1
Let m be ((-8)/4)/(-1) - -3. Suppose 0*b = -m*b + 10. Determine f so that -b + f**2 + 2 = 0.
0
Suppose 3*p = 33 - 12. Let t