. Factor k(z).
5*(z + 2)*(2*z - 1)/3
Let h(s) be the first derivative of 5*s**3/3 + 5*s**2 - 75*s + 137. Solve h(f) = 0.
-5, 3
Let j(c) = -c**2 - c. Let m(b) = -25*b**2 + 15*b - 30. Let u(q) = -20*j(q) + m(q). Suppose u(i) = 0. What is i?
1, 6
Let m(t) be the second derivative of t**8/2100 - t**7/1050 + 7*t**3/3 + 20*t. Let z(j) be the second derivative of m(j). Factor z(c).
4*c**3*(c - 1)/5
Suppose -5*m - 5004 = 4*j, -6*m + 4*j - 2996 = -3*m. Let i be 5/(m/32)*15/(-2). Let 6/5*p**2 + 0 - i*p**4 - 2/5*p**5 - 2/5*p**3 + 4/5*p = 0. Calculate p.
-2, -1, 0, 1
Factor -3/4 - 5/4*d**2 + 1/4*d**3 + 7/4*d.
(d - 3)*(d - 1)**2/4
Let a(w) = 5*w**3 - 89*w**2 + 1058*w + 3. Let u(m) = -16*m**3 + 266*m**2 - 3174*m - 10. Let s(y) = -10*a(y) - 3*u(y). Factor s(o).
-2*o*(o - 23)**2
Let w(n) = 12*n**3 + 9*n**2 + 22*n + 5. Let l(i) = -5*i**3 - 5*i**2 - 11*i - 3. Let a(j) = -5*l(j) - 2*w(j). Determine k so that a(k) = 0.
-5, -1
Let r(z) be the second derivative of -z**4/7 - 20*z**3/21 - 6*z**2/7 + 24*z. Factor r(p).
-4*(p + 3)*(3*p + 1)/7
Let z(t) = -12*t**3 - 120*t**2 - 76*t. Suppose 5*v - 160 = -0*v. Let u(x) = 10*x**2 + x**3 + 5*x**2 + 7*x - 4*x**2. Let p(i) = v*u(i) + 3*z(i). Factor p(q).
-4*q*(q + 1)**2
Suppose 4*z + 318 = 330. Let w(b) be the second derivative of -19/66*b**4 + 0 + 7/110*b**5 + 0*b**2 + 4*b - 2/11*b**z. Factor w(m).
2*m*(m - 3)*(7*m + 2)/11
Suppose c = -3*c. Suppose r + 0*r - 5*x + 2 = 0, c = -2*r - 3*x + 9. Suppose -2*a**5 + 2*a**5 + r*a**3 + 3*a**4 + 3*a**5 + 3*a**4 = 0. What is a?
-1, 0
Factor 6875 - w**2 - 31*w - 6945 - 6*w.
-(w + 2)*(w + 35)
Let r(o) be the third derivative of o**6/360 + o**5/45 - 2*o**4/9 - 32*o**3/9 + 2*o**2 + 13. Find i such that r(i) = 0.
-4, 4
Let t(z) = -7*z**2 - 14*z - 23. Let i(v) be the third derivative of -v**5/60 + v**4/24 + v**3/6 - 9*v**2. Let a(h) = 4*i(h) - t(h). Find l such that a(l) = 0.
-3
Let t(y) be the third derivative of 14*y**2 + 0*y**3 + 1/20*y**5 + 0 + 0*y + 1/40*y**6 + 1/210*y**7 + 1/24*y**4. Solve t(w) = 0.
-1, 0
Let h(f) be the first derivative of f**5/30 - f**4/24 - 7*f**3/18 + f**2/12 + f + 37. Solve h(s) = 0.
-2, -1, 1, 3
Let l(w) = w + 3. Let i be l(-3). Let b(c) = -c**2 + 30*c - 204. Let r be b(11). Let 8/5*q**r - 2/5*q**3 + 0 + 0*q**2 + 0*q**4 + i*q = 0. Calculate q.
-1/2, 0, 1/2
Find y, given that 0 - 16/5*y - 12/5*y**2 - 2/5*y**3 = 0.
-4, -2, 0
Let m(o) be the second derivative of o**5/20 + 2*o**4/3 + o**3/6 + 4*o**2 + o. Let l be m(-8). Factor 6*g + l + 9 + 2*g**2 - g**2.
(g + 3)**2
Suppose -3/5*x**4 + 6/5*x**3 + 36/5 + 21/5*x**2 - 12*x = 0. Calculate x.
-3, 1, 2
Let z(b) = 4*b**4 - 5*b**3 + 9*b**2 + 43*b + 22. Let c(h) = 5*h**4 - 4*h**3 + 10*h**2 + 44*h + 21. Let q(o) = -3*c(o) + 4*z(o). What is y in q(y) = 0?
-1, 5
Let k = 3/6446 + 206263/19338. Find a such that 52*a**2 + k*a**3 + 98/3 + 2/3*a**4 + 224/3*a = 0.
-7, -1
Let a(v) be the second derivative of 3*v**5/20 - 21*v**4 + 882*v**3 + 4*v - 12. Factor a(h).
3*h*(h - 42)**2
Let m(q) be the second derivative of -5*q**4/12 - 5*q**3/3 - 3*q + 2. Suppose m(a) = 0. Calculate a.
-2, 0
Let g(r) = -2*r**3 - 19*r**2 + 5*r + 7. Let s(x) = -x**3 - 22*x**2 + 5*x + 6. Let k(z) = 4*g(z) - 3*s(z). Solve k(y) = 0.
-2, -1, 1
Let c = -809 - -812. Factor 2/5 - n + 2/5*n**2 - 4/5*n**4 + 4/5*n**c + 1/5*n**5.
(n - 2)*(n - 1)**3*(n + 1)/5
Let p be (16/28*-1)/((-18)/35). Factor -4/3*k**2 + 2/9*k**3 + 0 + p*k.
2*k*(k - 5)*(k - 1)/9
Let s(n) be the third derivative of 0 - 1/30*n**6 + 11*n**2 + 1/168*n**8 + 1/105*n**7 + 0*n**3 + 0*n**5 + 0*n + 0*n**4. Determine z so that s(z) = 0.
-2, 0, 1
Let k = 924 - 4608/5. Factor 8/5*l + 0 + 4/5*l**3 - k*l**2.
4*l*(l - 2)*(l - 1)/5
Let n(c) be the first derivative of 8/5*c**3 + 10 + 0*c + 18/5*c**2 + 1/5*c**4. Suppose n(b) = 0. What is b?
-3, 0
Let u = -41 - -43. Let r(d) be the second derivative of 0 - 1/8*d**4 + 1/40*d**5 + 0*d**u - 2*d + 1/6*d**3. Factor r(v).
v*(v - 2)*(v - 1)/2
Let r(y) = -y**3 + 8*y**2 + 53*y - 393. Let g be r(9). What is c in c**g + 1/2*c**4 + 2 - 2*c - 3/2*c**2 = 0?
-2, 1
Let a(s) be the first derivative of 4*s**3/3 + 2*s**2 - 111. Factor a(i).
4*i*(i + 1)
Let i = -9310 + 19229/2. Let r = i + -304. Factor r*u**4 + 0*u + 0 - u**3 + 1/2*u**2.
u**2*(u - 1)**2/2
Let k(x) be the third derivative of 12*x**3 - 3*x**2 + 4*x + 0 - x**4 + 1/30*x**5. Solve k(r) = 0.
6
Let r be 3/(-2)*(-84)/9. What is h in h**2 + 0*h**2 - h**5 + 5*h**4 - 20*h**4 + r*h**4 + h**3 = 0?
-1, 0, 1
Let d = 2744/5 - 548. Find z such that -2/5*z**2 - d*z + 6/5 = 0.
-3, 1
Let b(j) be the first derivative of -2*j**3/9 - 10*j**2/3 - 50*j/3 - 75. Solve b(g) = 0 for g.
-5
Let m(c) be the first derivative of 6*c**7/35 + 22*c**6/75 + 2*c**5/25 - 2*c + 25. Let k(f) be the first derivative of m(f). Factor k(a).
4*a**3*(a + 1)*(9*a + 2)/5
Solve 2/11*c**3 - 2/11*c**5 + 0*c + 0 + 80/11*c**2 - 80/11*c**4 = 0.
-40, -1, 0, 1
What is l in 108/7 - 6/7*l**2 + 18/7*l = 0?
-3, 6
Let z be 12/(-9) - (88/(-12) + 2). Determine t, given that -8/11*t**z - 4/11*t**2 + 14/11*t**3 + 0 - 2/11*t = 0.
-1/4, 0, 1
Let f(l) = l**2 - 7*l - 3. Let q be f(15). Let c = q - 114. Find h such that -14/5*h**c - 42/5*h**4 + 34/5*h**2 + 8/5 + 32/5*h - 18/5*h**5 = 0.
-1, -2/3, 1
Let d(u) be the first derivative of -2*u**4 + 10*u**3 - 19*u**2/2 + 3*u + 224. Find t such that d(t) = 0.
1/4, 1/2, 3
Suppose 2*g = c - 4, 5*g - 12 = -0*c - 3*c. Factor 3*t**c + 3*t + 5*t**3 + 41 + 9*t**2 - 41 + 4*t**3.
3*t*(t + 1)**3
Let a = -94 + 118. Let h(y) = -y + 29. Let p be h(a). Let 2*i**p + 0 - 4/7*i**2 - 2*i**3 + 4/7*i**4 + 0*i = 0. What is i?
-1, -2/7, 0, 1
Let l(d) be the third derivative of -1/20*d**4 + 1/150*d**5 + 0 + 0*d**3 + d**2 + 0*d. Factor l(o).
2*o*(o - 3)/5
Let g = 32 + -29. Let -1062*i**4 + 1065*i**4 + 2*i**g - 21*i**2 + 18 - 3*i + i**3 = 0. Calculate i.
-3, -1, 1, 2
Suppose -2*t + 28 - 4 = 0. Let n = 12 - t. Let -2/3*r + n - 1/3*r**2 = 0. Calculate r.
-2, 0
Let a(r) be the second derivative of r**6/150 + 7*r**5/100 - 13*r**4/10 + 827*r. Factor a(j).
j**2*(j - 6)*(j + 13)/5
Let k(u) be the first derivative of 3/2*u**2 - 10/9*u**3 + 11 + 1/3*u. Find i, given that k(i) = 0.
-1/10, 1
Factor 19/4*y**2 - 16*y + 1/4*y**3 + 11.
(y - 2)*(y - 1)*(y + 22)/4
Let o(q) be the third derivative of -q**6/120 - q**5/20 + 2*q**4/3 - 2*q**3 + 6*q**2 - q. Factor o(r).
-(r - 2)*(r - 1)*(r + 6)
Let r(z) be the second derivative of -z**7/189 + 11*z**6/135 - 4*z**5/15 - 2*z**4/3 - 2*z + 53. Factor r(g).
-2*g**2*(g - 6)**2*(g + 1)/9
Let o = -793 + 7141/9. Let 0*m - 2/9*m**3 + 0*m**2 + o*m**4 - 2/9*m**5 + 0 = 0. What is m?
0, 1
Let m(i) be the first derivative of 2*i**3/3 + 249*i**2 - 500*i + 1015. Factor m(l).
2*(l - 1)*(l + 250)
Let t = -240 + 240. Let h = 9 + -44/5. Determine a, given that h*a**2 + 0*a + t = 0.
0
Let m be ((-1)/(-7) - 3)/(2/(-7)). Suppose 3*d = 8*d - m. Factor -9/5*y**d + 3/5*y + 0.
-3*y*(3*y - 1)/5
Determine z, given that 0*z**2 - 1/3 - 1/6*z**3 + 1/2*z = 0.
-2, 1
Suppose 3 = 3*z - 6. Factor 92 - 36*t + 70 - 2*t**2 + t**2 + z*t**2.
2*(t - 9)**2
Let a(b) be the first derivative of -5*b**4/2 + 172*b**3/3 - 17*b**2 + 435. Factor a(o).
-2*o*(o - 17)*(5*o - 1)
Let v be (-2)/27*3 + 160/180. Let f(g) be the first derivative of g**2 - 2/3*g + 1/6*g**4 - v*g**3 - 2. Factor f(l).
2*(l - 1)**3/3
Let r(p) be the second derivative of p**6/420 - p**5/105 + p**4/84 + 3*p**2/2 + 16*p. Let o(l) be the first derivative of r(l). Let o(m) = 0. Calculate m.
0, 1
Let v(z) = 3*z**5 + z**4 - 5*z**3 - 3*z**2 - 2*z. Let a(o) = 30*o**5 + 9*o**4 - 51*o**3 - 30*o**2 - 21*o. Let f(l) = -2*a(l) + 21*v(l). Factor f(i).
3*i**2*(i - 1)*(i + 1)**2
Let s(p) be the first derivative of -13 + p**2 + 1/3*p**3 + 0*p. Factor s(x).
x*(x + 2)
Let o(l) be the second derivative of -l**5/20 + 5*l**4/6 - 13*l**3/6 - 12*l**2 + 6*l + 8. What is d in o(d) = 0?
-1, 3, 8
Let z(g) be the first derivative of g**6/42 + 6*g**5/35 + g**4/14 - 12*g**3/7 - 27*g**2/14 + 54*g/7 - 53. What is f in z(f) = 0?
-3, 1, 2
Let l = -13 + 13. Suppose l = 4*h - 5*b - 21, 5*h - b - 1 = 20. Let -3*w**4 + 5*w**3 - 6*w**2 + 2*w + w**4 + h*w**3 - 3*w**3 = 0. Calculate w.
0, 1
Determine a so that 0 + 0*a - 2/7*a**3 + 74/7*a**2 = 0.
0, 37
Let a(i) be the third derivative of -i**6/120 + 3*i**5/40 - i**4/4 + 7*i**3/6 - 4*i**2. Let y(p) be the first derivative 