**4.
-b**3*(b - 1)*(b + 1)/4
Let k(p) be the third derivative of 1/10*p**5 + 0*p - 1/112*p**8 + 0*p**3 + 41*p**2 - 1/35*p**7 + 0*p**6 + 0 + 1/8*p**4. Determine t, given that k(t) = 0.
-1, 0, 1
Let z be ((-24)/(-100))/(12/60). Factor -2/5*g**4 + 0 - 2/5*g - z*g**3 - 6/5*g**2.
-2*g*(g + 1)**3/5
Let m = -29075 - -872363/30. Let o = m - 19/6. Factor o*f**3 + 0 + 0*f - 3/5*f**2.
3*f**2*(f - 1)/5
Let j(d) be the third derivative of 0 + 1/120*d**7 + 0*d - 10*d**2 - 23/480*d**6 + 9/80*d**5 - 13/96*d**4 + 1/12*d**3. Factor j(n).
(n - 1)**3*(7*n - 2)/4
Suppose 6 + 0 = 3*g + 2*f, 4*g + 4*f - 12 = 0. Let h(c) be the third derivative of -7*c**2 + 1/16*c**4 + g*c + 1/6*c**3 + 0 + 1/120*c**5. Solve h(r) = 0.
-2, -1
Let j(s) be the second derivative of 2*s**6/15 + 7*s**5/5 + 3*s**4 - 14*s**3/3 - 20*s**2 + 53*s. What is i in j(i) = 0?
-5, -2, -1, 1
Let h(g) = g**2 + 4*g + 4. Let y be h(-4). Suppose -y*x + 9 = -5*a - 9, x - 6 = 2*a. Let -4/3*q**x - 1/3 + 5/3*q = 0. What is q?
1/4, 1
Let i(o) = o**4 - o**3 + o - 1. Let r(b) = -5*b**4 - 260*b**3 + 3645*b**2 - 10*b + 10. Let u(h) = 10*i(h) + r(h). Let u(f) = 0. Calculate f.
0, 27
Let m = 4478/7763 + -6/1109. Find s such that -m + 8/7*s**5 - 40/7*s**4 - 64/7*s**2 + 74/7*s**3 + 26/7*s = 0.
1/2, 1, 2
Let u(s) be the third derivative of 5*s**8/336 + 5*s**7/42 + s**6/4 + 87*s**2. Suppose u(y) = 0. What is y?
-3, -2, 0
Let n be -7 + (-7680)/(-378) - 12/(-108). Solve -48/7*w**4 - n*w**2 - 44/7*w - 97/7*w**3 - 8/7 - 9/7*w**5 = 0.
-2, -1, -2/3
Let q(f) = -f**3 + 4*f**2 + 2*f - 2. Let u be q(4). Suppose -u*c + 10 = -14. Factor -2*m**2 - m**3 - 5*m**5 + 264*m + 8*m**c - 264*m.
-m**2*(m - 1)**2*(5*m + 2)
Let v(k) = 20*k + 1. Let i be v(-1). Let g = -13 - i. What is x in -g*x**3 + x**3 - 78*x - 40*x**2 + 2*x**3 - 36 - 3*x**3 = 0?
-3, -2/3
Let u(p) = -20*p**3 - 443*p**2 - 126*p + 22. Let g(d) = -4*d**3 - 89*d**2 - 25*d + 4. Let f(z) = 22*g(z) - 4*u(z). Suppose f(l) = 0. Calculate l.
-23, -1/4, 0
Let i(n) be the third derivative of n**7/1365 + n**6/260 - 3*n**5/130 + 5*n**4/156 - 2*n**2 - 52. Factor i(b).
2*b*(b - 1)**2*(b + 5)/13
Let d = 51 - 23. Suppose d*w**2 - 13*w**2 - 14*w**2 = 0. Calculate w.
0
Let -387/5*h - 3/5*h**3 - 198/5*h**2 - 192/5 = 0. Calculate h.
-64, -1
Let j(c) be the second derivative of -1/20*c**5 + 4*c - 1/120*c**6 - 1/8*c**4 - c**3 + 0 + 0*c**2. Let o(f) be the second derivative of j(f). Factor o(i).
-3*(i + 1)**2
Suppose 0 = 49*p - 43*p - 36. Let w(h) be the second derivative of 3/70*h**5 + 1/98*h**7 - 3/70*h**p + 0*h**2 + 0*h**4 + 2*h + 0 + 0*h**3. Factor w(d).
3*d**3*(d - 2)*(d - 1)/7
Factor 1 - 4*z + 1/2*z**4 - 11/4*z**3 + 21/4*z**2.
(z - 2)**2*(z - 1)*(2*z - 1)/4
Let b(l) = -12*l**2 + 206*l + 6036. Let i(h) = h**2 + h + 1. Let r(z) = -2*b(z) - 28*i(z). Factor r(w).
-4*(w + 55)**2
Suppose -211*b + 502 = 40*b. Factor 0 + 2/3*t**3 + 1/3*t**4 - t**b + 0*t.
t**2*(t - 1)*(t + 3)/3
Let x(c) = 8*c**2 - 45*c. Let t(z) be the third derivative of z**5/15 - 11*z**4/12 + 3*z**2. Let u(r) = 5*t(r) - 2*x(r). What is v in u(v) = 0?
0, 5
Let o(w) be the third derivative of 2*w - 6*w**2 + 2/3*w**4 - 7/30*w**6 + 0*w**3 + 0 - 4/5*w**5. Solve o(p) = 0.
-2, 0, 2/7
Let s(t) = 8*t**3 + 28*t**2 + 52*t + 4. Let y(c) = -15*c**3 - 56*c**2 - 103*c - 7. Let v(m) = 7*s(m) + 4*y(m). Find a such that v(a) = 0.
-4, -3, 0
Suppose -v - 3*n = -n + 5, -5*v = 2*n - 7. Let p(z) be the first derivative of -9/2*z**2 - 3/4*z**4 + 9 + v*z + 3*z**3. Factor p(c).
-3*(c - 1)**3
Suppose -2*c = -13*c + 528. Let d be c/(-78)*(-3)/12*1. Factor 0 - 2/13*f + d*f**2.
2*f*(f - 1)/13
Let s = 379/17 - 1120/51. Find d such that d**3 - d + 1/3*d**2 - s = 0.
-1, -1/3, 1
Let k(l) be the first derivative of -l**6/8 - 9*l**5/5 + 81*l**4/16 - 7*l**3/2 + 4. Factor k(y).
-3*y**2*(y - 1)**2*(y + 14)/4
Let n(q) be the third derivative of q**8/672 - q**7/840 - q**6/40 + 11*q**5/120 - 7*q**4/48 + q**3/8 - q**2 - 18*q. Factor n(x).
(x - 1)**3*(x + 3)*(2*x - 1)/4
Let f(g) be the first derivative of -3*g**5 + 3*g**4/2 + 5*g**3 - 3*g**2 + 130. Factor f(m).
-3*m*(m - 1)*(m + 1)*(5*m - 2)
Let u(x) be the third derivative of 0*x**3 + 0 + 18*x**2 - 2/15*x**6 + 8/105*x**7 + 1/15*x**5 + 0*x**4 + 0*x. Let u(z) = 0. What is z?
0, 1/2
Let d(k) be the third derivative of k**10/30240 + k**9/12096 - k**8/2016 + k**5/15 - 3*k**2. Let b(i) be the third derivative of d(i). Factor b(h).
5*h**2*(h - 1)*(h + 2)
Let x be 62/48 - (-570)/(-912). Factor 8/3*r + x*r**2 + 2.
2*(r + 1)*(r + 3)/3
Solve 6*u**3 - 5/2*u**5 - 7/2*u - 5*u**2 + 3 + 2*u**4 = 0.
-6/5, -1, 1
Let x be 349/(-4) - (-1)/((-9)/(-36)). Let b = x + 90. Solve -9/2*z + b + 3/4*z**2 = 0 for z.
3
Let w(x) = 2*x - 21. Let o be w(12). Let a(k) = k**2 + 3*k + 5. Let r(q) = -3*q**2 - 7*q - 11. Suppose b - 7 = -0*b. Let z(l) = b*a(l) + o*r(l). Factor z(y).
-2*(y - 1)*(y + 1)
Let t(l) be the first derivative of -l**6/15 + 2*l**5/25 + l**4/5 - 4*l**3/15 - l**2/5 + 2*l/5 - 145. Factor t(q).
-2*(q - 1)**3*(q + 1)**2/5
Let q(l) = -11*l**2 + 16*l + 6. Let o(k) = -34*k - 16*k - 23 + 45*k**2 - 15*k - 2. Let h(f) = -6*o(f) - 25*q(f). Find i such that h(i) = 0.
0, 2
Find v, given that 1/2*v**5 + 1/2*v**4 + 1/2 - v**3 - v**2 + 1/2*v = 0.
-1, 1
Let k(j) be the second derivative of j**9/6048 - j**8/336 + j**7/63 + 5*j**4/6 + 21*j. Let s(x) be the third derivative of k(x). Let s(o) = 0. Calculate o.
0, 4
Let s(z) = -z + 4. Let v be s(4). Suppose 4*g - 6*g + 8 = v. Factor 0 - 2/13*j**5 + 4/13*j**3 + 0*j**g + 0*j**2 - 2/13*j.
-2*j*(j - 1)**2*(j + 1)**2/13
Let z(l) = l**2 - 11*l - 32. Let i be z(13). Let r be (i/(-9))/(2/6). Solve -1/5*n**r - 1/5 - 2/5*n = 0.
-1
Let o(g) be the second derivative of -g**8/10080 - g**7/630 - g**6/120 + 7*g**4/6 + 3*g. Let m(x) be the third derivative of o(x). Factor m(p).
-2*p*(p + 3)**2/3
Let x(k) be the third derivative of -k**6/160 + k**5/80 + 3*k**4/16 + 36*k**2 + 3*k. Factor x(d).
-3*d*(d - 3)*(d + 2)/4
Factor 39 + 7 - 54*l + 2*l**2 - 27 + 33.
2*(l - 26)*(l - 1)
Factor 58/19*m - 2/19*m**2 - 156/19.
-2*(m - 26)*(m - 3)/19
Let d = -15180 + 15182. Find z, given that -2/5*z**d - 6/5*z + 0 = 0.
-3, 0
Let d(r) = 0*r**2 + 3*r - 8 - 7*r**2 - 3*r. Let y(t) = -3*t**2 - 4. Let i(w) = 4*d(w) - 9*y(w). Factor i(z).
-(z - 2)*(z + 2)
Let x(s) = 4*s - 3. Let z be x(2). Factor 0*p**z + 3*p**5 + 2*p**3 - 7*p**3 + 2*p**3.
3*p**3*(p - 1)*(p + 1)
Suppose 0*b - 3*b + 2 = -5*f, -5*f = -b + 4. Let o be f - ((-6)/(-2) + -49). Suppose -22*k**4 + 7*k**2 + o*k**2 + 11*k**4 - 25*k**4 - 16 = 0. Calculate k.
-1, -2/3, 2/3, 1
Let s(j) be the first derivative of -j**6/30 - 14*j**5/25 - 9*j**4/5 - 34*j**3/15 - 11*j**2/10 - 110. Factor s(v).
-v*(v + 1)**3*(v + 11)/5
Let b be (-27234)/110 + (6/(-10) - -1). Let f = -247 - b. Find u such that 0 + f*u**2 + 4/11*u = 0.
-2, 0
Suppose 2 = -f - o, -4*f + 3*o = f - 30. Factor -3315*y + 9*y**2 - 25*y**2 + 4*y**f + 3327*y.
4*y*(y - 3)*(y - 1)
Let w(o) = -o - 6. Let s be w(-10). Solve 37*u**2 + 35*u**2 - 68*u**2 + s*u = 0.
-1, 0
Factor 6 + 16*k + 5*k**2 - 5*k**2 + 4*k**2 + 6.
4*(k + 1)*(k + 3)
Let h(r) be the third derivative of r**6/200 + 267*r**5/100 + 23763*r**4/40 + 704969*r**3/10 + 2*r**2 + 3. Factor h(c).
3*(c + 89)**3/5
Let d(i) be the first derivative of 128*i**4/3 - 64*i**3/3 + 4*i**2 - i/3 - 53. Let d(c) = 0. What is c?
1/8
Let i be (-10)/650*-13*(-15)/(-6). Suppose 0 = -4*z + 2*z. Suppose 0 - i*t**4 + z*t**2 + 0*t**3 + 0*t + 1/4*t**5 = 0. Calculate t.
0, 2
Let i(d) = 170*d**4 + 1315*d**3 - 595*d**2 - 7200*d + 2715. Let j(n) = -19*n**4 - 146*n**3 + 66*n**2 + 800*n - 302. Let r(q) = -6*i(q) - 55*j(q). Factor r(h).
5*(h - 2)*(h + 4)**2*(5*h - 2)
Factor 2/7*x**4 + 0*x + 0 + 22/7*x**3 - 52/7*x**2.
2*x**2*(x - 2)*(x + 13)/7
Factor 0*a + 11/4*a**3 + 0 + 1/4*a**4 - 3*a**2.
a**2*(a - 1)*(a + 12)/4
Let x(m) be the second derivative of 1/45*m**6 - 9*m + 1/3*m**2 - 1/63*m**7 - 1/9*m**3 + 1/15*m**5 - 1/9*m**4 + 0. What is j in x(j) = 0?
-1, 1
Let r = 73 - 79. Let n be (18/(-14))/(-3)*(-4)/r. Find v such that -n*v**2 - 8/7 - 8/7*v = 0.
-2
Suppose 0 = p - 4*k - 26, -9*p + 7*p - 4*k = -64. Let x be 2/(-4)*(-12)/p. Factor -1/5 + 1/5*g - x*g**3 + 1/5*g**2.
-(g - 1)**2*(g + 1)/5
Let f(r) = -2*r**3 + r**2 + r. Let z(a) be the first derivative of -a**3/3 + a**2/2 + 3. Let g(q) = f(q) - 3*z(q). What is y in g(y) = 0?
0, 1
