. Let u(m) = 0. Calculate m.
0, 1
Let c(o) = o**2 + 4*o - 1. Let h(p) = p + 17. Let j be h(-13). Let d be c(j). Factor 4*k**5 - 4*k**2 + 4*k**4 - 35*k**3 + 0*k**4 + d*k**3.
4*k**2*(k - 1)*(k + 1)**2
Let d(z) = z**2 - 3*z - 7. Let b be d(5). Determine x, given that -3*x**2 + x**b - 7 - 4*x**3 + 7 = 0.
-1, 0
Let o(l) be the second derivative of -3*l**5/80 - 3*l**4/2 + 25*l**3/8 - 461*l. Suppose o(i) = 0. What is i?
-25, 0, 1
Let c(x) = 6*x**2 - 54*x. Let d be c(9). Find h, given that 0 + 18/7*h**4 + 0*h**2 + 4/7*h**3 + 2*h**5 + d*h = 0.
-1, -2/7, 0
Let z(w) be the third derivative of w**11/1829520 - w**10/277200 + 11*w**5/12 + 15*w**2. Let r(v) be the third derivative of z(v). Let r(s) = 0. What is s?
0, 3
Let i(d) be the first derivative of 6*d**5/55 + 7*d**4/11 + 40*d**3/33 + 8*d**2/11 - 147. Let i(a) = 0. Calculate a.
-2, -2/3, 0
Let v = 3/326 + 16279/2282. Let z = v - 93/14. Suppose b + z + 1/2*b**2 = 0. Calculate b.
-1
Suppose -5*q = -w - 9 - 5, 4*w + 10 = -3*q. Let a(z) be the first derivative of -2*z**q + 4 + z**4 + 0*z - 4/3*z**3 + 4/5*z**5. Find k, given that a(k) = 0.
-1, 0, 1
Let z be (-294)/56 - (-2)/8. Let y = -1 - z. Factor 3*p**3 + 2*p**5 + 2*p**4 - 4*p**5 - p**3 + 2*p**2 - 4*p**y.
-2*p**2*(p - 1)*(p + 1)**2
Let h be (-5 + -1 + 3)*21. Let u = h - -65. Factor 8/7 + 2/7*g**3 - 6/7*g**u + 0*g.
2*(g - 2)**2*(g + 1)/7
Let j(g) be the third derivative of g**8/50400 + g**7/12600 - g**6/900 - 3*g**5/4 - 11*g**2. Let n(i) be the third derivative of j(i). Factor n(z).
2*(z - 1)*(z + 2)/5
Let d(y) = 6*y - 113. Let k be d(20). Let t(s) be the first derivative of 1/5*s**2 - 2/15*s**3 + 0*s + k. Factor t(q).
-2*q*(q - 1)/5
Let s(h) be the first derivative of 4*h**3/3 + 2*h**2 - 48*h + 7. Factor s(y).
4*(y - 3)*(y + 4)
Let u(v) be the first derivative of 2*v**5/5 - 304*v**4 + 92416*v**3 - 14047232*v**2 + 1067589632*v - 50. Suppose u(t) = 0. Calculate t.
152
Factor 3*o**3 - 24*o**2 + 20*o**2 - 16*o**4 + 17*o**4.
o**2*(o - 1)*(o + 4)
Factor -6/7*d - 44/21 + 2/21*d**2.
2*(d - 11)*(d + 2)/21
Factor 33 - 31 - 38 - 3*u**2 + 24*u.
-3*(u - 6)*(u - 2)
Let k be (-4 - -4)/(-2) - 26. Let r = k + 138/5. Find z, given that r*z**4 - 8/5*z**3 - 2/5*z**5 - 4/5*z**2 - 4/5 + 2*z = 0.
-1, 1, 2
Let u(r) be the third derivative of 0*r + 1/3*r**4 + 1/45*r**5 + 0*r**3 + 0 + 5*r**2. Suppose u(p) = 0. What is p?
-6, 0
Let y be 3*(26/(-6) + 2). Let f(o) = -o + 10. Let s be f(y). Factor -19*l**4 - 3*l + 4*l**3 + s*l**4 - l + 2.
-2*(l - 1)**3*(l + 1)
Let d be (-404)/(-84) - (8 - 7)*2/14. Factor -1/3*q**2 - 49/3 + d*q.
-(q - 7)**2/3
Suppose 63/10*j - 18/5*j**4 - 2/5*j**5 - 69/10*j**3 + 9/5 + 14/5*j**2 = 0. What is j?
-6, -3, -1/2, 1
Let w(c) be the first derivative of -14*c**3/15 - 2*c**2/5 + 2*c + 194. Factor w(o).
-2*(o + 1)*(7*o - 5)/5
Let n(h) be the third derivative of -h**6/540 + 58*h**5/135 + 206*h**2 - 2*h. Suppose n(q) = 0. What is q?
0, 116
Suppose -k - 7*d + 5*d = -70, 2*d = 5*k - 362. Let g be (-3)/(-2)*32/k. Factor 10/3*t - g*t**2 - 8/3.
-2*(t - 4)*(t - 1)/3
Let g = -11/733 - -64156/25655. Let b = g + -16/7. Solve -b*y + 1/5 - 2/5*y**2 + 2/5*y**3 + 1/5*y**4 - 1/5*y**5 = 0.
-1, 1
Suppose 0*u - 5*u = 3*g + 2, -g = -5*u + 14. Find n such that 10/9*n**3 + 2/9*n + 16/3*n**5 - 76/9*n**4 + 16/9*n**u + 0 = 0.
-1/4, -1/6, 0, 1
Find g, given that 1/3*g**2 - 7/3 - 9/2*g = 0.
-1/2, 14
Let r(y) be the first derivative of -15/28*y**4 + 0*y + 2/7*y**3 + 16 + 9/35*y**5 + 0*y**2. Factor r(k).
3*k**2*(k - 1)*(3*k - 2)/7
Let l(c) be the third derivative of -11*c**6/180 - 31*c**5/90 - 29*c**4/36 - c**3 - 292*c**2. Factor l(p).
-2*(p + 1)**2*(11*p + 9)/3
Let i(o) = -2*o**2 - 271*o + 66. Let s(c) = -c**2 - 90*c + 22. Let h(m) = 3*i(m) - 10*s(m). Find f such that h(f) = 0.
-22, 1/4
Suppose -a - a = 26. Let i(j) = -j**3 - 14*j**2 - 12*j + 16. Let o be i(a). Factor -12*q**3 + 4*q + 2*q + 33*q**2 + o*q.
-3*q*(q - 3)*(4*q + 1)
Let u be (-30*(-2)/120)/(3 + -1). Factor -5/2*d**2 + 3/2*d**3 + 3/4*d**4 - u*d**5 - 21/4*d - 9/4.
-(d - 3)**2*(d + 1)**3/4
Let v(w) be the first derivative of 2*w**5/45 - w**4/3 - 8*w**3/27 + 8*w**2/3 + 20. Suppose v(n) = 0. What is n?
-2, 0, 2, 6
Let o(q) be the first derivative of -4/7*q**2 + 6 - 2/21*q**3 - 6/7*q. Factor o(d).
-2*(d + 1)*(d + 3)/7
Suppose p + 5 = -4*p. Let y be 2 - -1 - (-1 + p/(-1)). Solve -a**y + 1/2*a + 0*a**2 + 0 + 1/2*a**5 + 0*a**4 = 0.
-1, 0, 1
Let b(y) = -y**3 + 8*y**2 + 5*y - 7. Let v be b(6). Suppose 6*c - 4*g = c + v, -c + 5 = 2*g. Find w such that c*w**2 + 9*w**2 - 5*w - 10*w**3 - 3*w = 0.
0, 2/5, 2
Let y be ((-1)/((-5)/10))/6. Let w(v) be the second derivative of -1/18*v**3 + 1/12*v**4 + 0 - y*v**2 + 1/60*v**5 + 2*v - 1/90*v**6. Factor w(t).
-(t - 2)*(t - 1)*(t + 1)**2/3
Let j(t) be the third derivative of -4/105*t**7 + 0*t**4 + 0*t**5 - 6*t**2 + 1/30*t**6 + 1/84*t**8 + 0 + 0*t**3 + 0*t. Factor j(a).
4*a**3*(a - 1)**2
Let a(n) = -8*n**4 - 45*n**3 - 267*n**2 - 699*n - 645. Let f(x) = -2*x**4 - x**3 + x**2 + x + 1. Let k(s) = 2*a(s) - 6*f(s). Factor k(m).
-4*(m + 3)**3*(m + 12)
Let u(o) be the third derivative of -o**8/13440 + o**6/120 - o**5/10 - 21*o**2. Let h(r) be the third derivative of u(r). Determine s so that h(s) = 0.
-2, 2
Let w be ((-1 - 2)/(-6))/((-7)/(-42)). Factor 0*u + 6*u - 6*u - 15*u**2 - 6*u - 3*u**4 - 12*u**w.
-3*u*(u + 1)**2*(u + 2)
Let u(w) be the third derivative of -2*w**7/105 - w**6/6 + 22*w**5/15 - 8*w**4/3 + 428*w**2. Determine d, given that u(d) = 0.
-8, 0, 1, 2
Let z be (((-48)/4)/(-6))/((-4)/18). Let v be 2 + (57/z - -5). Factor 0*c + 0 - v*c**3 + 2/9*c**5 - 4/9*c**2 + 0*c**4.
2*c**2*(c - 2)*(c + 1)**2/9
Determine x, given that -242/9*x**2 - 32/9 + 176/9*x = 0.
4/11
Let b(j) be the first derivative of -1/3*j**2 + 0*j - 32/15*j**5 - 5/9*j**6 - 3*j**4 - 16/9*j**3 + 55. Factor b(v).
-2*v*(v + 1)**3*(5*v + 1)/3
Suppose -3*s + y + 8 = -y, 5*s = -2*y + 8. Factor 4*g**s - g**4 - 5*g**2 - 2*g**3 - g**4 + g**4.
-g**2*(g + 1)**2
Let q(x) be the first derivative of -2*x**4/3 - 814*x**3/9 - 3434*x**2 + 1734*x - 32. Factor q(b).
-2*(b + 51)**2*(4*b - 1)/3
Let t = -712 - -715. Let v(k) be the first derivative of -1/4*k**2 + k - 1/6*k**t + 11. Factor v(w).
-(w - 1)*(w + 2)/2
Let n(y) = 10*y - 28. Let j be n(3). Let v(p) = -p**2 - 6*p. Let f be v(-5). Suppose f*s**2 + 2*s**4 + j*s - 7*s**4 - s + 3*s**5 - 3*s - s**3 = 0. What is s?
-1, 0, 2/3, 1
Let k(c) = -4*c**5 - 17*c**4 + 13*c**3 + 17*c**2 - 9*c. Let a(n) = n**5 + 4*n**4 - 3*n**3 - 4*n**2 + 2*n. Let g(z) = 9*a(z) + 2*k(z). Let g(m) = 0. What is m?
-2, -1, 0, 1
Let -4*v**4 - 16/7*v**2 + 0 + 0*v - 6/7*v**5 - 38/7*v**3 = 0. What is v?
-8/3, -1, 0
Factor 5*m**2 + 2*m - 4 + 13*m**2 - 8*m**2 - 8*m**2.
2*(m - 1)*(m + 2)
Let p(b) be the second derivative of -3/5*b**5 - 13/9*b**4 + 0 + 3/7*b**7 - b**3 + 3/5*b**6 - 1/3*b**2 - 40*b. Suppose p(z) = 0. Calculate z.
-1, -1/3, 1
Find u such that -143/3*u**2 + 32*u + 256/3 - 1/6*u**4 + 11/2*u**3 = 0.
-1, 2, 16
Let i = 10971 + -10969. Factor 1/8*g**3 + 0 - 3/8*g**i + 1/4*g.
g*(g - 2)*(g - 1)/8
Suppose 3*w - 3*g + 0*g = -9, -15 = -3*g. Factor m**w - 2218 + 2218 - 11*m.
m*(m - 11)
Let l(k) be the second derivative of -120*k**5/7 - 20*k**4/7 - k**3/7 - 733*k. Find n, given that l(n) = 0.
-1/20, 0
Let t(q) be the second derivative of q**5/30 + 29*q**4/6 + 841*q**3/3 + 24389*q**2/3 - 54*q. Factor t(d).
2*(d + 29)**3/3
Let a = -5266/3 + 1756. Factor -1/3*b - a*b**2 + 2/3 + 1/3*b**3.
(b - 2)*(b - 1)*(b + 1)/3
Let l(b) be the third derivative of b**8/420 + b**7/210 - 7*b**6/120 + 7*b**5/60 - b**4/24 - 2*b**3/15 + 4*b**2 + 2. Factor l(w).
(w - 1)**3*(w + 4)*(4*w + 1)/5
Determine j so that 1/7*j**2 + 4/7*j - 5/7 = 0.
-5, 1
Suppose -49*n + 7 = -287. Let j(d) be the second derivative of -12*d**2 + 0 - 3/2*d**4 + n*d**3 - 8*d + 3/20*d**5. Factor j(h).
3*(h - 2)**3
Let q(n) = 2*n**2 + 2. Let y(j) = -3*j**2 - j - 3. Let w(m) = m + 8. Let d be w(-3). Let p(u) = d*q(u) + 4*y(u). Let p(t) = 0. Calculate t.
-1
Let c be (-10 - -15) + (-1 - 223/56). Let p(u) be the third derivative of -c*u**4 + 0*u + 1/140*u**5 + 0*u**3 - u**2 + 0. Factor p(k).
3*k*(k - 1)/7
Factor 2/9*k**2 + 28/9*k + 98/9.
2*(k + 7)**2/9
Let s be (-49)/(-21) + 1/(3 + -4). Let x(t) be the first derivative of -9 - 1/2*t**4 - t**2 - s*t**3 + 0*t. Suppose x(b) = 0. What is b?
-1, 0
Let x(t