+ 2)/11
Find p such that 44/15*p**3 + 352/5*p - 338/15*p**2 - 384/5 - 2/15*p**4 = 0.
3, 8
Find g such that 1/3*g**5 + 20/3 + 4/3*g + 5/3*g**4 - 5/3*g**3 - 25/3*g**2 = 0.
-5, -2, -1, 1, 2
Let m(f) be the second derivative of -1/4*f**4 + 0 - 8*f**3 - f - 96*f**2. What is o in m(o) = 0?
-8
Solve 201/4*f**2 - 225/4 - 435/4*f - 21/4*f**3 = 0 for f.
-3/7, 5
Let f = -49/4 + 739/60. Let g(a) be the first derivative of -4 - f*a**3 + 1/10*a**2 + 0*a. Determine w, given that g(w) = 0.
0, 1
Factor 172*i + 1051*i**2 - 44 - 2105*i**2 + 1070*i**2.
4*(i + 11)*(4*i - 1)
Factor -93209*l**2 + 24 - l**4 + 56*l + 4*l**3 + 93247*l**2 - l**4.
-2*(l - 6)*(l + 1)**2*(l + 2)
Let l(z) be the first derivative of -z**5/150 + z**4/60 + z**2 - 2. Let j(r) be the second derivative of l(r). Determine i, given that j(i) = 0.
0, 1
Let l(w) be the second derivative of 1/18*w**4 + 1/3*w**3 + 0*w**2 - 5*w + 0 - 1/45*w**6 - 1/10*w**5. What is s in l(s) = 0?
-3, -1, 0, 1
Let n = -10 + -5. Let f = 41 - 38. Let k(j) = -j**5 + 2*j**4 + 2*j**3 - 4*j**2 + 4*j + 7. Let w(m) = m + 1. Let t(i) = f*k(i) + n*w(i). Let t(s) = 0. What is s?
-1, 1, 2
Suppose 4*t - 22 = -4*n + 2*t, 0 = 4*t - 12. Determine k so that -2*k**3 + 4*k**5 + 9*k**n - 3*k**4 - 2*k**5 - 6*k**2 = 0.
-3, -1, 0, 1
Let y(w) be the second derivative of -w**8/8400 + w**7/2100 - 5*w**3/6 + 15*w. Let d(g) be the second derivative of y(g). Factor d(o).
-o**3*(o - 2)/5
Let y be 8/(-3)*6/(-8). Suppose 5*k + q = y, -3*k - 2*q + 0*q = -4. Factor -8*c + k*c - c - c**3 + 6 + 4*c**3.
3*(c - 1)**2*(c + 2)
Let o(u) be the first derivative of -u**3 - 3*u**2 - 3*u + 263. Factor o(c).
-3*(c + 1)**2
Let v(u) be the first derivative of -u**5/50 - 7*u**4/60 - 4*u**3/15 - 9*u**2/2 - 11. Let f(k) be the second derivative of v(k). Let f(s) = 0. Calculate s.
-4/3, -1
Let q be 2246/8 + 3 - 11/(-44). Let n = q + -280. Factor 0*k**2 + 0*k**n + 4/7*k**3 - 2/7*k**5 + 0 - 2/7*k.
-2*k*(k - 1)**2*(k + 1)**2/7
Suppose 3*f = -z + 23, 3 = -95*z + 100*z - f. Find l, given that -24/5 - 8/5*l**z - 28/5*l = 0.
-2, -3/2
Let l = -23 + 6. Let h = l - -29. Find q such that -4*q**2 + 6*q**4 + 10*q**5 - h*q**3 - 2*q**5 - 2*q**4 + 4*q = 0.
-1, 0, 1/2, 1
Let w(d) be the third derivative of d**6/300 + 7*d**5/75 + 43*d**4/60 + 2*d**3 + 9*d**2 + 7. Factor w(m).
2*(m + 1)*(m + 3)*(m + 10)/5
Let n(d) be the second derivative of -d**4/36 + 26*d**3/9 - 338*d**2/3 + 78*d. Suppose n(t) = 0. What is t?
26
Let i(c) = -c**3 - 7*c**2 - 9. Let u be i(-6). Let q = u - -47. Factor 0 - 1/5*z**3 - 1/5*z**4 + 1/5*z + 1/5*z**q.
-z*(z - 1)*(z + 1)**2/5
Let d = -593/4 + 3037/20. Factor 6*t - 14/5*t**2 - d + 2/5*t**3.
2*(t - 3)**2*(t - 1)/5
Let t = 12261/10 + -1226. Let d(k) be the second derivative of 4*k + 0*k**2 + 0 - t*k**3 + 1/20*k**4. What is i in d(i) = 0?
0, 1
Let k be 1/(-2*((-3)/18 + 0)). Let p be 1 - (k + -4 + (1 - -1)). Find u, given that p - 8/7*u**4 + 2/7*u**2 + 6/7*u**3 + 0*u = 0.
-1/4, 0, 1
Factor 8*c + 4/3*c**2 + 12.
4*(c + 3)**2/3
Let v(y) be the third derivative of -1/112*y**8 - 18*y**2 + 1/8*y**6 + 0*y + 0 + 1/14*y**7 - 5/4*y**5 - 5*y**4 - 8*y**3. Find g, given that v(g) = 0.
-1, 4
Let h(s) = 5*s**5 + s**3 + 3*s**2 + s + 4. Let q(y) = 2*y**5 + y**3 + y**2 + 2. Let k(b) = -2*b + 23. Let g be k(15). Let p(j) = g*q(j) + 3*h(j). Factor p(n).
(n - 1)**3*(n + 1)*(n + 2)
Let y = 18 - 15. Let 14*c**2 + y*c**5 - 60*c**3 + 51*c**4 - 2*c**2 - 15*c**5 = 0. What is c?
0, 1/4, 2
Suppose 0 = g + 3*g - 40. Let m(n) = n + 1. Let r be m(g). Factor v**2 + r - 8*v - 2 + 2*v.
(v - 3)**2
Let q(j) = 88*j**2 + 180*j + 96. Let n(y) = y**3 - 175*y**2 - 360*y - 191. Let m(k) = -4*n(k) - 7*q(k). Factor m(c).
-4*(c - 23)*(c + 1)**2
Let r(g) = 2*g**3 + 2*g**2 - 8*g - 8. Let f(v) = -8*v**3 - 9*v**2 + 29*v + 30. Let s(o) = -4*f(o) - 18*r(o). Find d such that s(d) = 0.
-2, -1, 3
Find m such that 3*m**5 - 24*m - 42*m**3 + 36*m**2 - 22*m**3 - 9*m**4 + 58*m**3 = 0.
-2, 0, 1, 2
Find r such that 2/7*r**2 - 74/7 + 72/7*r = 0.
-37, 1
Let t(p) be the third derivative of -2/3*p**5 + 2 + 0*p**3 + 0*p + 2/3*p**4 - 7/10*p**6 - 1/42*p**8 - 23/105*p**7 - 35*p**2. Factor t(c).
-2*c*(c + 2)**3*(4*c - 1)
Let s be 262/917 - (4/7)/(-4). Factor 12/7*w**2 + 0 + 0*w - s*w**3.
-3*w**2*(w - 4)/7
Let c = -234 - -1171/5. Solve 0 + 0*k + c*k**3 + 1/5*k**2 = 0.
-1, 0
Let z be (-4)/((-16)/20) - 3. Determine p so that -2*p**z + 22*p - p**2 - 7*p - 12*p = 0.
0, 1
Let s(r) be the second derivative of r**5/2 + 25*r**4/12 + 5*r**3/6 - 5*r**2 - r + 113. Suppose s(h) = 0. What is h?
-2, -1, 1/2
Let w(g) = 5*g**3 + g**2 - 6*g. Let x(t) = -t + 8. Let k be x(5). Let r(h) = h. Let b be r(k). Let m(p) = p**3 - p. Let d(u) = b*w(u) - 12*m(u). Factor d(z).
3*z*(z - 1)*(z + 2)
Determine v so that 2/3*v**2 - 12*v**3 + 12*v + 14/3*v**4 - 16/3 = 0.
-1, 4/7, 1, 2
Let k(t) = 11*t**3 + 4*t**2 - 11*t**4 + 9*t**4 - 4*t**5 - 2*t + 2*t**5 - 2. Let d(b) = -b**3. Let r(x) = -14*d(x) - 2*k(x). Suppose r(j) = 0. Calculate j.
-1, 1
Suppose -10*w - 23*w = -8*w. Let a(h) be the third derivative of -15/2*h**3 - 11/6*h**5 + w + 0*h - 1/42*h**7 + 11*h**2 - 5*h**4 - 1/3*h**6. Factor a(c).
-5*(c + 1)**2*(c + 3)**2
Suppose -5*v + 2*h = -14, 0 = 5*v - 4*h - h - 5. Find s such that 265*s**v + s**2 - 264*s**4 - s**3 + s**5 - 2*s**2 = 0.
-1, 0, 1
Let y = -25982 + 25984. Suppose 32/5*z**3 - 156/5*z**y + 224/5*z - 98/5 - 2/5*z**4 = 0. Calculate z.
1, 7
Let y = -3 - -18. Let p = y - 12. Solve o**5 - 4*o**3 - o**3 + 3*o**p - 3*o**3 + 4*o = 0 for o.
-2, -1, 0, 1, 2
Find y, given that -2/15*y**4 + 2/15*y**3 + 0 + 32/15*y**2 + 8/3*y = 0.
-2, 0, 5
Let d = -7 + 13. Let n(g) = -g**2. Let h(v) = -14*v**3 + 13*v**2 + 4*v. Let q = 1245 + -1243. Let j(x) = d*n(x) + q*h(x). Suppose j(f) = 0. Calculate f.
-2/7, 0, 1
Let y = 12/25 + 8/25. Factor -8/5*h + 4/5*h**2 + y.
4*(h - 1)**2/5
Suppose -480 = -u - 352. Let i be (6/(-4))/((-1)/2). Factor 44*a**3 - 96*a**2 - 5 - 4*a**4 - 12*a**i + u*a - 59.
-4*(a - 2)**4
Let t be 1 + 0 + -1 + -4. Let d be t/10 - (-72)/30. Find i such that -3 + 0 - 2*i**2 + 5 - i**3 - d*i + 3*i**3 = 0.
-1, 1
Let v = -11987 + 11989. Factor 0 - 3/7*d**v + 0*d.
-3*d**2/7
Let g(p) be the third derivative of 49/60*p**6 + 28*p**2 - 16*p**4 + 0 + 0*p + 28/3*p**3 + 21/2*p**5. Factor g(n).
2*(n + 7)*(7*n - 2)**2
Factor 1/3*o**4 - 4/3*o - o**2 + 4/3 + 2/3*o**3.
(o - 1)**2*(o + 2)**2/3
Determine f, given that 9/10*f**3 - 83/10*f**2 - 8/5 + 9*f = 0.
2/9, 1, 8
Determine p so that 54*p - 87*p + 2*p**2 - 15*p = 0.
0, 24
Factor 406*n**3 - 194*n**3 - 8*n**4 - 207*n**3 + 50*n**2 + n**5.
n**2*(n - 5)**2*(n + 2)
Let p be (-4)/6*(-48)/8*(-2)/(-16). Find v such that 1/2*v - v**3 + 1/2 - v**2 + p*v**5 + 1/2*v**4 = 0.
-1, 1
Factor 24/5 - 1029/5*n**4 - 147/5*n**3 - 228/5*n + 126*n**2.
-3*(n + 1)*(7*n - 2)**3/5
Let g = -791 - -113905/144. Let o(k) be the third derivative of 0*k**5 - 1/720*k**6 + 0*k**3 - 4*k**2 + g*k**4 + 0 + 0*k. Factor o(b).
-b*(b - 1)*(b + 1)/6
Let d(w) = 4*w**2 + 2*w - 2. Let c be d(-2). Suppose -7*k + 12*k - c = 0. Determine y, given that -2 + y - y - y**k + y + 2*y = 0.
1, 2
Let u(n) be the first derivative of -n**7/2520 - n**6/45 - 8*n**5/15 - 64*n**4/9 - 4*n**3 + 20. Let g(l) be the third derivative of u(l). Factor g(i).
-(i + 8)**3/3
Let w = 11/124 + 7/620. Determine a, given that 1/10*a**2 - w + 1/10*a**3 - 1/10*a = 0.
-1, 1
Let t(c) be the third derivative of 0 + 0*c**3 - c**2 + 0*c - 1/60*c**6 + 2/15*c**5 - 1/4*c**4. Factor t(h).
-2*h*(h - 3)*(h - 1)
Let u(y) = -3*y + 57. Let r be u(18). Factor -8*f**2 - 5*f**3 + 5*f**3 - 2*f**3 + 0*f**r.
-2*f**2*(f + 4)
Let r be (-2634)/(-54) + (-4)/(-18). Let s = r - 49. Factor s*g + 3/7 - 3/7*g**2.
-3*(g - 1)*(g + 1)/7
Find l such that 0 - 5/3*l**4 + 0*l**3 - 5/3*l**5 + 0*l**2 + 0*l = 0.
-1, 0
Suppose q - 2*p = 2*q + 6, 4*p + 24 = -5*q. Let h be q/(-3)*(-18)/(-12). Factor -i + 9*i**2 + 14*i**2 - 25*i**h - i**3.
-i*(i + 1)**2
Let l(v) be the first derivative of v**8/112 - v**7/70 - v**6/20 + 15*v**2/2 + 16. Let w(h) be the second derivative of l(h). Factor w(k).
3*k**3*(k - 2)*(k + 1)
Let r(k) be the first derivative of 16/3*k**2 + 15 + 14/9*k**3 + 8/3*k. Factor r(a).
2*(a + 2)*(7*a + 2)/3
Determine m so that -16/9*m**3 + 0*m - 8/3*m**2 - 70/9*m**5 + 0 + 218/9*m**4 = 0.
-2/7, 0, 2/5, 3
Let t(k) = 8*k**3 - 16*k**2 + 32*k. Let b(m) = 