-5*s**2 - 3*s**2 - 15*s**3 + g*s**2 - 2*s**2 = 0?
-2/5, 0
Let n be -8 - (-6)/(-195)*-265. Determine o so that n*o**2 - 8/13*o**3 + 0*o - 10/13*o**4 + 0 = 0.
-1, 0, 1/5
Let m(u) = 32*u**2 - 800*u + 804. Let g(j) = 35*j**2 - 800*j + 805. Let t(l) = 9*g(l) - 10*m(l). Let t(y) = 0. What is y?
1, 159
Let u = -1165 + 1168. Let t(a) be the first derivative of 0*a**2 - 4/5*a**5 + 0*a**u + 0*a**4 + 0*a - 5. Determine l so that t(l) = 0.
0
Suppose 11*g - 285 = -186. Let f(t) be the first derivative of 0*t + 1/12*t**4 - 1/9*t**3 - 1/3*t**2 - g. Determine c so that f(c) = 0.
-1, 0, 2
Suppose -5*n + n - 669 = 3*q, -n - 146 = 5*q. Let w = -2221/13 - n. Let -2/13*s**3 + 2/13*s - 2/13*s**2 + w = 0. What is s?
-1, 1
Let y(a) = 3*a - 8. Let g be y(4). Suppose 27 - 27 + 8*p**3 - 32*p + g*p**4 + p**2 - 17*p**2 = 0. Calculate p.
-2, 0, 2
Let w(a) = -a**3 + 2*a + 5. Let u be w(2). Let v be 4 - (63/15 - u). Suppose v*o**2 - 2/5 + 0*o**3 + 0*o - 2/5*o**4 = 0. Calculate o.
-1, 1
Let n(k) be the third derivative of -k**7/42 - 45*k**6/4 - 17953*k**5/12 + 7650*k**4 - 46240*k**3/3 + k**2 + 220. Factor n(w).
-5*(w - 1)**2*(w + 136)**2
Factor 288/17 + 2/17*i**2 - 148/17*i.
2*(i - 72)*(i - 2)/17
Let u(n) be the first derivative of -n**4 - 16*n**2 + 20/3*n**3 + 16*n - 14. Factor u(l).
-4*(l - 2)**2*(l - 1)
Let s be (-3)/(-1) - -1*107. Suppose 11*u - s = 6*u. Factor 25*p - 3*p**2 - 41*p + u*p.
-3*p*(p - 2)
Let a(d) = -6*d. Let k be a(1). Let c(q) = 14*q**4 + 24*q**3 + 6*q**2 - 4*q - 3. Let n(r) = -1. Let j(m) = k*n(m) + 2*c(m). Determine f, given that j(f) = 0.
-1, 0, 2/7
Let o = -2053/5 - -383. Let g = -359/15 - o. Solve -u**2 - g*u**3 + u**5 - 1/3*u**4 + 4/3 + 8/3*u = 0 for u.
-1, -2/3, 1, 2
Suppose -162 = -3*w - 4*y, -4*y + 88 = 2*w - 20. Suppose -3*s = -w + 9. Factor -s*j + 5*j**3 - 4 - 8 + 2.
5*(j - 2)*(j + 1)**2
Let i(k) be the first derivative of -k**4/8 + 2*k**3/3 - 5*k**2/4 + k + 9. Factor i(x).
-(x - 2)*(x - 1)**2/2
Suppose 3*s - 20 = -4*d, -4*s - 8 = 5*d - 34. Let r = s + -1. Solve -30*n**2 + n**4 - r + 30*n**3 - 16*n**4 + 2*n**5 + n**5 + 15*n = 0.
1
Let o be 328/70 - (3696/440 - (-8)/(-1)). Factor 22/7*k**3 - o*k**2 + 18/7*k - 6/7*k**4 - 4/7.
-2*(k - 1)**3*(3*k - 2)/7
Suppose 0 - 144/19*f**3 + 2/19*f**4 + 0*f + 142/19*f**2 = 0. What is f?
0, 1, 71
Suppose 5*a - 24 = -0*a - 2*q, 4*a = -q + 18. Let z(m) be the first derivative of -2 - 1/8*m**a - 1/3*m**3 + m + 1/4*m**2. Factor z(s).
-(s - 1)*(s + 1)*(s + 2)/2
Let f(z) = z**2 + 6*z + 10. Let y be f(-5). Let n be y/5 - (2 + -4). Suppose 1/3*s**n + 2/3 - s + 0*s**2 = 0. Calculate s.
-2, 1
Solve -2/7*y**2 - 120/7 - 122/7*y = 0 for y.
-60, -1
Let m(o) = -o**2 - 7*o - 9. Let x be m(-4). Factor 7*u**3 + 4*u**2 + 12*u**3 + 3*u**3 - 4*u**x.
2*u**2*(9*u + 2)
Suppose -13*l + 169 = -0*l. Suppose l*u - 33 = -7. Factor 2/9 + 8/9*g + 8/9*g**u.
2*(2*g + 1)**2/9
Let q(u) be the second derivative of -u**7/27720 - u**6/7920 - 2*u**4 - 22*u. Let c(y) be the third derivative of q(y). Factor c(d).
-d*(d + 1)/11
Let l(b) = -41*b + 251. Let a be l(6). Let o(d) be the first derivative of 0*d + 0*d**3 + 0*d**4 - 5/24*d**6 - 1/20*d**a - 5 + 0*d**2. Factor o(k).
-k**4*(5*k + 1)/4
Let j be -1*0/((-64)/8). Let p(b) be the first derivative of j*b**3 - 3/5*b**5 - 2 + 6*b**2 + 0*b - 9/4*b**4. Factor p(q).
-3*q*(q - 1)*(q + 2)**2
Suppose 3*m = 4*d - 30, 17*m = -4*d + 16*m + 6. Factor -2/11*v + 0*v**2 + 2/11*v**d + 0.
2*v*(v - 1)*(v + 1)/11
Let j = -98 + 101. Determine q so that -4*q**j + 44*q - 28*q + 1 - 1 = 0.
-2, 0, 2
Let l(u) be the first derivative of -u**7/4200 - u**3/3 - 3. Let r(g) be the third derivative of l(g). Determine z so that r(z) = 0.
0
Let j(w) be the second derivative of w**7/21 + w**6/24 - w**5/6 - 5*w**4/24 - 5*w**2/2 + 2*w. Let x(m) be the first derivative of j(m). Factor x(t).
5*t*(t - 1)*(t + 1)*(2*t + 1)
Let p(k) = -5*k**2 + 68*k - 1152. Let v(h) = -27*h**2 + 340*h - 5758. Let w(j) = -11*p(j) + 2*v(j). Determine r so that w(r) = 0.
34
Let k be (-2)/(-5) - 115/(-25). Factor 4*s**3 - 3*s**3 + 3*s**k - 3*s**3 - s**3.
3*s**3*(s - 1)*(s + 1)
Let i(u) be the first derivative of u**2 - 8/5*u - 2/15*u**3 - 7. Suppose i(q) = 0. Calculate q.
1, 4
Solve -1/7*s**2 + 0 + 16/7*s = 0 for s.
0, 16
Let t(x) = 2*x**4 + x**3 - x. Let v(s) = 10*s**4 + 17*s**3 - 9*s**2 - 2*s. Let p(g) = -2*t(g) + v(g). Factor p(n).
3*n**2*(n + 3)*(2*n - 1)
Let h = -5 + 7. Let x = -222/5 + 45. Determine o so that 0 - x*o**h - 3/5*o = 0.
-1, 0
Let b(z) = -34*z + 21*z + 29*z**2 - 2*z**3 - 27*z - 7*z**3 + 20. Let j(n) = 55*n**3 - 175*n**2 + 240*n - 120. Let p(s) = -25*b(s) - 4*j(s). Factor p(u).
5*(u - 2)**2*(u - 1)
Factor -1/6*z**2 - 20/3 + 41/6*z.
-(z - 40)*(z - 1)/6
Let 24*f**2 - f**4 + 8*f**3 - 3*f**4 - f**3 + 5*f**3 - 32*f = 0. Calculate f.
-2, 0, 1, 4
Let z(g) = 2*g**4 + 65*g**2 + 141*g + 83. Let w(a) = -4*a**4 - 196*a**2 - 424*a - 248. Let b(s) = -3*w(s) - 8*z(s). Factor b(j).
-4*(j - 5)*(j + 1)*(j + 2)**2
Let q(w) be the first derivative of -w**6/450 - 7*w**5/75 - 49*w**4/30 - 8*w**3 - 33. Let i(m) be the third derivative of q(m). Factor i(x).
-4*(x + 7)**2/5
Suppose -2*t - 39 = t. Let k = t - -16. What is i in 16*i - 312*i**2 - 704*i**k - 4394*i**4 - 543*i**3 + 1504*i**3 + 1771*i**3 = 0?
0, 2/13
Let o(v) = -v**2 - 2*v + 2. Let x(b) = 6*b**2 + 260*b - 7458. Let a(j) = 8*o(j) + x(j). Determine m so that a(m) = 0.
61
Factor 6*z**2 + 36 - 24*z**3 + 15*z**3 - 3*z**2 + 58*z + 2*z.
-3*(z - 3)*(z + 2)*(3*z + 2)
Suppose 5*v - 31 = -16. Let -10*b**2 + 2*b**5 + 5*b**2 + v*b**2 + 4*b**3 - 6*b**4 + 2*b**3 = 0. What is b?
0, 1
Let g(b) be the second derivative of -5*b**7/126 + 4*b**6/9 - 3*b**5/2 + 20*b**4/9 - 25*b**3/18 + 60*b. Suppose g(k) = 0. Calculate k.
0, 1, 5
Let y(u) = 4*u**4 + 61*u**3 + 54*u**2 - 51*u. Let p(b) = b**4 - b**3 + b**2 + b. Let q(r) = 6*p(r) + y(r). Find o such that q(o) = 0.
-3, 0, 1/2
Let f(u) be the second derivative of -2*u**6/15 - 38*u**5/5 - 397*u**4/3 - 456*u**3 - 648*u**2 + u + 27. Suppose f(c) = 0. What is c?
-18, -1
Let d(u) = u**2 + 6*u - 10. Let m be d(2). Suppose 37 = -m*y + 55. Find f, given that -2/5*f**y - 2/5*f + 0 + 4/5*f**2 = 0.
0, 1
Suppose -5*d + 3*d + 56 = 0. Let x = -20 + d. Let x*w + 0*w - 3*w**2 - 27 + 0*w**2 + 10*w = 0. Calculate w.
3
Let u(r) = 3*r**4 + 12*r**3 + 12*r**2 - 12*r + 3. Let a(g) = -3*g**4 - 13*g**3 - 12*g**2 + 13*g. Let l(p) = -6*a(p) - 5*u(p). Suppose l(t) = 0. Calculate t.
-5, -1, 1
Let w(z) be the first derivative of -z**5 - 15*z**4/4 + 5*z**3/3 + 15*z**2/2 + 36. Factor w(y).
-5*y*(y - 1)*(y + 1)*(y + 3)
Let t(i) be the third derivative of -1/900*i**6 + 0*i**4 + 2*i**2 + 0 + 0*i - 5/3*i**3 + 0*i**5. Let b(x) be the first derivative of t(x). Factor b(r).
-2*r**2/5
Let h = -292 - -142. Let i = h - -1060/7. Suppose 2/7*x + 0 - 8/7*x**5 + 6/7*x**3 - i*x**2 + 10/7*x**4 = 0. What is x?
-1, 0, 1/4, 1
Let a = 524 + -521. Let n(x) be the first derivative of -1/5*x**5 + a*x - 1 + 2*x**2 - x**4 - 2/3*x**3. Find w such that n(w) = 0.
-3, -1, 1
Let p(f) be the third derivative of f**5/15 + 68*f**4/3 + 9248*f**3/3 - 563*f**2. Factor p(r).
4*(r + 68)**2
Suppose 5*j = 7*j - 178. Let m = j + -87. Let 10/7*n - 4/7 + 2/7*n**3 - 8/7*n**m = 0. Calculate n.
1, 2
Let q be 1484/49 - (-2)/(-7). Let f be (32/q - 1)/((-18)/(-36)). Solve 0 + 2/15*o**2 - f*o = 0.
0, 1
Let x(g) be the second derivative of g**6/105 + g**5/7 + 16*g**4/21 + 32*g**3/21 + 110*g. Find t such that x(t) = 0.
-4, -2, 0
Solve -8 - 1/2*z**5 - 7/2*z**4 + 4*z - 7/2*z**3 + 23/2*z**2 = 0 for z.
-4, -1, 1
Suppose -2*w = 3*w - 30. Let q = w - 4. Find i, given that -2*i + q*i**2 - 4*i**2 + 4*i**3 + 0*i**2 = 0.
-1/2, 0, 1
Find x such that 0*x + 0*x**2 + 2/9*x**3 + 0 = 0.
0
Suppose -3*b - 3*n = -18, -5*b + 5*n = 6*n - 46. Let i = -6 - -14. Let 2*u**4 - b*u**4 - 4*u**3 + i*u**3 = 0. What is u?
0, 1/2
Let -4/3*z + 2/3*z**2 + 2/3 = 0. What is z?
1
Let k(m) be the first derivative of m**5/30 + m**4/4 + 5*m**3/18 - 2*m**2 - 6*m + 129. Factor k(g).
(g - 2)*(g + 2)*(g + 3)**2/6
Let y(m) be the second derivative of m**8/47040 + m**7/2205 + m**6/1008 - 5*m**5/84 - 31*m**4/12 - 27*m. Let f(h) be the third derivative of y(h). Factor f(b).
(b - 2)*(b + 5)**2/7
Let s(r) be the first derivative of -3*r**5/10 - 33*r**4/4 - 97*r**3/2 + 198*r**2 - 216*r - 54. Factor s(y).
-3*(y - 1)**