 0, 1, 3
Suppose 27 = 30*u - 63. Suppose -12 = 5*z + 3*h, -3*z + 2*h = -u*h - 20. Find c such that z + 2/7*c**4 - 2/7*c**2 - 4/7*c**3 + 4/7*c = 0.
-1, 0, 1, 2
Let s(n) be the third derivative of n**6/450 - 2*n**5/75 + n**4/10 - 17*n**3/6 + 15*n**2. Let v(w) be the first derivative of s(w). Suppose v(j) = 0. What is j?
1, 3
Let i(a) be the second derivative of a**8/5880 - a**7/735 + a**6/315 - 5*a**3/6 + 14*a. Let n(u) be the second derivative of i(u). Find q, given that n(q) = 0.
0, 2
Let q be 1121/(-2478) + 54/42. Factor -7/3*z + 1/3*z**3 - q*z**2 + 4/3.
(z - 4)*(z + 2)*(2*z - 1)/6
Let i = -1191 - -3574/3. Let x(p) be the first derivative of 2*p**2 - i*p**3 - 6 - 3*p. Find f such that x(f) = 0.
1, 3
Let a(k) be the second derivative of -k**5/14 + k**4 - 32*k**3/7 + 32*k**2/7 + 22*k. Suppose a(r) = 0. Calculate r.
2/5, 4
Let i(t) be the second derivative of 22*t - 1/9*t**3 + 1/9*t**2 + 1/18*t**4 + 0 - 1/90*t**5. Suppose i(x) = 0. Calculate x.
1
Suppose 0 = -2*c - c - 4*t, 7 = c - t. Factor 12*i**3 - i**c + 49*i**2 - i**4 - 211*i**2 - 48*i**3.
-2*i**2*(i + 9)**2
Let p(y) = 2*y**2 - 111*y - 203. Let h(o) = -2*o**2 + 106*o + 202. Let c(m) = -3*h(m) - 2*p(m). Suppose c(i) = 0. What is i?
-2, 50
Factor 2/9*i**2 + 6 + 8/3*i.
2*(i + 3)*(i + 9)/9
Let l(b) = -10*b**2 + 33*b + 14. Let i(q) = 3*q**2 - 11*q - 4. Let w(u) = -7*i(u) - 2*l(u). Find p such that w(p) = 0.
0, 11
Factor 1/3*c**2 + 0 + 0*c + 2/9*c**3 - 1/9*c**4.
-c**2*(c - 3)*(c + 1)/9
Let u = 49 - 49. Find v such that u*v - v + 1 + 6*v**2 + 7*v + 1 + 2*v**3 = 0.
-1
Find p, given that -10*p**5 - 5*p - 18*p**3 - 16*p**4 - 21*p**3 - 13*p + 83*p**3 = 0.
-3, -3/5, 0, 1
Let l be (27/9)/(3/2)*10. Factor 0*h - l*h**2 - 16 + 17*h + 3*h + 4*h**3 + 12*h.
4*(h - 2)**2*(h - 1)
Solve -8*b + 17*b**2 - 421 + b**3 + 421 - 10*b = 0 for b.
-18, 0, 1
Solve 1032*n - 15*n**4 + 105*n**2 - 109*n**3 - 47*n**3 - 966*n = 0.
-11, -2/5, 0, 1
Let n(j) be the second derivative of j**6/6 + 9*j**5/4 + 35*j**4/4 + 95*j**3/6 + 15*j**2 - 4*j + 27. Factor n(a).
5*(a + 1)**3*(a + 6)
Suppose 4*h + l - 11 = 0, 2*l + 0*l = -2*h + 4. Let v = 7698/19295 + 4/3859. Factor 2/5*a - v - 2/5*a**h + 2/5*a**2.
-2*(a - 1)**2*(a + 1)/5
Let g be (-29)/(-203) + (-4)/(-21). Let r(c) be the second derivative of c - 1/18*c**3 - 1/36*c**4 + g*c**2 + 0. Determine s so that r(s) = 0.
-2, 1
Suppose -14*w + 11*w = -3. Let t(s) be the first derivative of 75/8*s**2 + 185/12*s**3 + 5/2*s + 205/16*s**4 + 5/6*s**6 + 21/4*s**5 + w. What is l in t(l) = 0?
-2, -1, -1/4
Let a(d) = -9*d**2 - 14*d - 8. Let c be ((-2)/3)/(11/(-66)). Let t(b) = 125*b**2 + 195*b + 110. Let w(n) = c*t(n) + 55*a(n). Factor w(r).
5*r*(r + 2)
Let x = 15180 + -15180. Let 5/3*o**5 - 50/3*o**4 + 0*o**2 + 0*o + x + 125/3*o**3 = 0. Calculate o.
0, 5
Let z be 2 + -3 + -3 - -1 - 140. Let y = z + 575/4. Factor -3/4*i**3 - 3/4*i**4 + 0 + y*i + 3/4*i**2.
-3*i*(i - 1)*(i + 1)**2/4
Suppose -14 = -4*c + 3*h, -8 = -c + 2*h - 2. Factor -14*r + 65 - 2*r**3 - 35 - 36 - 10*r**c.
-2*(r + 1)**2*(r + 3)
Let y be -2*(-95)/70 - (-2)/7. Factor -12*f**2 + 14*f**2 + 0*f**3 + f**y.
f**2*(f + 2)
Let x be ((-3)/13 + 0)/(139/(-834)). Factor 8/13*i + 0 + 32/13*i**2 + x*i**4 + 42/13*i**3.
2*i*(i + 1)*(3*i + 2)**2/13
Let c(b) be the third derivative of b**7/1260 - b**5/60 + b**4/18 - 4*b**3 - 6*b**2. Let n(d) be the first derivative of c(d). Factor n(g).
2*(g - 1)**2*(g + 2)/3
Find z such that -711/8*z - 135/4 + 1/8*z**5 - 159/2*z**2 - 109/4*z**3 - 11/4*z**4 = 0.
-3, -1, 30
Let j(w) = w**2 - 19*w + 25. Let x be j(18). Let y(a) = -a**3 + 8*a**2 - 24*a + 122. Let z be y(x). Factor -2*r**2 + 0 + 5/2*r**z - 1/2*r.
r*(r - 1)*(5*r + 1)/2
Let h(a) = a**2 - 4*a - 17. Let f be h(7). Suppose f*s = 7*s. Determine w so that -3*w**3 + s*w**3 + 4*w + 6*w**2 + 2*w**3 + 3*w**3 = 0.
-2, -1, 0
Factor 52*n**3 - 56*n**3 - 18*n - 2*n**4 + 30*n + 10*n**2.
-2*n*(n - 2)*(n + 1)*(n + 3)
Let q(j) be the third derivative of j**5/20 + 11*j**4/8 + 5*j**3 - 43*j**2 + 1. Solve q(k) = 0.
-10, -1
Let r be (-4 - -23) + (-4 - 0). Find a such that 8*a**2 + 3*a**3 + 4*a**4 - 8*a**3 + r*a**3 + 2*a = 0.
-1, -1/2, 0
Let l(u) be the third derivative of 1/12*u**4 + 0*u - 1/9*u**3 + 2*u**2 + 0 + 1/180*u**6 - 1/30*u**5. Find z such that l(z) = 0.
1
Let y(i) be the second derivative of -3*i - 1/3*i**3 + 1/12*i**4 + 0 - 3/2*i**2. Let y(u) = 0. Calculate u.
-1, 3
Let t(n) = -n**2 + 14*n + 4. Let i be t(14). Suppose 3 = -x + 5*m - i, 0 = m - 3. Find b such that b**2 + 8*b**2 - x*b**2 - 3*b**2 = 0.
0
Let a(h) be the first derivative of h**6/105 + h**5/35 - h**4/42 - 2*h**3/21 + 15*h + 4. Let s(c) be the first derivative of a(c). Factor s(f).
2*f*(f - 1)*(f + 1)*(f + 2)/7
Let r(p) be the second derivative of p**5/20 + 5*p**4/12 - 7*p**3/3 - 74*p - 1. Find d, given that r(d) = 0.
-7, 0, 2
Let f(o) = -8*o**3 - 13*o**2 + 56*o + 48. Let h(w) = 4*w**3 - 14*w - 12*w + 6*w**2 + 13*w - 15*w - 24. Let q(l) = 6*f(l) + 13*h(l). Find t, given that q(t) = 0.
-2, -1, 3
Let d be ((-220)/(-15) - 7) + -7. Let f(o) be the first derivative of -6 - 4*o - d*o**3 + 3*o**2. Factor f(s).
-2*(s - 2)*(s - 1)
Let o(v) = -4*v**2 + v - 1. Let p = 47 + -41. Let s(k) = -3*k**2 - 1. Let n(b) = p*s(b) - 4*o(b). Factor n(g).
-2*(g + 1)**2
Let m = -19 + 29. Suppose 8*v + 306 = m*v. Find s such that -150*s**5 + v*s**5 + 0*s**3 - 3*s**3 = 0.
-1, 0, 1
Solve m**3 - 13 + 27*m + 3*m**2 - 21*m - 31*m - 14*m**2 = 0 for m.
-1, 13
Factor -7*o + o**3 + o**2 - 5*o**2 - 10*o + 9*o + 6*o**2.
o*(o - 2)*(o + 4)
Let r be -4 + 8 + 305354/5. Let i = r + -60526. Factor -4802/5*l**4 - i*l**3 - 2/5 - 56/5*l - 588/5*l**2.
-2*(7*l + 1)**4/5
Let n(o) be the second derivative of o**6/240 + 13*o**5/160 + 41*o**4/96 + 47*o**3/48 + 9*o**2/8 - 8*o - 4. Solve n(u) = 0.
-9, -2, -1
Suppose 0*y + 6 = -2*y, 0 = 2*j + 3*y + 5. Suppose -9*u + 11 + 25 = 0. Factor 0 - 3*i**3 - 3/2*i**j + 0*i - 3/2*i**u.
-3*i**2*(i + 1)**2/2
Let c(a) = -2*a**5 + 8*a**4 - 29*a**3 + 8*a**2 + 22*a - 13. Let s(q) = q**5 - 9*q**4 + 28*q**3 - 6*q**2 - 23*q + 13. Let n(k) = 4*c(k) + 6*s(k). Factor n(j).
-2*(j - 1)**3*(j + 1)*(j + 13)
Let i(o) = -o**3 + 26*o**2 - 23*o - 38. Let m be i(25). Let p be 0 + 1 - (-14)/2. Factor 2*g**4 - 13*g**3 + 0*g - g**5 - p*g**4 - 4*g - m*g**2.
-g*(g + 1)**2*(g + 2)**2
Let z(t) be the third derivative of t**8/182 + 31*t**7/1365 + t**6/52 + t**5/195 + t**2 - 9*t. Solve z(n) = 0 for n.
-2, -1/3, -1/4, 0
Determine w so that 2/9*w**5 + 0 + 2/9*w + 4/3*w**3 + 8/9*w**4 + 8/9*w**2 = 0.
-1, 0
Let k(m) be the first derivative of -27 + 16/11*m**3 - 4/11*m**2 + 0*m + 13/22*m**4. Factor k(o).
2*o*(o + 2)*(13*o - 2)/11
Let q(b) be the first derivative of 4*b**5/45 + 14*b**4/3 - 908*b**3/27 + 248*b**2/3 - 752*b/9 + 128. Determine h, given that q(h) = 0.
-47, 1, 2
Suppose 14*v - 66 = 4. Let s(t) be the third derivative of 0*t**3 + 1/60*t**v + 0*t + 2*t**2 - 1/120*t**6 + 0*t**4 + 0. Factor s(g).
-g**2*(g - 1)
Let c(v) be the third derivative of v**6/1020 - v**5/102 - v**4/204 + 5*v**3/51 - 29*v**2. Factor c(u).
2*(u - 5)*(u - 1)*(u + 1)/17
Let -120 + m**3 - 4*m + 8*m**2 - 112*m + 3*m**3 = 0. What is m?
-6, -1, 5
Factor -58*d**2 + 42233 - 2*d**3 - 42233.
-2*d**2*(d + 29)
Suppose -3*n = 2*n - 325. Let q = 68 - n. What is y in -18 + 2/3*y**q + 18*y - 6*y**2 = 0?
3
Let a(c) = -3*c**4 + 37*c**3 - 126*c**2 + 200*c - 120. Let d(m) = -3*m**4 + 38*m**3 - 126*m**2 + 199*m - 120. Let n(p) = 5*a(p) - 4*d(p). Solve n(z) = 0.
2, 5
Let l be 0/(0/6 + 1). Let k(r) be the second derivative of -1/30*r**5 - 1/9*r**4 + 1/9*r**3 + 2/3*r**2 + r + l. Factor k(d).
-2*(d - 1)*(d + 1)*(d + 2)/3
Suppose 16*m + 4*m**3 + 20 + 12*m**2 - 17*m - 35*m = 0. What is m?
-5, 1
Let c be (3 - (-90)/(-27))*-6*2/8. What is q in -q**2 - 9/4*q - c = 0?
-2, -1/4
Let t = -5 - -7. Let c = -6 + 10. Factor -t*s**2 + 2*s**3 - s**3 + 11*s**4 + 4*s**c.
s**2*(3*s - 1)*(5*s + 2)
Let d(a) be the first derivative of -a**5/10 + a**4 - 5*a**3/3 - 16*a - 42. Let s(o) be the first derivative of d(o). Determine v, given that s(v) = 0.
0, 1, 5
Determine b, given that 8 + 50*b - 71*b**2 + 3*b**3 - 65*b**2 + 167*b**2 - 14*b**3 = 0.
-1, -2/11, 4
Determine p, given that -33/4*p + 3*p**2 + 9/2 = 0.
3/4, 2
Let c(s) be the first derivative of -32/13*s**4 + 5/13*s**2 + 4/13*s - 7/13*s**6 - 9 - 12/13*s**3 - 128/65*s**5.