et f(y) = -y**2 + 503*y + 4610. Let c be f(-9). Let 1/3*k**4 - 1/3*k**c - k**3 + 1/3*k**5 + 2/3*k + 0 = 0. Calculate k.
-2, -1, 0, 1
Let m = -6 - -11. Suppose -2*x - x - 2 = -y, -m*y + 29 = 4*x. Factor -y*f**2 + 2*f + f**2 + f + f**2.
-3*f*(f - 1)
Let n = 317523/11 + -28865. What is r in -n*r**3 + 0*r - 8/11*r**2 + 0 + 6/11*r**4 = 0?
-2/3, 0, 2
Suppose 40*s - 46*s - s**3 - 6*s**2 - s**2 + 0*s**2 = 0. What is s?
-6, -1, 0
Let a(n) = -100*n**2 + 11985*n + 505835. Let j(k) = 7*k**2 - 856*k - 36131. Let z(g) = 6*a(g) + 85*j(g). Factor z(x).
-5*(x + 85)**2
Let b(a) be the second derivative of a**4/3 - 34*a**3/3 - 36*a**2 - 6*a + 5. Let b(f) = 0. Calculate f.
-1, 18
Suppose 4*h - 31 = -s, -s - s = -2*h + 18. Let l be (h/(-12))/(4/(-30)). Solve -2*x**3 - l*x**2 - 4*x**4 + x**2 + 10*x**3 = 0.
0, 1
Solve -a**2 + 24*a**3 - 41*a**5 - 8*a + 43*a**5 - 4*a**4 + 23*a**4 = 0.
-8, -1, 0, 1/2
Suppose 104*m + 0*m**3 - 104*m - 54*m**2 - 20*m**3 - 7*m**3 - 3*m**4 = 0. Calculate m.
-6, -3, 0
Factor -1/3*o**5 + 2/3*o**4 + 7/3*o - 2/3 - 8/3*o**2 + 2/3*o**3.
-(o - 1)**4*(o + 2)/3
Let q = 3416 + -3416. Solve q*f - 2/11*f**2 + 8/11 = 0 for f.
-2, 2
Let p(g) = g**5 - 4*g**4 - 2*g**3 + 7*g + 2. Let t(i) = -4*i**5 + 12*i**4 + 5*i**3 + i**2 - 22*i - 6. Let v(l) = 14*p(l) + 4*t(l). Factor v(b).
-2*(b - 1)*(b + 1)**3*(b + 2)
Let o(t) be the third derivative of 15*t**2 - 1/1344*t**8 - 1/105*t**7 + 0*t**4 + 0*t**5 + 0 - 1/30*t**6 + 0*t + 0*t**3. Factor o(m).
-m**3*(m + 4)**2/4
Let t(m) = 16*m**2 - 281*m + 19318. Let b(w) = -5*w**2 + w + 1. Let g(k) = -6*b(k) - 2*t(k). Find y such that g(y) = 0.
139
Suppose -4*a - a = -10, -3*t + 4*a = -4. Factor 30 - s**t + 2*s**3 - 4*s + 2*s + 0*s**3 - 29.
-(s - 1)**3*(s + 1)
Let -15*p**4 - p + 56 - 29*p**3 + 12*p + 13*p**4 + p**5 + 9*p - 46*p**2 = 0. What is p?
-2, 1, 7
Let z = 2/43383 - -130139/216915. Determine a, given that 6/5*a**3 + 0 - 3/5*a**2 + 0*a - z*a**4 = 0.
0, 1
Suppose -5*w + 35 = -0. Factor -108 + w*o**2 - 36*o + 3*o**2 - 13*o**2.
-3*(o + 6)**2
Let j(w) = -w**3 + w**2 + 1. Let r(n) = 5*n**3 - 30*n**2 + 25*n - 6. Let c(k) = 6*j(k) + r(k). Solve c(z) = 0 for z.
-25, 0, 1
Let y(q) = -8*q**3 + 624*q**2 - 32452*q + 562432. Let v(j) = 7*j**3 - 624*j**2 + 32451*j - 562432. Let d(r) = 4*v(r) + 3*y(r). Suppose d(w) = 0. What is w?
52
Let d be 3 - -13*(3 + 5)/(-56). Suppose -d*s**2 - 2/7*s**3 - 10/7*s - 4/7 = 0. What is s?
-2, -1
Let q(w) = -28*w**2 - 32*w + 104. Suppose p = -2*p - 6, 2*r - 4*p - 24 = 0. Let g(c) = 10*c**2 + 11*c - 35. Let h(u) = r*g(u) + 3*q(u). Factor h(d).
-4*(d - 2)*(d + 4)
What is v in -v**3 + 2/3*v - 1/3*v**2 + 1/3*v**5 + 0 + 1/3*v**4 = 0?
-2, -1, 0, 1
Suppose -5*w = -3*y - 18 - 14, 25 = 3*w + 4*y. Let t(u) be the first derivative of u**4 + 3*u**3 - 9 - w*u**3 + 3 + 4*u**2. What is p in t(p) = 0?
0, 1, 2
Let w(k) be the first derivative of -k**6/18 - k**5/3 - k**4/4 + k**3 + 76. Determine b, given that w(b) = 0.
-3, 0, 1
Let n(m) = -12*m**4 - 136*m**3 - 244*m**2 - 112*m - 8. Let f(y) = y**4 + y**3 - y + 1. Let b(u) = -8*f(u) - n(u). What is l in b(l) = 0?
-30, -1, 0
Let z(g) be the first derivative of -g**3 + 54*g**2 - 105*g - 272. Suppose z(f) = 0. Calculate f.
1, 35
Let u(d) = d**3 + 21*d**2 + 20*d + 2. Let r be u(-20). Factor 5*z**3 + 2*z**2 - 3*z**2 - 25*z - 8 + 23 + 6*z**r.
5*(z - 1)**2*(z + 3)
Suppose 0*z + 2*m + 6 = 5*z, z - 2*m = -2. Let 6*t**4 + z*t**4 + 5*t**5 - 3*t**2 + 40*t - 25*t**3 - 2*t**2 - 3*t**4 - 20 = 0. Calculate t.
-2, 1
Suppose 301 = 6*w - 65. Let r = w - 56. Factor -2/13*k**r - 6/13*k**4 - 6/13*k**3 - 2/13*k**2 + 0*k + 0.
-2*k**2*(k + 1)**3/13
Factor 5/3*n - 1/3*n**2 + 2.
-(n - 6)*(n + 1)/3
Let l be 186/8 + -1 + 9/12. Suppose 0 = s - 5*n + l - 3, 12 = 2*s + 3*n. Let 0 - 2/3*p + 2/3*p**5 + s*p**3 + 4/3*p**2 - 4/3*p**4 = 0. Calculate p.
-1, 0, 1
Let u(k) be the first derivative of k**6/69 - 8*k**5/115 + 3*k**4/46 + 8*k**3/69 - 4*k**2/23 + 190. Let u(r) = 0. Calculate r.
-1, 0, 1, 2
Find c such that 14/3*c**2 + 104/3 + 368/3*c = 0.
-26, -2/7
Suppose 11 = -u + 15. What is j in -56*j + 3*j**u + 56*j + 3*j**3 - 3*j**5 - 3*j**2 = 0?
-1, 0, 1
Let r(j) be the second derivative of j**9/7560 + j**8/840 + j**7/420 - j**6/90 - j**5/15 - 2*j**4/3 + j. Let q(w) be the third derivative of r(w). Factor q(s).
2*(s - 1)*(s + 1)*(s + 2)**2
Let 0 - 2/7*o**4 - 8/7*o**3 - 4*o + 38/7*o**2 = 0. What is o?
-7, 0, 1, 2
Factor 512*x + 2*x**4 - 53*x**3 + 2*x**3 - 5*x**3 - 2*x**4 + 4*x**4 + 128*x**2.
4*x*(x - 8)**2*(x + 2)
Let t(q) = -28*q**2 + 26*q + 2. Let n(f) = 3*f**2 - f - 2. Let a(k) = 36*n(k) + 4*t(k). Let a(l) = 0. Calculate l.
1, 16
Let a(m) = -36*m**2 - 100*m - 104. Let c(h) be the first derivative of -7*h**3/3 - 10*h**2 - 21*h + 38. Let i(b) = -3*a(b) + 16*c(b). Factor i(l).
-4*(l + 2)*(l + 3)
Let m(l) be the third derivative of -l**7/105 - l**6/30 + 4*l**5/5 + 8*l**4/3 - 128*l**3/3 + 664*l**2. Determine c so that m(c) = 0.
-4, 2, 4
Let t be 4 - -6*4/(-12). Let h(j) = -j**2. Let i(v) = -7*v**2 - 16*v - 32. Let w(a) = t*i(a) - 10*h(a). Let w(l) = 0. What is l?
-4
Let f(h) be the first derivative of h**4/18 + 44*h**3/9 + 484*h**2/3 + 21296*h/9 - 20. Factor f(a).
2*(a + 22)**3/9
Let l(u) be the second derivative of u**7/126 + 7*u**6/90 - 13*u**5/60 - 43*u**4/36 - 4*u**3/3 + 79*u. Factor l(q).
q*(q - 3)*(q + 1)**2*(q + 8)/3
Let m(i) be the first derivative of 4 + 1/16*i**4 + 0*i**3 - 1/8*i**2 + 0*i. Suppose m(p) = 0. What is p?
-1, 0, 1
Let w = 340 - 340. Let h(o) be the first derivative of -4 + 3/2*o**4 - 3/5*o**5 - o**3 + w*o**2 + 0*o. Factor h(n).
-3*n**2*(n - 1)**2
Let w(q) be the first derivative of 1/42*q**4 + 2/7*q + 10/63*q**3 + 20 + 1/3*q**2. Factor w(c).
2*(c + 1)**2*(c + 3)/21
Let j = 57 - 61. Let w be (55/(-10) + 3)*(j + 2). Find s such that -2/9*s + 4/9*s**3 - 2/9 - 2/9*s**w - 2/9*s**4 + 4/9*s**2 = 0.
-1, 1
Factor 34/3*y**3 - 2/3*y**5 + 0 - 32/3*y**4 + 0*y + 0*y**2.
-2*y**3*(y - 1)*(y + 17)/3
Factor -264*l**2 - 4*l + 0*l**4 - 76*l**3 - l + 113 + 239 - 11*l + 4*l**4.
4*(l - 22)*(l - 1)*(l + 2)**2
Let u(j) = -j**2 - 8*j - 7. Let g be -3 + (27 + 3)/5. Let t(d) = 8*d**2 + 72*d + 64. Let a(r) = g*t(r) + 28*u(r). Let a(s) = 0. Calculate s.
-1
Let d(u) = -42*u + 12*u**2 - 17*u**2 - 28 + 3*u**2. Let o(i) = i**2 + 14*i + 9. Let k(m) = 5*d(m) + 16*o(m). Factor k(c).
2*(c + 2)*(3*c + 1)
Let d = 185/56 - 23/8. Let z be (249/84 + -3)/((-50)/200). Factor -2/7 + d*o - z*o**2.
-(o - 2)*(o - 1)/7
Let a be 0*(-13)/468*-12. Factor a*y + 2/7*y**2 - 8/7.
2*(y - 2)*(y + 2)/7
Let c(t) = t**2 + 3*t + 3. Let v be c(-3). Factor 14 - b - 23 + 9*b**2 + v*b**3 - 2*b.
3*(b - 1)*(b + 1)*(b + 3)
Let q(i) be the third derivative of -i**5/60 + 35*i**4/12 - 1225*i**3/6 - 134*i**2. Determine n so that q(n) = 0.
35
Let y(s) be the second derivative of s**6/120 + 3*s**5/80 + s**4/16 + s**3/24 + 61*s. Suppose y(o) = 0. What is o?
-1, 0
Let x(f) = 3*f**2 + 9*f + 9. Let a(n) be the second derivative of n**4/4 + 3*n**3/2 + 5*n**2 - 8*n. Let i(v) = 3*a(v) - 4*x(v). Solve i(t) = 0.
-2, -1
Let o be 6/(-87) + 1536/2088. Suppose -o*u**4 - 1/3*u + 2/3*u**2 + 0 + 1/3*u**5 + 0*u**3 = 0. Calculate u.
-1, 0, 1
Let w(g) = -g**3 - 2*g**2 - 2*g + 1. Let k be w(-2). Let z be -5*(9/k)/(-1). Factor 2*u**2 + 9*u**4 + u**2 + z*u**3 - 7*u**5 + 10*u**5.
3*u**2*(u + 1)**3
Let k(d) be the second derivative of -d**6/105 - d**5/35 + 5*d**4/42 + 2*d**3/7 + 108*d - 2. Factor k(j).
-2*j*(j - 2)*(j + 1)*(j + 3)/7
Factor 0*y - 2/3*y**5 - 4/3*y**4 + 0*y**3 + 0 + 0*y**2.
-2*y**4*(y + 2)/3
Let o = -813/2 + 409. Let h(u) be the first derivative of -3*u - 11 + 21/4*u**2 - o*u**3. Determine m so that h(m) = 0.
2/5, 1
Let v(c) be the first derivative of -3*c**4/4 - 645*c**3 - 416025*c**2/2 - 29815125*c + 555. Let v(w) = 0. Calculate w.
-215
Let i(p) be the third derivative of -1/3*p**3 + 0*p + 1/540*p**6 - 1/18*p**4 + 0 + 2*p**2 + 1/180*p**5. Let w(g) be the first derivative of i(g). Factor w(d).
2*(d - 1)*(d + 2)/3
Let x(t) be the second derivative of -1/30*t**5 - 3*t + 5/18*t**4 - 3*t**2 + 0 - 1/3*t**3. Factor x(s).
-2*(s - 3)**2*(s + 1)/3
Suppose x + 7*x = 24. Factor -45*h**x + 4*h + 0*h - 34*h - 145*h**2.
-5*h*(h + 3)*(9*h + 2)
Let l(v) be the first derivative of v**7/189 + 4*v**6/135 + v**5/18 + v**4/27 - 18*v - 21. Let d(o) be the first derivative of l(o). Factor d(u)