 + 6*q + 3 = 0. Determine h, given that -3/4*h**4 + 0*h + 3/4*h**2 - 3/4*h**5 + 3/4*h**3 + j = 0.
-1, 0, 1
Let m = 8165 - 24493/3. Factor -2*v**2 - m*v**3 + 8/3*v + 0.
-2*v*(v - 1)*(v + 4)/3
Let x be 14 + (-7 - -10) + -8. Let k(a) be the second derivative of a**2 - 2/3*a**4 - x*a - a**3 + 0. Factor k(p).
-2*(p + 1)*(4*p - 1)
Let m = 76 + -74. Let -28*b**2 + 35*b**2 - 16*b**m - 2*b**3 - 2 - 3 - 12*b = 0. Calculate b.
-5/2, -1
Let t = 4821 + -4818. Factor 0*g + t - 3/4*g**3 - 9/4*g**2.
-3*(g - 1)*(g + 2)**2/4
Let k be 466/12 - 3/(-18). Factor -4 + 18*j**3 + 6 + 6*j**4 + k*j**2 - 3*j**4 + 36*j + 10.
3*(j + 1)**2*(j + 2)**2
Suppose -s + 19 = -2*s. Let t = 73 + s. Factor 1 - 2*j - 2*j**3 + t*j**2 - 58*j**2 - 1.
-2*j*(j + 1)**2
Let 35/2*s**3 + 47*s**2 + 4 + 26*s = 0. What is s?
-2, -2/5, -2/7
Let z = 16 - 16. Let o = -17/3 - -7. Suppose 4/3*u**5 - 10/3*u**2 + z*u**3 + 0 - o*u + 10/3*u**4 = 0. What is u?
-2, -1, -1/2, 0, 1
Let t(b) = 25*b**4 - 150*b**3 + 230*b**2 + 150*b - 5. Let z(s) = 13*s**4 - 75*s**3 + 116*s**2 + 75*s - 3. Let w(l) = 3*t(l) - 5*z(l). Factor w(p).
5*p*(p - 5)*(p - 3)*(2*p + 1)
Let y(u) be the second derivative of u**4/12 + 15*u. Let c(q) = -2*q**3 - 8*q**2 - 4*q - 1. Let z(i) = -c(i) - 3*y(i). Find t such that z(t) = 0.
-1, -1/2
Let h(z) be the first derivative of -z**4/28 + 133. Factor h(s).
-s**3/7
Suppose m + t + 10 + 16 = 0, -t + 46 = -2*m. Let n be (-4)/(m/9)*(-7)/(-3). Let 0*c + c**4 + n*c**5 - 7/2*c**3 - c**2 + 0 = 0. Calculate c.
-1, -2/7, 0, 1
Suppose -5*v + v = 5*k + 5, -2*k - 2 = -3*v. Let h(y) = -y**2 - 10*y - 9. Let c be h(-1). Factor -2/3*n**4 + v*n**2 + 0*n + 0 + c*n**3.
-2*n**4/3
Factor -4*y**3 - 2/9*y**5 + 0*y + 0*y**2 - 22/9*y**4 + 0.
-2*y**3*(y + 2)*(y + 9)/9
Let f(h) be the second derivative of -h**6/360 + h**5/30 - h**4/6 + 7*h**3/6 + 8*h. Let d(a) be the second derivative of f(a). Find o, given that d(o) = 0.
2
Let f be (-245)/(-147)*(-9)/(-35). Find z, given that -24/7*z**2 - f*z**4 + 12/7*z + 0 + 15/7*z**3 = 0.
0, 1, 2
Let u = 1/8258 + 668893/41290. Factor u*r**2 + 6/5 - 9*r.
3*(3*r - 1)*(9*r - 2)/5
Let j(d) be the third derivative of -11*d**6/4 + 233*d**5/20 + 101*d**4/8 + 5*d**3 - 19*d**2. Determine m so that j(m) = 0.
-1/5, -2/11, 5/2
Solve 1/6*x**3 + 0 + 59/6*x**2 + 0*x = 0.
-59, 0
Let v(z) = 80*z**3 - 35*z**2 - 125*z - 120. Let m(c) = 3*c**3 - c**2 - c. Let f(x) = -25*m(x) + v(x). Suppose f(d) = 0. Calculate d.
-2, 6
Let q(m) be the first derivative of -2 + 1/7*m**2 + 2/21*m**3 - 4/7*m. Let q(d) = 0. What is d?
-2, 1
Let f(k) be the second derivative of k**6/90 + k**5/15 - 11*k**3/6 - k. Let q(n) be the second derivative of f(n). Let q(o) = 0. Calculate o.
-2, 0
Let l = -1389 - -1391. Factor 0*i**l - 3/2*i**3 + 0*i + 3/2*i**5 + 0 + 0*i**4.
3*i**3*(i - 1)*(i + 1)/2
Let y be (-8)/(64/(-84)) - 2. Let a = 55/6 - y. Solve 2*c**3 + 4/3*c**2 - a*c + 0 = 0.
-1, 0, 1/3
Suppose 9*j = 30*j - 63. Let x(v) be the third derivative of 5*v**2 - 1/12*v**5 - 10/3*v**j - 5/6*v**4 + 0 + 0*v. Factor x(p).
-5*(p + 2)**2
Let o(m) be the first derivative of 5*m**6/6 - 5*m**4 + 10*m**3/3 + 15*m**2/2 - 10*m - 343. Factor o(b).
5*(b - 1)**3*(b + 1)*(b + 2)
Let i = -1223 - -1227. Suppose -2/3*x**2 + 3*x**3 - i*x**4 + 5/3*x**5 + 0 + 0*x = 0. What is x?
0, 2/5, 1
Let t(w) be the first derivative of w**3/4 - 33*w**2/8 + 15*w/2 + 492. Suppose t(b) = 0. What is b?
1, 10
Suppose 2/11*v**4 + 6/11*v**2 - 48/11 + 12/11*v**3 - 52/11*v = 0. Calculate v.
-4, -3, -1, 2
Let r(o) be the first derivative of -2/33*o**3 - 23 + 0*o**2 + 0*o. Solve r(n) = 0 for n.
0
Let 1/3*s**2 + 11*s - 70/3 = 0. Calculate s.
-35, 2
Let n(p) be the second derivative of 3*p**4/8 + p**3/6 + p - 4. Factor n(r).
r*(9*r + 2)/2
Let d be 2 + (-2)/6*0. Suppose 0 = 2*o - 3*p - 16, 5*p = -5*o + d*o - 14. Factor -7*l**o + 0*l**5 + 15*l**3 + 3*l**5 - 12*l**4 + l**2.
3*l**2*(l - 2)*(l - 1)**2
Let c be -3*(-4)/36*45. Suppose -3*k + c = -3*f, -k = -2*f - 2 - 5. Suppose -3*n**2 + 6*n - k*n**3 + 29 - 29 = 0. Calculate n.
-2, 0, 1
Suppose 65 = f - 2*f. Let s be 0 + -1 + 1 - f/39. Factor -1/3*v**3 - s*v**2 - 4/3 - 8/3*v.
-(v + 1)*(v + 2)**2/3
Let z be (-2334)/(-30) - 5/(-2)*(-12)/(-15). Find y such that -3/5*y**5 - 6*y**3 - 318/5*y**2 - z*y - 147/5 + 33/5*y**4 = 0.
-1, 7
Suppose 48/5*f**3 - 324 - 1539/5*f + 6*f**4 - 378/5*f**2 + 3/5*f**5 = 0. Calculate f.
-5, -3, 4
Let f(d) be the third derivative of -17*d**2 - 1/4*d**3 + 0 + 1/448*d**8 + 1/40*d**5 + 0*d + 0*d**7 - 1/40*d**6 + 3/32*d**4. Factor f(n).
3*(n - 1)**3*(n + 1)*(n + 2)/4
Let f(j) = j**2 + 3*j. Let x(h) = 2*h - 24. Let s(o) = -4*f(o) - 2*x(o). Factor s(m).
-4*(m - 2)*(m + 6)
Find a, given that 32/3*a**3 - 8/3*a - 6*a**2 + 0 + 14*a**4 = 0.
-1, -1/3, 0, 4/7
Factor -3/7*p**4 - 21 - 36*p + 36/7*p**3 - 66/7*p**2.
-3*(p - 7)**2*(p + 1)**2/7
Let w(i) be the third derivative of 0*i**3 + 0*i**4 - 1/105*i**7 + 5*i**2 - 1/15*i**6 + 0 + 0*i + 1/168*i**8 + 2/15*i**5. Find q, given that w(q) = 0.
-2, 0, 1, 2
Let 66*k**2 + 2 - 261*k**3 - 2 - 840*k**4 + 1092*k**4 + 12*k**5 = 0. Calculate k.
-22, 0, 1/2
Let z(v) = -v**4 - v**3 - v**2 + 2. Let i(d) = 11*d**4 - 74*d**3 + 101*d**2 - 50*d + 8. Let m(q) = -i(q) + 4*z(q). Factor m(t).
-5*t*(t - 2)*(t - 1)*(3*t - 5)
Let b(n) be the first derivative of n**3/6 - 25*n**2 + 1250*n + 26. Factor b(i).
(i - 50)**2/2
Factor -2*z**2 + 59*z - 6 + 14 - 65*z.
-2*(z - 1)*(z + 4)
Let u(c) be the second derivative of 0*c**2 - 5/12*c**4 + 1/6*c**6 + 0 + 0*c**5 - 15*c + 0*c**3. Factor u(n).
5*n**2*(n - 1)*(n + 1)
Factor 396*i**2 - 281*i**2 - 34*i + 144*i + 5*i**3.
5*i*(i + 1)*(i + 22)
Suppose 85*i = -75 + 330. Find o such that -8/5*o**2 + 2/5*o**i + 8/5 - 2/5*o = 0.
-1, 1, 4
Let k(a) be the first derivative of 1/3*a**5 + 5/36*a**6 - 5/12*a**2 - 5/9*a**3 + 0*a + 0*a**4 + 20. What is p in k(p) = 0?
-1, 0, 1
Let z be 0/3 + 3 + -1. Let x = 11/510 - -53/170. What is k in x*k**z + 0*k + 0 + k**3 = 0?
-1/3, 0
Let m = 7664 + -53388/7. Let k = m - 36. Let -8/7 + k*a - 2/7*a**2 = 0. What is a?
2
Let q = 1/30 + 2/15. Let i(v) be the second derivative of 0*v**2 - 1/15*v**6 + 0*v**3 - q*v**4 + 3*v + 0 + 1/5*v**5. Factor i(f).
-2*f**2*(f - 1)**2
Suppose -4*j - 1 + 37 = 0. Let o(n) be the first derivative of -4 + 2 + 6 - j - n**3 - 75*n - 15*n**2. Factor o(u).
-3*(u + 5)**2
Let q(l) be the third derivative of 0 + 0*l + 1/300*l**6 + 0*l**3 + 1/15*l**4 - 10*l**2 - 2/75*l**5. Factor q(y).
2*y*(y - 2)**2/5
Let y = -856 + 861. Let a(r) be the first derivative of 1/9*r**3 + 4/3*r**2 + y + 16/3*r. Factor a(x).
(x + 4)**2/3
Let a(l) be the first derivative of -121*l**3/3 - 11*l**2/2 - l/4 - 2. Solve a(p) = 0 for p.
-1/22
Let g be -3 + ((-6274)/(-9))/(-2). Let q = g + 352. Factor 2/9*k**2 + q*k**3 + 0 + 0*k + 2/9*k**4.
2*k**2*(k + 1)**2/9
Suppose 8 = -4*s + 16. Let i(m) be the first derivative of 0*m - 1/15*m**3 + 0*m**2 + 1/25*m**5 + s + 0*m**4. Factor i(p).
p**2*(p - 1)*(p + 1)/5
Let t be -3*2/(-21)*784/168. Let x(l) be the second derivative of -t*l**4 - 1/2*l**2 + 5*l + 4/3*l**3 + 0. Let x(o) = 0. What is o?
1/4
Suppose -9*l = 12*l - 126. Let b be -1 - (4/(-4) - 15/l). Factor -b*a**3 + 0*a + 3/2*a**4 + 0 + a**2.
a**2*(a - 1)*(3*a - 2)/2
Factor -h**2 - 4/5*h + 0 - 1/5*h**3.
-h*(h + 1)*(h + 4)/5
Let v(z) be the first derivative of z**4/30 + z**3/15 - 6*z**2/5 + z + 4. Let o(f) be the first derivative of v(f). Determine q so that o(q) = 0.
-3, 2
Let t = -13421 - -53685/4. Determine z, given that 1/2 + 5/4*z**3 + 7/4*z + t*z**4 + 9/4*z**2 = 0.
-2, -1
Factor 43*n**3 + 2*n**2 - 81*n**3 - n**5 + 41*n**3.
-n**2*(n - 2)*(n + 1)**2
Let u(c) be the second derivative of c**7/2520 - c**6/180 + c**5/40 - c**4/6 + 10*c. Let o(r) be the third derivative of u(r). Let o(b) = 0. What is b?
1, 3
Let l be 378/77 + 1/33*3. Let w(f) be the second derivative of -1/2*f**2 - 1/5*f**l - 5/6*f**3 + 0 + 3*f - 2/3*f**4. Suppose w(b) = 0. What is b?
-1, -1/2
Let s(k) be the third derivative of 2/21*k**3 + 4*k**2 + 1/12*k**4 - 1/105*k**6 - 1/42*k**5 + 0*k + 0. Solve s(y) = 0.
-2, -1/4, 1
Let p be -3 + -4 + 3 - -4. Determine x, given that -176*x**2 - 49*x + 156*x**2 - 2*x**3 - x + p*x**3 = 0.
-5, 0
Let q(g) be the third derivative of 0*g**4 + 1/100*g**6 + 0*g**3 + 0*g + 0 - 3/50*g**5 - 11*g**2. Factor q(f).
6*f**2*(f - 3)/5
Let x(d) be the second derivative of 5*