be the second derivative of -w**7/14 + 9*w**5/5 - 4*w**4 + 211*w. Let q(k) = 0. What is k?
-4, 0, 2
Suppose 63*m - 18 = 60*m. Let g(r) be the second derivative of 0*r**2 - m*r - 1/105*r**6 + 1/14*r**4 - 2/21*r**3 + 0 + 0*r**5. Factor g(c).
-2*c*(c - 1)**2*(c + 2)/7
Suppose -3*v = h, 20*h = -2*v + 14*h. Factor v - 3/4*m**2 + 0*m**3 + 1/4*m**4 - 1/2*m.
m*(m - 2)*(m + 1)**2/4
Factor -8*b + 42/5 - 2/5*b**2.
-2*(b - 1)*(b + 21)/5
Suppose 0 = -2*j - 4*q + 30, -2*q = 2*j - 0*q - 20. Determine x so that 0*x**4 - 2*x**3 + x**j - 3*x**4 + 2*x**4 + 2*x**2 + x - 1 = 0.
-1, 1
Find n, given that -2/7*n**2 - 90/7 - 36/7*n = 0.
-15, -3
Suppose -3*z = 4*o - 308, 0*o - 4*z - 58 = -o. Factor 3 + 8*p**5 - 3 - 4*p**3 - o*p**4 + 70*p**4.
4*p**3*(p - 1)*(2*p + 1)
Let l be (4 + (-3)/2 + -2)*172. Let r = 90 - l. Factor -6/11*u**r + 0 + 0*u - 2/11*u**2 + 6/11*u**3 + 2/11*u**5.
2*u**2*(u - 1)**3/11
Suppose 0 = -3*g + 4*n, 0*g + 3*g + n - 15 = 0. Factor 12*b - 6*b**2 + g*b + 2*b**3 + 14*b + 20*b**2 + 18.
2*(b + 1)*(b + 3)**2
Let a(p) = 56*p**2 - 278*p + 296. Let c(i) = 5*i**2 - 25*i + 27. Let t(h) = -6*a(h) + 68*c(h). Factor t(z).
4*(z - 5)*(z - 3)
Let x = 0 + -8. Let b(z) = -2*z**2 - 8*z + 6. Let s(k) = 5*k**2 + 23*k - 18. Let m(l) = x*b(l) - 3*s(l). Find n, given that m(n) = 0.
2, 3
Let m(q) = -5*q - 45. Let y be m(-19). Let z = y - 47. Determine c so that -14/3*c**4 + 0 + 4/3*c**z + 14/3*c**2 - 4/3*c = 0.
-1, 0, 2/7, 1
Let r(m) be the third derivative of -m**6/300 + m**4/20 + 2*m**3/15 + 51*m**2 + 2. Determine j so that r(j) = 0.
-1, 2
Let x(n) be the first derivative of -n**4/8 - 3*n**3/2 - 2*n**2 - 74. Factor x(q).
-q*(q + 1)*(q + 8)/2
Let w be 5/(-720)*-56*((-18)/21 - -2). Let -2*b + 10/9 - w*b**2 = 0. What is b?
-5, 1/2
Suppose -2*j + w + 9 = 0, -5*w - 24 - 1 = 0. Find d such that -6 + 18 + 8 + 5*d**3 - 5*d**j - 20*d = 0.
-2, 1, 2
Let q(l) = -24*l**3 - 8*l**2 + 14. Let r(s) = 5*s**3 + 2*s**2 - 3. Let p(u) = -3*q(u) - 14*r(u). Factor p(i).
2*i**2*(i - 2)
Let 2/7*w**5 + 6/7*w**3 + 46/7*w**2 - 64/7*w + 24/7 - 2*w**4 = 0. Calculate w.
-2, 1, 6
Let v be ((-6)/(-12))/(1/6). Suppose 0 = -2*u - v*u + 10. Factor -2*d + 2*d**2 + 1 - d**2 + 2*d - u*d.
(d - 1)**2
Let g = -2280 - -2284. Factor -2/5*i**g - 4/5*i**2 + 0 - 6/5*i**3 + 0*i.
-2*i**2*(i + 1)*(i + 2)/5
Let v(k) be the third derivative of k**7/140 + k**6/10 + 11*k**5/20 + 3*k**4/2 + 9*k**3/4 + k**2 + 9. Suppose v(h) = 0. What is h?
-3, -1
Let z(t) = -t**2 - 40*t + 63. Let o be z(-40). Let a = o - 61. Factor 2/5*g**a + 8/5*g + 6/5.
2*(g + 1)*(g + 3)/5
Find w such that 39/2*w**4 - 1125/2 - 3/2*w**5 + 1425/2*w - 105*w**2 - 63*w**3 = 0.
-3, 1, 5
Let n(f) be the first derivative of f**8/560 - 3*f**7/280 + f**6/40 - f**5/40 - 7*f**3/3 - 9. Let u(j) be the third derivative of n(j). Factor u(c).
3*c*(c - 1)**3
Let h(t) = 50*t - 94. Let a be h(2). Let r(y) be the second derivative of 19/4*y**4 - a*y**2 + 0 - 4*y**3 - 21/20*y**5 + 3*y. Factor r(o).
-3*(o - 2)*(o - 1)*(7*o + 2)
Let h(x) be the second derivative of x**4/30 - 2*x**3/15 - 8*x**2/5 - 9*x + 2. What is b in h(b) = 0?
-2, 4
Suppose -30*a + 6*a**2 + 6*a - 3*a**2 + 0*a**2 + 21 = 0. What is a?
1, 7
Let w = 4716 + -23563/5. Determine d so that -13/5*d**3 + 28/5*d**2 - w*d + 2/5 = 0.
2/13, 1
Let x(v) be the second derivative of 43*v + 0*v**4 + 0*v**3 + 0 + 1/189*v**7 + 2/135*v**6 + 0*v**2 - 4/45*v**5. What is a in x(a) = 0?
-4, 0, 2
Suppose -q = q + 330. Let d = q - -168. Suppose -2/3*m**2 + 2/9*m - 2/9*m**d + 2/3 = 0. Calculate m.
-3, -1, 1
Let b be (-12)/(-126)*-6 + (-222)/(-315). Let z(o) be the first derivative of 2/5*o**2 - b*o**3 - 2/5*o + 4. Factor z(j).
-2*(j - 1)**2/5
Determine w, given that 4 - 26*w**2 + 20 - 4*w + 10*w**2 + 0*w - 8*w**2 + 4*w**3 = 0.
-1, 1, 6
Factor -95/2*s**3 + 0 - 25/2*s**4 - 49/2*s - 119/2*s**2.
-s*(s + 1)*(5*s + 7)**2/2
Let h = 23 - 21. Factor 2*l**4 - 8*l + 3*l**2 - 8*l**3 + 0*l**h + 8*l**2 + l**2 + 2.
2*(l - 1)**4
Suppose 3*c - 15 = -2*c. Factor -3*y**4 - 119*y**c + 4*y + 128*y**3 - 16*y.
-3*y*(y - 2)**2*(y + 1)
Let y(n) = n - 36*n**3 + 69*n**3 + 0*n**2 + 1 - n**2 - 34*n**3. Let g be y(-2). Determine l so that 3/2*l - 3/2*l**g + 3/2 - 3/2*l**2 = 0.
-1, 1
Let i(n) = -50*n**3 - 204*n**2 - 292*n - 126. Let q(t) = -7*t**3 - 29*t**2 - 42*t - 18. Let h(m) = -6*i(m) + 44*q(m). What is v in h(v) = 0?
-3, -1/2
Let o be ((-216)/(-81))/((-12)/(-9)). Find z, given that 0*z**3 + 0 + 0*z + 2/15*z**o - 2/15*z**4 = 0.
-1, 0, 1
Let c(b) = b**3 - 2*b**2 + 4. Let y be c(2). Suppose y*t + 6 = 14. Factor 2/9*o - 4/9 + 2/9*o**t.
2*(o - 1)*(o + 2)/9
Suppose -26*f**2 - 35*f**2 + 63*f**2 - 504*f + 31752 = 0. What is f?
126
Let b(q) be the first derivative of -q**4/18 - 2*q**3/3 + 4*q**2/3 + 40*q/9 - 58. Factor b(f).
-2*(f - 2)*(f + 1)*(f + 10)/9
Let a(n) be the first derivative of -3*n**5/50 + n**4/2 + 6*n**3/5 + 39*n - 1. Let f(t) be the first derivative of a(t). Factor f(z).
-6*z*(z - 6)*(z + 1)/5
Suppose -3*q = 2*q. Factor q*t**2 + 5*t**3 - t**3 - 2*t**2 - 2*t**3.
2*t**2*(t - 1)
Let t(r) be the second derivative of -r**6/25 + 9*r**5/50 + 2*r**4/5 - 12*r**3/5 + 63*r. Find i, given that t(i) = 0.
-2, 0, 2, 3
Let d(w) be the third derivative of 5*w**8/2856 - 6*w**7/595 + 7*w**6/1020 + 13*w**5/255 - w**4/17 - 8*w**3/51 + w**2 + 52. What is k in d(k) = 0?
-1, -2/5, 1, 2
Let j be (-3 - (-98)/21)*72/45. Factor 2/3*g**3 + j + 0*g - 2*g**2.
2*(g - 2)**2*(g + 1)/3
Let p(j) be the first derivative of 54/5*j - 9 + 24/5*j**3 - 4/5*j**4 - 54/5*j**2. Find a, given that p(a) = 0.
3/2
Let f = 15557 - 62219/4. Find u such that -f*u - 3/2 + 3/4*u**3 + 0*u**2 = 0.
-1, 2
Let n(m) = -211*m - 1052. Let x be n(-5). Factor -3/10*y**2 + 0 + 1/10*y**x + 1/5*y.
y*(y - 2)*(y - 1)/10
Let i(k) be the second derivative of k**6/30 + 7*k**5/10 + 5*k**4 + 25*k**3/3 - 125*k**2/2 - 3*k - 11. Factor i(x).
(x - 1)*(x + 5)**3
Suppose -8*w = 3*c - 17, 5*w + 15 = 5*c + 5. Determine r so that 0 + 21/4*r**5 - 75/4*r**c + 0*r - 9/2*r**2 - 9*r**4 = 0.
-1, -2/7, 0, 3
Let q = 19 - -11. Let v = -148/5 + q. Factor 0*p + 0*p**2 - v*p**4 - 2/5*p**5 + 0 + 4/5*p**3.
-2*p**3*(p - 1)*(p + 2)/5
Solve -24*a**4 + 20*a**2 - 38*a**3 + 40*a**4 - 338*a**5 + 340*a**5 = 0.
-10, 0, 1
Let w(c) be the second derivative of c**4/18 - 2*c**3/9 - 40*c**2 + 115*c - 1. Factor w(f).
2*(f - 12)*(f + 10)/3
Let y be 4/22 + 312/715*25/(-115). Find z, given that 68/23*z**3 - y*z + 52/23*z**4 + 14/23*z**5 - 4/23 + 32/23*z**2 = 0.
-1, 2/7
Let l(q) be the third derivative of q**8/84 + 16*q**7/105 + 8*q**6/15 - 6*q**5/5 - 27*q**4/2 - 36*q**3 - 35*q**2. Suppose l(d) = 0. What is d?
-3, -1, 2
Suppose 5*u = 4*y - 3 - 2, -2*u + 6 = 0. Suppose 2*k - 19 = 4*j - y, 4*k + 2*j - 18 = 0. Factor -b**4 + 12*b**5 + b**3 + b**3 - 13*b**k + 0*b**4.
-b**3*(b - 1)*(b + 2)
Let d(t) = -3*t**4 - 6*t**3 - 3*t**2 + 6*t - 6. Let r(v) = -3*v**4 - 6*v**3 - 2*v**2 + 6*v - 5. Let m = 44 - 38. Let z(q) = m*r(q) - 5*d(q). Factor z(x).
-3*x*(x - 1)*(x + 1)*(x + 2)
Let k(r) be the first derivative of -3*r**4/4 - 9*r**3 - 45*r**2/2 - 21*r - 108. Factor k(x).
-3*(x + 1)**2*(x + 7)
Let a = -72253/9 + 8029. Find x, given that 0 - 8/9*x**2 - a*x - 2/9*x**5 + 4/9*x**4 + 2/3*x**3 = 0.
-1, 0, 2
Let x(n) = -n**4 + n**2 - 1. Let v(u) = -u**5 - 7*u**4 - 14*u**3 - 15*u**2 - 9*u - 3. Let y be (-9 - -8 - -1) + 4 + 0. Let w(f) = y*x(f) - 4*v(f). Factor w(i).
4*(i + 1)**4*(i + 2)
Let t = -43576 + 392186/9. Suppose t - 10/9*y + 2/3*y**2 + 10/9*y**3 - 8/9*y**4 = 0. Calculate y.
-1, 1/4, 1
Factor 0*i**4 - 2*i**2 + 2*i**5 + 16*i - 3226 + 2*i**4 - 10*i**3 + 3218.
2*(i - 1)**3*(i + 2)**2
Suppose 65/2*r + 16 + 17*r**2 + 1/2*r**3 = 0. Calculate r.
-32, -1
Let m(c) = -c**3 + 27*c - 10. Let n be m(5). What is g in 4/7*g**3 + n + 6/7*g**4 + 4/7*g - 2*g**2 = 0?
-2, 0, 1/3, 1
Let k = -24 - -27. Factor -7*c + 2 - 2*c**2 + c**k + 15*c - 9*c.
(c - 2)*(c - 1)*(c + 1)
Let b(t) be the third derivative of 1/120*t**6 + 2/3*t**3 + 0 + 0*t + 2*t**2 + 1/10*t**5 + 3/8*t**4. Factor b(a).
(a + 1)**2*(a + 4)
Let r = -41473/5 + 8295. Factor 0*k**3 + 2/5*k**4 - 4/5*k**2 + 0*k + r.
2*(k - 1)**2*(k + 1)**2/5
Let k(x) be the first derivative of -2*x**5/5 - 8*x**4 - 160*x**3/3 - 128*x**2 + 512. Find m such that k(m) = 0.
-8, -4, 0
Let b(l) = -3*l**4 - 24*l**3 - 18*l**2 + 117*l - 72. Let u(w) = -3*w**4 - 24*w**3 - 18*w**