 2*a + 4 = -k, 3*k - 5*a = -0*a + 10. Let c be 7 + 1 + -3 + k. Determine p, given that -5*p**c + 7*p**5 - 6*p**5 - 16*p**3 + 16*p**4 = 0.
0, 2
Let o(s) be the third derivative of -1/24*s**4 + 43*s**2 + 5/24*s**3 - 1/240*s**5 + 0 + 0*s. Factor o(k).
-(k - 1)*(k + 5)/4
Let l(p) = p**2 - 2*p + 1. Let n be l(1). Suppose f - 5*f + 24 = n. Factor f*h + 5*h - 2*h**2 - 13*h + 4.
-2*(h - 1)*(h + 2)
Factor f**3 + 0 - 5*f + 1/3*f**4 - 13/3*f**2.
f*(f - 3)*(f + 1)*(f + 5)/3
Let w(m) be the first derivative of -m**3/4 + 63*m**2/8 - 89. Factor w(f).
-3*f*(f - 21)/4
Find w, given that -2*w**5 + 25 - 83*w + 6*w**5 - 2898*w**3 - 3*w**5 + 32*w**2 + 17 - 10*w**4 + 2916*w**3 = 0.
-2, 1, 3, 7
Let v(h) be the second derivative of -h**4/24 - 5*h**3/12 + 91*h - 1. Suppose v(u) = 0. What is u?
-5, 0
Factor -30*p**2 + 10*p**4 + 5088*p + 5*p**3 + 5079*p + 10 - 10162*p.
5*(p - 1)**2*(p + 2)*(2*p + 1)
Solve -1/4*m**2 + 7/4*m + 2 = 0.
-1, 8
Let j(z) be the third derivative of -z**7/245 + z**6/210 + 3*z**5/70 - 4*z**3/21 - 54*z**2. What is g in j(g) = 0?
-1, 2/3, 2
Suppose 0 = -17*y + 14*y + 30. Find a such that 3*a**3 - 2*a**2 + 8*a - 5*a**3 - 6*a**3 - y*a**2 + 12*a**4 = 0.
-1, 0, 2/3, 1
Let t be (-13 + (-776)/(-64))*(-60)/42. What is v in 1/4*v**4 + 0 - t*v**2 - 3/4*v - 1/4*v**3 = 0?
-1, 0, 3
Suppose 0 = -4*x + x + y + 15, -3*y - 3 = -2*x. Let g be ((-15)/x - -3)*1. Factor 1 + g*s**2 - 3/2*s.
(s - 2)*(s - 1)/2
Let d be (13 + -7)/(1 + 0 - -1). Let -31*j**4 + 28*j**4 + 0*j**2 + d*j**2 + 0*j**2 = 0. Calculate j.
-1, 0, 1
Let n(i) = -i**5 - i**4 + i**3 - i**2 - i - 1. Let h = 19 + -20. Let m(c) = 46*c**5 + 36*c**4 - 11*c**3 + c**2 + c + 1. Let x(r) = h*n(r) - m(r). Factor x(q).
-5*q**3*(q + 1)*(9*q - 2)
Let y(w) = -3*w**2 + w - 1. Let a(q) = 10*q**2 + 7*q - 8. Let i(b) = -a(b) - 3*y(b). Let i(m) = 0. What is m?
-11, 1
Suppose 440*m - 788 - 230 - 302 = 0. Solve -12/7*d - 3/7*d**m + 0 + 12/7*d**2 = 0.
0, 2
Let c(z) be the second derivative of 10*z**3 + 4*z**2 + 21*z + 13/3*z**4 + 0. Factor c(j).
4*(j + 1)*(13*j + 2)
Let z(g) = -g**4 + 19*g**3 + 60*g**2 - 96*g - 236. Let v(y) = -2*y**4 + 58*y**3 + 180*y**2 - 287*y - 707. Let w(d) = 4*v(d) - 13*z(d). Factor w(s).
5*(s - 4)*(s - 3)*(s + 2)**2
Let b(p) = -2*p**2 + 272*p + 8804. Let j be b(-27). Suppose -2/7*u**2 + j + 12/7*u = 0. Calculate u.
-1, 7
Let -2/13*x**4 - 16/13*x**3 + 196/13*x + 38/13*x**2 + 144/13 = 0. Calculate x.
-9, -2, -1, 4
Let b be -8 + (3 - -1 - -6). Determine q so that 36/7*q**b + 4*q - 8/7 = 0.
-1, 2/9
Let b = -2/999 + 335/999. Find s, given that b*s**2 - 1/3*s**3 + 1/3*s + 0 - 1/3*s**4 = 0.
-1, 0, 1
Let b(h) be the second derivative of -1/33*h**3 + 1/66*h**4 - 2*h + 0*h**2 + 0. Factor b(q).
2*q*(q - 1)/11
Suppose -223*j**2 + 19471 - 225*j**2 + 408*j + 676*j**2 - 226*j**2 + 1337 = 0. Calculate j.
-102
Suppose -p + 4*g - 8*g = 8, -g - 15 = -3*p. Let w(j) be the first derivative of -20/3*j**3 + 8 + j**p - 16*j + 16*j**2. Factor w(a).
4*(a - 2)**2*(a - 1)
Let g(m) be the second derivative of -m**5/90 - 9*m**2 + 17*m. Let p(o) be the first derivative of g(o). Factor p(k).
-2*k**2/3
Let f = -79 + 84. Suppose f*d - 17 = 2*i, 0 = -4*d - 2*i + 10 - 0. Factor 4/5*a**d + 4/5*a**2 - 4/5 - 4/5*a.
4*(a - 1)*(a + 1)**2/5
Factor 16/5 + 56/5*h - 14/5*h**3 - 4/5*h**2.
-2*(h - 2)*(h + 2)*(7*h + 2)/5
Let c = -627/2 + 321. Let h = 9 - c. Find o, given that -9/2*o**3 - h*o**2 - 3/2*o**4 + 9/2*o + 3 = 0.
-2, -1, 1
Suppose -5*z - 24 = -44. Factor -16*f + 45*f**3 - 41*f**3 + 48 - z*f**2 - 8*f**2.
4*(f - 3)*(f - 2)*(f + 2)
Let n be (504/(-476) + 2/34)*(-33)/9. Factor -3*v**2 + 1/3*v**3 + n*v + 1/3*v**4 - 4/3.
(v - 1)**3*(v + 4)/3
Let r(k) be the third derivative of k**6/450 + 7*k**5/300 + k**4/10 - 14*k**3/3 + k**2. Let c(m) be the first derivative of r(m). Factor c(z).
2*(z + 2)*(2*z + 3)/5
Let i(y) be the first derivative of 7*y**4/8 - 2*y**3 - 25*y**2/4 - 3*y + 3. Factor i(h).
(h - 3)*(h + 1)*(7*h + 2)/2
Let g = 206 + -206. Let q(h) be the first derivative of g*h - 1/12*h**3 - 1/16*h**4 + 1/8*h**2 + 1/20*h**5 + 4. Factor q(j).
j*(j - 1)**2*(j + 1)/4
Let q(f) be the third derivative of 5*f**8/168 - 5*f**7/42 - f**6/4 + 2*f**5/3 + 5*f**4/6 - 5*f**3/2 - 285*f**2 - 2*f. Let q(p) = 0. What is p?
-1, 1/2, 1, 3
Let g(v) = 5*v**3 - 4*v**3 + 8*v**2 + 0*v**3. Let h be g(-8). Factor -1/6*p**2 - 1/3*p + 1/6*p**3 + h.
p*(p - 2)*(p + 1)/6
Factor 0 - 162/19*g + 360/19*g**2 - 2/19*g**5 - 236/19*g**3 + 40/19*g**4.
-2*g*(g - 9)**2*(g - 1)**2/19
Let p(l) be the second derivative of -l**9/1890 + l**8/1680 + l**7/315 - l**6/180 + 11*l**4/12 + 10*l. Let h(q) be the third derivative of p(q). Factor h(n).
-4*n*(n - 1)*(n + 1)*(2*n - 1)
Factor 2/13*c**4 + 0 - 12/13*c**2 + 0*c + 2/13*c**3.
2*c**2*(c - 2)*(c + 3)/13
Let y(x) be the third derivative of x**5/330 - 43*x**4/66 + 1849*x**3/33 + 330*x**2 - 2. Factor y(s).
2*(s - 43)**2/11
Factor 327 - 2*i**2 - 171*i - 135 - 12*i - 7*i.
-2*(i - 1)*(i + 96)
Suppose 4*o + 2*v - 238 = 0, -2*o - 3*o + 297 = 3*v. Let m be (-8)/o + (-57)/(-90). Factor 0 - m*f**2 - f + 4*f**3 - 5/2*f**4.
-f*(f - 1)**2*(5*f + 2)/2
Let 582924 - 4422010 - j**3 + 4*j**3 + 176400*j - 4392914 - 1260*j**2 = 0. What is j?
140
Let d(h) = 109*h**2 - 140*h**2 - 1 - 81*h**2 - 332*h**2 - 81*h. Let b(q) = -1331*q**2 - 244*q - 4. Let a(s) = 3*b(s) - 8*d(s). Suppose a(f) = 0. Calculate f.
-2/21
Let y(j) = 35*j**5 + 220*j**4 + 372*j**3 + 90*j**2. Let d(c) = -105*c**5 - 660*c**4 - 1117*c**3 - 270*c**2. Let h(u) = -3*d(u) - 8*y(u). What is f in h(f) = 0?
-3, -2/7, 0
Let u(f) = 2*f + 5*f - 7 - 2*f**2 + f**2 - 5*f. Let v(s) = s - 1. Let i(m) = 3*u(m) - 15*v(m). Solve i(t) = 0.
-2, -1
Let k(u) be the third derivative of -u**7/420 + u**6/90 + u**5/60 - u**4/6 - 5*u**3/3 + 4*u**2. Let z(r) be the first derivative of k(r). Factor z(c).
-2*(c - 2)*(c - 1)*(c + 1)
Suppose -220*u - 10 = -225*u. Factor -6/5*g**u + 12 + 18/5*g.
-6*(g - 5)*(g + 2)/5
Suppose 19*h + 2064 = 86*h + 19*h. Factor 4/3*y**5 + 28/3*y**4 + 0 + 32/3*y + 80/3*y**2 + h*y**3.
4*y*(y + 1)*(y + 2)**3/3
Suppose 535*v**3 - 5*v**2 + v**2 - 102 - 12*v + 22 - 531*v**3 - 52*v = 0. What is v?
-2, 5
Determine d, given that 196 - 56*d + 9517*d**2 - 4760*d**2 - 4753*d**2 = 0.
7
Determine l so that -2/3*l**5 + 0 - 3*l**2 - 2/3*l**3 + 3*l**4 + 4/3*l = 0.
-1, 0, 1/2, 1, 4
Let z(g) = g**3 - g**2 - g + 1. Let s be 40/16*(-15 + -1). Let v(b) = -9*b**3 + 13*b**2 - 4. Let u(p) = s*z(p) - 5*v(p). Find j, given that u(j) = 0.
1, 2
Let c(d) = -5*d**2 - 10*d - 6. Let v(s) = s**2 - 6*s - 1. Let z be v(7). Let l(t) = 1. Let i(f) = z*l(f) + c(f). Factor i(w).
-5*w*(w + 2)
Suppose p = -2*d + 102, -2*p = -d + 9 + 32. Let f be (32/12)/(d/42). Factor 1/7*z**2 + 8/7*z + f.
(z + 4)**2/7
Let f(m) be the first derivative of 1/4*m - 3/8*m**2 - 1/16*m**4 - 19 + 1/4*m**3. Solve f(g) = 0.
1
Let m(x) = x**2 + 9*x + 12. Let r be m(-8). Suppose -f = s + r, -16 = -4*f + 5*s - s. Let -1/6*d**2 + f + 0*d = 0. Calculate d.
0
Suppose 3*b + 20*b = 138. Suppose 5*w = -2*o + 2*w + 3, -o + 3*w = -6. Suppose -b*v**2 - v**o - 2*v + v - 2*v**3 - 2*v = 0. What is v?
-1, 0
Suppose 3*i + 5*a = 28, 6*a - 14 = i + 3*a. Let g(t) = 15*t**4 - 5*t**3 + 5*t**2 - 5*t. Let x(v) = -v**4 - v**2 + v. Let n(l) = i*g(l) + 10*x(l). Factor n(j).
5*j*(j - 1)**2*(j + 1)
Let g(m) = 4*m**2 + 4*m**2 + 17*m**3 - 18*m**3 - 9*m + 16. Let n be g(7). Factor 10*t**2 + 15 + 15*t**n - 4*t**3 + 35*t + 9*t**3.
5*(t + 1)**2*(t + 3)
Let a(c) be the first derivative of -c**7/210 + c**6/150 + c**5/100 - c**4/60 + 9*c - 16. Let d(o) be the first derivative of a(o). Let d(k) = 0. Calculate k.
-1, 0, 1
Let w = -17 - -20. Determine u so that 3*u**3 + 13*u + 2*u**w - 5*u + 3*u**3 + 12*u**2 + 2*u**4 + 2 = 0.
-1
Suppose 47*n = 49*n + 164. Let f = 248/3 + n. Solve -f*q**3 + 2/3*q + 4/3*q**2 - 4/3 = 0.
-1, 1, 2
Let t(o) be the third derivative of o**7/945 - 2*o**6/135 - 4*o**5/45 + 8*o**4/27 + 80*o**3/27 + 54*o**2 - o. Determine l so that t(l) = 0.
-2, 2, 10
Let c(u) be the second derivative of -u**6/70 + 27*u**5/140 - 23*u**4/28 + 15*u**3/14 - 2*u + 82. Factor c(x).
-3*x*(x - 5)*(x - 3)*(x - 1)/7
Let f(x) be the first derivative of x**3/27 - 3*x**2/2 - 28*x/9 + 107. Suppose f(v) = 0. Calculate v.
-1, 28
Let y be -7*(-1)/4 + 7*14/(-56). Factor 2/3*c**3 + 0*c**2 + y - 1/3*c**5 - 1/3*c + 0*c**4.
-