
Let r(p) be the third derivative of 2*p**8/35 + 8*p**7/1575 - 383*p**6/900 + 103*p**5/150 - 43*p**4/90 + 8*p**3/45 + 45*p**2. Let r(a) = 0. What is a?
-2, 1/4, 4/9, 1
Let i(v) = 7*v**3 + 2*v**2. Let u be i(1). Let p(t) = -t**3 + 8*t**2 + 8*t + 9. Let r be p(u). Determine y, given that 2/11*y**3 + 2/11*y + 4/11*y**2 + r = 0.
-1, 0
Let v(y) = -24*y**3 + 28*y**2 - 22*y - 22. Let f(t) = t**3 - t**2 + t + 1. Let s(z) = -44*f(z) - 2*v(z). Factor s(c).
4*c**2*(c - 3)
Let u(g) be the third derivative of 0*g**3 + 0 + 0*g + 1/16*g**4 + 5*g**2 + 1/80*g**5. Determine k, given that u(k) = 0.
-2, 0
Determine p, given that -3*p**4 + 0*p + 0 + 0*p**2 + 3/5*p**5 + 18/5*p**3 = 0.
0, 2, 3
Let p(a) be the first derivative of 4*a**3/3 - a**2 - 8*a - 4. Let y(l) = 8*l**2 - 3*l - 16. Let g(x) = 11*p(x) - 6*y(x). Factor g(j).
-4*(j - 1)*(j + 2)
Let p(q) be the first derivative of 25*q**7/42 + 7*q**6/6 + q**5/2 - 13*q + 4. Let b(o) be the first derivative of p(o). Let b(k) = 0. What is k?
-1, -2/5, 0
Let m(a) be the second derivative of a**7/378 + a**6/135 - a**5/90 - a**4/27 + a**3/54 + a**2/9 + a - 6. Find t such that m(t) = 0.
-2, -1, 1
Let b(k) = k**2 + k + 2. Let i(g) = -25*g - 15. Let n(m) = -5*b(m) + i(m). Factor n(f).
-5*(f + 1)*(f + 5)
Let y(s) be the first derivative of 2*s**5/5 - s**4/4 + s**3/3 + s**2/2 - 7. Let v(a) = -a**4 + a**3 - a**2 - a. Let t(l) = 4*v(l) + 4*y(l). Factor t(u).
4*u**4
Let c(s) be the first derivative of -10*s**2 + 28 + 22*s - 2/3*s**3. Factor c(v).
-2*(v - 1)*(v + 11)
Let j(r) be the first derivative of -2*r**5/13 + 19*r**4/26 - 32*r**3/39 - 4*r**2/13 + 54. Determine a so that j(a) = 0.
-1/5, 0, 2
Let r(a) = 4*a - 47. Let f be r(13). Suppose -f*p - 6 = -16. Find k such that 2*k + 0 - 2*k**2 - 1/2*k**5 + p*k**4 - 3/2*k**3 = 0.
-1, 0, 1, 2
Factor 41/2 + 1/2*f**3 + 43/2*f**2 + 83/2*f.
(f + 1)**2*(f + 41)/2
Let i = -2/75665 - -75679/529655. What is n in 0 + 3/7*n**2 - 1/7*n**5 + 2/7*n - 3/7*n**4 - i*n**3 = 0?
-2, -1, 0, 1
Let k = 9 + -5. Let b = -77 - -80. Let f(g) = 7*g**3 - 9*g**2 + 13*g - 3. Let u(a) = -6*a**3 + 9*a**2 - 12*a + 3. Let r(x) = b*f(x) + k*u(x). Factor r(c).
-3*(c - 1)**3
Let x be ((6/(-39))/((-1)/(-1)))/(2/(-26)). Factor -2/5*g**4 - 4/5*g**3 + 0*g**x + 0*g + 0.
-2*g**3*(g + 2)/5
Suppose 3*g + 4*j - 25 = 0, 5*g + 1 - 24 = -2*j. Suppose 4*l = -2*p + 8, -4*l - g*p - p = -16. Solve 8/7*b - 4/7*b**2 + l = 0 for b.
0, 2
Suppose -4*z + 25 = 13. Suppose -2 = -w - 0. Factor s**w - s + 4 + z*s + 2*s.
(s + 2)**2
Suppose 0 = 7*x - 3*x - 8. Suppose -5*z = -z - 8. Factor 2*h**z - 2*h**x - 5*h**2.
-5*h**2
Let w be (-58)/(-30) + 591/(-985). Let h = -2 + 4. Factor -2/3*g**3 + 8/3*g - 16/3 + w*g**h.
-2*(g - 2)**2*(g + 2)/3
Let z(k) = 13*k**4 - 7*k**3 + 7*k**2. Let a(n) be the second derivative of n**6/5 - 3*n**5/20 + n**4/4 + 31*n. Let b(y) = -7*a(y) + 3*z(y). Factor b(m).
-3*m**4
Let t(b) be the second derivative of -b**5 - 65*b**4/6 - 245*b**3/24 - 15*b**2/4 - 4*b - 15. Let t(l) = 0. What is l?
-6, -1/4
Let h(x) be the third derivative of x**6/90 + x**5/15 + x**4/6 + 13*x**3/3 - 9*x**2. Let a(s) be the first derivative of h(s). Suppose a(f) = 0. What is f?
-1
Factor -121/2*x + 0 + 1/4*x**2.
x*(x - 242)/4
Let g be ((-4 - 110/(-28))*2)/((-21)/245). Factor -u**3 + 4/3 - g*u**2 + 4/3*u.
-(u - 1)*(u + 2)*(3*u + 2)/3
Let a(d) = -35*d + 665. Let n be a(19). Solve n - 3/5*i**3 + 12/5*i + 9/5*i**2 = 0 for i.
-1, 0, 4
Let g(y) = y. Suppose 0*i - 5 = -i. Let c be g(i). Suppose 6*z - z - z**3 - 5*z + c*z + 3 + z**2 = 0. What is z?
-1, 3
Let z(h) = h**3 + 5*h**2 + 6*h. Let m be (-4 - (-20)/8)/((-2)/(-4)). Let b be z(m). Factor b*g + 0 + 2/11*g**3 + 2/11*g**4 - 2/11*g**2 - 2/11*g**5.
-2*g**2*(g - 1)**2*(g + 1)/11
Factor -5*p**2 + 3*p**3 - 225*p - 8*p**3 + 18*p**2 - 93*p**2 + 810.
-5*(p - 2)*(p + 9)**2
Let b be 10/(-7)*84/(-48). Find r such that -1/2*r**3 - b*r - 1 - 2*r**2 = 0.
-2, -1
Let s(r) = 10*r**3 - 362*r**2 - 22326*r - 453966. Let j(x) = -7*x**3 + 363*x**2 + 22326*x + 453965. Let z(c) = 4*j(c) + 3*s(c). Find t such that z(t) = 0.
-61
Let j = 54 + -50. Let s(q) = 2*q. Let l be s(0). Factor -p**j + 0 + 1/3*p**5 + l*p + p**3 - 1/3*p**2.
p**2*(p - 1)**3/3
Let j(n) be the first derivative of -n**5/5 + 3*n**4/2 - 3*n**3 + 2*n**2 - 56. Determine g so that j(g) = 0.
0, 1, 4
Suppose -2*k + k + 4 = 0. Suppose -p = -6 + 2, 3*n + 10 = k*p. Factor 2 - 5 + n*m**3 + 3.
2*m**3
Let b(c) = -2*c**3 - 8*c**2 - 3*c + 7. Let m be b(-5). Let l be m/20*(-1 - -16). Factor -36*u**2 - u**3 - 42 + 11*u**3 + 15 + l*u - u**4.
-(u - 3)**3*(u - 1)
Solve -171*o**3 + 550*o - 78 + 36*o**4 - 59*o**3 + 3*o**4 - 47 - 14*o**4 + 420*o**2 = 0.
-1, 1/5, 5
Let s be 9/5 - 1/(-5). Suppose s*t = -3*t + 10. Find u such that -3/2*u**t - 3/4*u**3 + 0 + 0*u = 0.
-2, 0
Let n(w) = 2*w**2 + w - 9. Let i be n(-3). Suppose -i*c + 2 = -5*c. What is h in 8/9 + 0*h + 20/9*h**3 - 14/3*h**c = 0?
-2/5, 1/2, 2
Let r = 23550 - 23547. Suppose 3*k**3 + 3/4*k**4 - 9/4 - r*k + 3/2*k**2 = 0. What is k?
-3, -1, 1
Let y(v) = -22*v - 5. Let i be y(12). Let b = i - -269. Let -1/7*h**2 + 1/7*h**3 + b - 2/7*h = 0. What is h?
-1, 0, 2
Let m(q) be the first derivative of -q**6/24 + 21*q**5/20 - 73*q**4/8 + 161*q**3/6 + 147*q**2/8 - 343*q/4 - 19. Factor m(f).
-(f - 7)**3*(f - 1)*(f + 1)/4
Let k = -1115/6 + 186. Let f(z) be the second derivative of 0 + 0*z**3 + 1/36*z**4 + z - k*z**2. Factor f(j).
(j - 1)*(j + 1)/3
Let p(k) be the first derivative of -k**3 - 15 + 9*k**2 - 9/8*k**4 - 12*k + 3/10*k**5. Factor p(t).
3*(t - 2)**2*(t - 1)*(t + 2)/2
Factor 168*z**2 + 175*z**3 + 4*z**5 + 84*z**2 + 108*z + 161*z**3 - 4*z**4 + 76*z**2 + 124*z**4.
4*z*(z + 1)**3*(z + 27)
Let f(m) be the first derivative of -28*m**6/27 - 34*m**5/9 - 29*m**4/6 - 62*m**3/27 - m**2/9 - 406. Factor f(d).
-2*d*(d + 1)**3*(28*d + 1)/9
Let u(t) be the third derivative of 0 + 0*t**3 + 0*t**4 + 1/140*t**7 - 1/40*t**5 + 0*t**6 - 7*t**2 + 0*t. Suppose u(w) = 0. What is w?
-1, 0, 1
Suppose -19*o - 64 = -35*o. Factor 2*x - o + 1/4*x**3 + 7/4*x**2.
(x - 1)*(x + 4)**2/4
Let k be 1/(-8) - (-1356)/96. Factor -4*i**2 + 4*i**4 + 33 + 8*i - 19 - k - 8*i**3.
4*i*(i - 2)*(i - 1)*(i + 1)
Factor 50*i + 75*i**3 + 12*i**2 - 2*i**2 - 39*i**3 - 35*i**3 + 5*i**2.
i*(i + 5)*(i + 10)
Let k(w) be the first derivative of w**9/6048 - w**7/560 - w**6/360 - w**3/3 - 22. Let r(s) be the third derivative of k(s). Factor r(z).
z**2*(z - 2)*(z + 1)**2/2
Let w(b) = -6*b**2 + 13*b + 10. Let d(p) = -p**2 + p + 2. Let i(q) = -5*d(q) + w(q). Factor i(t).
-t*(t - 8)
Factor 2/11*f**2 - 2/11*f**3 + 0 - 2/11*f**4 + 2/11*f.
-2*f*(f - 1)*(f + 1)**2/11
Let n = -333 + 338. Let f(h) be the third derivative of 0*h**3 - 5*h**2 - 1/4*h**4 - 1/40*h**6 + 0 + 0*h + 3/20*h**n. Suppose f(j) = 0. What is j?
0, 1, 2
Let z(r) be the second derivative of -r**7/168 + r**6/18 + 8*r**3/3 - 16*r. Let h(u) be the second derivative of z(u). Factor h(b).
-5*b**2*(b - 4)
Suppose -i + 4*i = -6*i. Let u(f) = -f**2 + 2*f + 5. Let x be u(i). What is z in 16/9*z - 23/9*z**3 - 4/9 - 1/9*z**2 + 7/9*z**x + 5/9*z**4 = 0?
-2, -1, 2/7, 1
Let z be (42/(-231) + -1 + 15/22)/(-1). Factor 1/4 + 1/4*p**2 + z*p.
(p + 1)**2/4
Determine k, given that -24 + 1592/19*k + 14/19*k**2 = 0.
-114, 2/7
Let t(u) = -4*u**3 - 4*u**2 - 2. Let r(v) = 13*v**3 + 12*v**2 - v + 7. Let z = 21 + -14. Let w(i) = z*t(i) + 2*r(i). Determine q, given that w(q) = 0.
-1, 0
Suppose 0 = 11*q - 6*q - 170. Let v(w) = -4*w**2 - 2. Let n(c) = -23*c**2 + c - 12. Let m(f) = q*v(f) - 6*n(f). What is k in m(k) = 0?
1, 2
Suppose -162 + 351/2*c + 21/2*c**3 - 1/2*c**4 - 135/2*c**2 = 0. What is c?
3, 12
Suppose 3*u = u - 5*j + 14, -5*j + 32 = -4*u. Let g be 3*u/81 - (-37)/9. Find k such that -512/7*k - 32/7*k**3 + 2/7*k**g + 192/7*k**2 + 512/7 = 0.
4
Let l(k) = -711*k - 14931. Let w be l(-21). Factor -2/3*q - 1/3*q**3 + w + q**2.
-q*(q - 2)*(q - 1)/3
Let i be 8/((-8)/7) + 6 + 1. Let d = 10 - 8. Factor 1/4*v**4 - 1/4*v**3 + i + 1/4*v - 1/4*v**d.
v*(v - 1)**2*(v + 1)/4
Factor -9/4*b + 0 - 3*b**2 + 21/4*b**3.
3*b*(b - 1)*(7*b + 3)/4
Let t(q) = -15*q**3 - 45*q**2 - 40*q + 5. Let i(k) = -7*k**3 - 22*k**2 - 20*k + 2. Let p(f) = 5*i(f) - 2*t(f). Let p(s) = 0. What is s?
-2, 0
Factor 0*t**2 + 0 + 1/6*t - 1/6*t**3.
-t*(t - 1)*(t + 1)/6
Let y(q) be the second derivative of q**6/60 +