e of -9/10*n**2 + 25 + 6/25*n**5 + 0*n + 1/30*n**6 - 2/5*n**3 + 2/5*n**4. Factor p(r).
r*(r - 1)*(r + 1)*(r + 3)**2/5
Let z = -30 + 25. Let a(b) = -20*b**2 - 41*b + 8. Let c(l) = -60*l**2 - 122*l + 24. Let v(t) = z*c(t) + 14*a(t). Suppose v(s) = 0. What is s?
-2, 1/5
Let v = -360 + 256. Let a = -102 - v. Factor 0*q**a + 0*q + 0 - 1/8*q**3.
-q**3/8
Let z(v) = -2*v - 3. Let b be z(-4). Factor -2*g**4 + 10*g**3 - 3*g**4 - b*g**2 + 0*g**4.
-5*g**2*(g - 1)**2
Factor 36*z**2 - 108*z - 4*z**3 + 329 - 113 - 108.
-4*(z - 3)**3
Let v(z) be the second derivative of -5*z**7/42 - 7*z**6/6 + z**5/2 + 35*z**4/6 - 5*z**3/6 - 35*z**2/2 - 461*z. Suppose v(g) = 0. Calculate g.
-7, -1, 1
Let x(h) = 3*h**5 - 20*h**4 - 23*h**3 - 2*h**2 - 2*h. Let i(b) = 8*b**5 - 60*b**4 - 68*b**3 - 7*b**2 - 7*b. Let u(q) = 2*i(q) - 7*x(q). Factor u(s).
-5*s**3*(s - 5)*(s + 1)
Find b such that -1682/13 + 2/13*b**3 - 118/13*b**2 + 1798/13*b = 0.
1, 29
Let q = -12563 - -12563. Factor q + 4/5*k - 2/5*k**2.
-2*k*(k - 2)/5
Let b(l) be the second derivative of 7*l**4/12 + l**3/2 - 2*l**2 + 289*l. Find o, given that b(o) = 0.
-1, 4/7
Let c(o) = o**2 - o + 2. Let l be c(3). Let y be (-16)/24 + l/3. Factor -1 - 5 - 8*d - 25*d - 39*d**y - 12*d**3.
-3*(d + 1)*(d + 2)*(4*d + 1)
Suppose 5*x - 4*s = -0*s - 16, -2*x + s = 7. Let y(z) = z**3 + 3*z**2 - 5*z - 1. Let i be y(x). Factor -1/4*q**2 + 0*q + 0 + 1/2*q**i.
q**2*(2*q - 1)/4
Let l(n) = -n**2 - 558*n + 8595. Let m be l(15). Let -8/5*a**3 + 0 + 8/5*a**2 + 2/5*a**4 + m*a = 0. Calculate a.
0, 2
Let k = -60282/19 + 3174. Solve 2/19*u**2 + 16/19*u - 2/19*u**3 - k = 0 for u.
-3, 2
Let t be (-2)/3 + 128/48 + 0. Factor t*y**3 - 70*y + 6*y**2 + 0*y**3 + 62*y.
2*y*(y - 1)*(y + 4)
Let o(x) be the second derivative of -x**6/60 - x**5/4 - x**4/2 + 29*x**3/6 - 35*x**2/4 - x + 55. Suppose o(d) = 0. Calculate d.
-7, -5, 1
Let x(i) be the second derivative of i**5/20 - 3*i**4/10 + 7*i**3/30 + 3*i**2/5 + 23*i. Solve x(l) = 0.
-2/5, 1, 3
Let b be 5/(8 + -2 + -3)*2. Suppose 4/3*m - b*m**2 + 0 = 0. Calculate m.
0, 2/5
Let k(t) be the third derivative of 1/140*t**5 + 0*t + 0*t**3 + 0 + 8*t**2 + 0*t**4 - 11/840*t**6 - 2/735*t**7. Factor k(g).
-g**2*(g + 3)*(4*g - 1)/7
Let 0*m + m**4 - 9/7*m**3 + 0 + 2/7*m**2 = 0. Calculate m.
0, 2/7, 1
Let f be 4/38 + 0 + 2998/38. Let d = 159/2 - f. Find p, given that 1/2*p + 0 + 1/4*p**4 - 1/4*p**2 - d*p**3 = 0.
-1, 0, 1, 2
Let n(d) be the second derivative of 3*d**5/10 - d**3/2 + 39*d. Let q(v) = -v**3 + v. Let b(o) = -5*n(o) - 35*q(o). Factor b(k).
5*k*(k - 2)*(k + 2)
Let f(j) be the first derivative of -j**4/21 - 4*j**3/7 - 16*j**2/7 - 49*j + 48. Let d(v) be the first derivative of f(v). Factor d(w).
-4*(w + 2)*(w + 4)/7
Let h(r) = -6*r - 2 - 16*r**2 - 21*r**2 + 36*r**2. Let k be h(-1). Let -v**2 + 1/2*v**k + 1 - 1/2*v = 0. What is v?
-1, 1, 2
Let o = 24118 - 24116. Factor -2 + o*f**2 + 1/5*f**3 - 1/5*f.
(f - 1)*(f + 1)*(f + 10)/5
Let r(d) be the second derivative of -d**7/21 - 8*d**6/75 - d**5/50 + d**4/15 - d - 23. Factor r(i).
-2*i**2*(i + 1)**2*(5*i - 2)/5
Factor -28/3 + 2/3*x**2 + 10/3*x.
2*(x - 2)*(x + 7)/3
Suppose 0 = -2*q - 5*x - 20, 3*q - 2*x - 2*x = 16. Suppose q = -i + 3*i - 5*j - 24, i + 2 = -j. Let -i*f - 2 + 5*f - f**2 + 0*f + 0*f = 0. Calculate f.
1, 2
Let i = 668 - 668. Let n(d) be the second derivative of -2*d + 3/40*d**5 + 0*d**2 + 4*d**3 + i + d**4. Suppose n(k) = 0. What is k?
-4, 0
Let v(y) be the third derivative of -y**6/240 + 7*y**5/24 + 3*y**4/4 - 34*y**2 - 2*y. Factor v(a).
-a*(a - 36)*(a + 1)/2
Let r(d) be the second derivative of 21*d - 1/24*d**3 + 1/4*d**2 + 1/80*d**5 - 1/24*d**4 + 0. What is k in r(k) = 0?
-1, 1, 2
Suppose -68 = -6*x - 38. Let y(z) be the first derivative of 0*z**2 - 2/5*z**x - 1/3*z**6 - 3 + 0*z**3 + 0*z**4 + 0*z. Factor y(k).
-2*k**4*(k + 1)
Let x = -6781/8 - -848. Let u(s) be the first derivative of 1/6*s**3 - s + 2 + x*s**4 + 1/10*s**5 - 3/4*s**2. Find f, given that u(f) = 0.
-2, -1, 1
Let j be ((-2)/4)/(-1*7/70). Let r(h) be the third derivative of 0*h + h**2 + 0*h**4 - 2/15*h**j + 0 + 0*h**3 + 1/30*h**6. Factor r(q).
4*q**2*(q - 2)
Let g be 2 + (3 - (-2 - -4)). Suppose -16*f**2 + g*f**3 - 2*f**3 + 14*f**2 = 0. What is f?
0, 2
Let w(r) be the first derivative of -r**3 + 3*r**2/2 + 168*r + 192. Factor w(q).
-3*(q - 8)*(q + 7)
What is w in 19*w**4 - 100*w**2 + 13*w**4 + 36*w**3 - 36*w**4 + 108*w - 40 = 0?
1, 2, 5
Let r = -1294 + 1296. Let q(x) be the second derivative of 6*x + 32/3*x**3 - 5/3*x**4 - 8*x**r + 0 - 7/5*x**5. Factor q(m).
-4*(m - 1)*(m + 2)*(7*m - 2)
Suppose 8*v + 1507 = 1531. Let w(d) be the third derivative of -1/48*d**4 - 3*d**2 + 0*d + 1/12*d**v + 0 + 1/480*d**5. Suppose w(y) = 0. Calculate y.
2
Let l(u) be the first derivative of -2/11*u - 4/55*u**5 + 9 - 1/22*u**4 + 2/11*u**3 + 1/11*u**2. Let l(a) = 0. Calculate a.
-1, 1/2, 1
Let t(x) be the third derivative of 0 + 2/15*x**4 + 0*x**6 + 0*x - 1/525*x**7 + 1/25*x**5 - 16*x**2 + 1/5*x**3. Suppose t(w) = 0. Calculate w.
-1, 3
Suppose -4232 - 1/2*a**2 + 92*a = 0. What is a?
92
Suppose -3*t = -5*g - 26, 0 = 4*t - 4*g + 2 - 26. Let 105*c + 4 - 4*c**t - 105*c = 0. Calculate c.
-1, 1
Let t(o) = 9*o**3 - 61*o**2 + 105*o - 48. Let g(m) = -44*m**3 + 304*m**2 - 524*m + 240. Let b(d) = 5*g(d) + 24*t(d). Suppose b(p) = 0. What is p?
1, 12
Let a(b) = b**2 - 13*b + 78. Let z be a(16). Factor 98*r**3 + 22*r + 8*r + 624 - z*r**2 - 626.
2*(r - 1)*(7*r - 1)**2
Let z(w) = w**2 - 11*w - 24. Let h be z(13). Let 23*i - 17*i - 10*i**2 + i**3 + h*i**4 + i**3 = 0. Calculate i.
-3, 0, 1
Let w(y) be the third derivative of 5*y**2 + 0*y + 0*y**5 + 0*y**3 - 2/105*y**7 - 1/30*y**6 + 0 + 0*y**4. Suppose w(k) = 0. Calculate k.
-1, 0
Let v = -31 + -63. Let q = 472/5 + v. Suppose q*s**2 - 4/5*s + 2/5 = 0. What is s?
1
Let t(o) be the second derivative of 7*o**5/90 + 8*o**4/27 - 17*o**3/27 - 2*o**2/3 + 3*o - 6. Find k such that t(k) = 0.
-3, -2/7, 1
Let f(g) be the second derivative of 14*g - 1/9*g**4 + 0*g**3 + 1/6*g**5 + 1/63*g**7 + 0 + 0*g**2 - 4/45*g**6. Factor f(r).
2*r**2*(r - 2)*(r - 1)**2/3
Let c(v) be the first derivative of 1/2*v + 7 + 1/6*v**3 - 1/2*v**2. Factor c(k).
(k - 1)**2/2
Let a(l) be the third derivative of -l**8/1680 + l**7/420 + l**6/72 - l**5/20 - 13*l**3/6 + 15*l**2. Let y(j) be the first derivative of a(j). Factor y(b).
-b*(b - 3)*(b - 1)*(b + 2)
Let d(y) be the second derivative of y**7/420 + y**6/90 - 13*y**3/6 + 6*y. Let n(x) be the second derivative of d(x). Suppose n(v) = 0. Calculate v.
-2, 0
Let m be 9/(-60)*3*35/(-3). Let c(k) be the first derivative of -9/2*k**4 - 5 - m*k**2 - 3/2*k - 8*k**3. Factor c(n).
-3*(2*n + 1)**2*(3*n + 1)/2
Let l = 168 - 166. Suppose -l*r + u + 0*u + 9 = 0, 2*r = -4*u - 6. Suppose 0*v + 3/4*v**2 + 3/4*v**4 + 0 + 3/2*v**r = 0. Calculate v.
-1, 0
Let g be 6/(-18)*(-9)/(-15) - 91/(-35). Factor -14/5*k - 6/5 + 2*k**4 + 2/5*k**5 + g*k**3 - 4/5*k**2.
2*(k - 1)*(k + 1)**3*(k + 3)/5
Factor 75*p**3 + 250*p**4 - 40*p**2 - 295*p**3 + 17*p**5 - 20*p**5 - 62*p**5.
-5*p**2*(p - 2)**2*(13*p + 2)
Suppose 20 + 10 = 15*j. Factor 3*b**j - 2*b**2 - 12*b + 2*b**2.
3*b*(b - 4)
Let g be 359*(-6)/360 + (5 - -1). Let s(t) be the third derivative of 8*t**2 + 1/45*t**5 + 0 + 0*t + 0*t**4 + 1/315*t**7 + g*t**6 + 0*t**3. Factor s(z).
2*z**2*(z + 1)*(z + 2)/3
Let f(r) be the second derivative of 2/15*r**3 + 0 - 1/75*r**6 + 0*r**5 + 1/10*r**4 - 4*r + 0*r**2. Determine u, given that f(u) = 0.
-1, 0, 2
Let z(y) be the second derivative of 1/60*y**5 + 15*y - 7/36*y**4 + 1/252*y**7 + 0 + 3/4*y**2 + 1/36*y**6 - 1/12*y**3. Let z(r) = 0. Calculate r.
-3, -1, 1
Let w = -296 - -298. Let 1/8 + 7/8*b**w + b = 0. Calculate b.
-1, -1/7
Let j(a) be the second derivative of -a**6/40 - 3*a**5/20 - 3*a**4/16 + a**3/2 + 3*a**2/2 + a + 5. Determine y so that j(y) = 0.
-2, -1, 1
Let l be 75/7 + 38/133. Factor 48*q + 17*q**3 - l*q**3 + 52*q**2 + 13 + 18*q**3 + 4*q**4 + 3.
4*(q + 1)**2*(q + 2)**2
Let v(s) be the second derivative of 3*s**5/100 - 3*s**4/10 - 5*s**3/2 - 27*s**2/5 - 7*s - 12. Factor v(h).
3*(h - 9)*(h + 1)*(h + 2)/5
Factor 49*a - 15*a - 242*a**2 + 142*a + 616 - 648.
-2*(11*a - 4)**2
Let j be 0/(-4 + 2 + 4). Suppose n = 2 - j. Suppose -14/11*k**n - 6/11*k**3 - 2/11 - 10/11*k = 0. What is k?
-1, -1/3
Let w(j) be the third de