x(n) = -20*n**3 - 2415*n**2 + 2440*n - 615. Let a(c) = -5*v(c) + 4*x(c). Factor a(t).
5*(t + 122)*(2*t - 1)**2
Let s be ((-869)/(-99) - 9) + 49/180. Let o(w) be the first derivative of -1/15*w**3 + 0*w**2 + 3 + s*w**4 + 0*w. Factor o(h).
h**2*(h - 1)/5
Let b(g) be the third derivative of -g**5/100 + 63*g**4/20 - 3969*g**3/10 + 238*g**2. Factor b(p).
-3*(p - 63)**2/5
Suppose -27 = -16*j + 69. Let s(r) be the second derivative of -8/3*r**3 + 1/3*r**4 + 8*r**2 + 0 - j*r. Solve s(x) = 0 for x.
2
Let z be (2 - 2 - 1)/(3/654). Let s = z - -656/3. Let 1/3*l**5 + 0 + s*l**4 + 0*l**2 + 0*l + 1/3*l**3 = 0. Calculate l.
-1, 0
Let h(l) = -4*l - 7. Let y be h(-7). Let f(d) = 2*d - 38. Let g be f(y). Find x such that 8/3*x + 8/3 - 2*x**2 - 4/3*x**3 + 2/3*x**g = 0.
-1, 2
Suppose 28 = 4*q - 4*o, -8*o - 3 = -7*o. Let j(z) be the first derivative of 4/7*z**3 + 6/7*z + 5 - 15/14*z**2 - 3/28*z**q. What is n in j(n) = 0?
1, 2
Let h = 51 + -55. Let n(w) = 3*w**2 - 3. Let b(i) = 2*i**2 + i - 3. Let v be (3/(-5))/((-2)/10). Let o(t) = h*b(t) + v*n(t). Factor o(p).
(p - 3)*(p - 1)
Let p(l) be the third derivative of -l**5/60 + 73*l**4/12 - 5329*l**3/6 - 37*l**2. Factor p(j).
-(j - 73)**2
Solve 2/23*y**2 + 24/23 - 16/23*y = 0.
2, 6
Let p(c) = -28*c**2 + 87*c + 12. Let q(a) = 27*a**2 - 82*a - 11. Let j(s) = -2*p(s) - 3*q(s). Solve j(n) = 0 for n.
-3/25, 3
Let b(z) be the second derivative of -81*z**5/160 + 411*z**4/32 - 328*z**3/3 + 256*z**2 - 565*z. What is l in b(l) = 0?
1, 64/9
Let b be 1/(-12) + (-6)/(-8). Let h be 170/850 - (44/(-30) + -1). Solve -b*s**3 - 2*s**2 + h + 0*s = 0 for s.
-2, 1
Let j be -4 + 15 + -22 + 13 - -1. Suppose -8/7*g + 4*g**2 + 20/7*g**4 - 4/7*g**5 + 0 - 36/7*g**j = 0. What is g?
0, 1, 2
Suppose 99*s - 11*s - 345 = -27*s. Find k, given that -5/4 + 3/4*k**5 - 27/2*k**2 - 19/2*k**s - 5/4*k**4 - 29/4*k = 0.
-1, -1/3, 5
Let i(s) be the third derivative of -s**8/10080 + s**7/720 - s**6/240 - s**5/20 + 7*s**2. Let f(y) be the third derivative of i(y). Factor f(u).
-(u - 3)*(2*u - 1)
Let q(c) be the first derivative of 1/5*c**2 + 1/15*c**6 + 0*c**5 + 0*c + 0*c**3 - 12 - 1/5*c**4. Factor q(x).
2*x*(x - 1)**2*(x + 1)**2/5
Let s(d) be the second derivative of -d**7/21 + 61*d**6/15 - 509*d**5/5 + 1349*d**4/3 - 2581*d**3/3 + 841*d**2 - 427*d. What is b in s(b) = 0?
1, 29
Let i(s) be the first derivative of -5/3*s**3 + 0*s - 5/2*s**2 + 15. Factor i(b).
-5*b*(b + 1)
Let o(k) be the first derivative of -3*k + 0*k**2 + 1/45*k**5 + 1/135*k**6 + 1/54*k**4 + 0*k**3 + 3. Let f(a) be the first derivative of o(a). Solve f(j) = 0.
-1, 0
Let t(v) be the second derivative of v**5/70 - 5*v**4/42 - 19*v**3/7 - 99*v**2/7 + v - 18. Factor t(g).
2*(g - 11)*(g + 3)**2/7
Let k(a) be the third derivative of a**6/40 - a**5/30 + a**4/12 - a**3/6 - a**2. Let p be k(1). Determine g so that g**2 - p - 1 + 3 = 0.
0
Let b be 118/(14 - 12 - (-24)/(-10)). Let f = b + 298. Factor -16/5*o**f + 24/5*o**2 + 4/5*o**4 - 16/5*o + 4/5.
4*(o - 1)**4/5
Let g(s) be the third derivative of s**5/100 + 27*s**4/20 + 53*s**3/10 - 76*s**2. Let g(b) = 0. What is b?
-53, -1
Let q(b) be the first derivative of b**6/6 + 4*b**5/5 - 23*b**4/4 - 38*b**3/3 + 110*b**2 - 200*b + 238. Factor q(z).
(z - 2)**3*(z + 5)**2
Suppose 19*q**3 - 3*q**4 - 44*q - 2 + 15 + 14*q**4 - 1 + 61*q**2 - 58*q**3 - q**5 = 0. What is q?
1, 2, 6
Let n(d) be the second derivative of -d**7/840 - d**6/60 - 3*d**5/40 + d**3/2 - 24*d. Let k(z) be the second derivative of n(z). Factor k(q).
-q*(q + 3)**2
Let q = 277 + -272. Let t(n) be the second derivative of 0*n**2 + 0 + 0*n**3 + 1/10*n**q - 4*n + 1/6*n**4. Determine c so that t(c) = 0.
-1, 0
Let n(x) be the third derivative of 1331*x**6/30 + 484*x**5/5 + 88*x**4 + 128*x**3/3 - 10*x**2 + 2. Factor n(m).
4*(11*m + 4)**3
Suppose 2*w = -10 + 18. Factor -2*h**w - 3*h**3 + h**3 - h**5 + 0*h**5 + h**3.
-h**3*(h + 1)**2
Let h(m) be the second derivative of -m**4/21 + 20*m + 1. Find a, given that h(a) = 0.
0
Let g(p) be the second derivative of p**4/36 + 13*p**3/18 - 8*p**2 + 364*p - 2. Solve g(y) = 0 for y.
-16, 3
Let p(m) = -5*m**4 - 13*m**3 - 38*m**2 - 48*m - 15. Let r(v) = -9*v**4 - 27*v**3 - 78*v**2 - 96*v - 31. Let q(y) = 10*p(y) - 6*r(y). Factor q(g).
4*(g + 1)**2*(g + 3)**2
Suppose 5*c = -f + 31 - 11, -4*f + c - 4 = 0. Let b(j) be the third derivative of 1/120*j**5 + 0*j**3 + 1/24*j**4 + 9*j**2 + 0 + f*j. Factor b(g).
g*(g + 2)/2
Suppose 0*o**2 - 2/11*o**5 + 16/11*o**4 + 0*o + 0 - 32/11*o**3 = 0. What is o?
0, 4
Let a be 117/(-10)*8775/(-15210). Suppose -243/4*h - 1/4*h**3 - 729/4 - a*h**2 = 0. What is h?
-9
Let s = 94/55 - 10/11. Let o(x) be the first derivative of -s*x**5 + 0*x + 1/3*x**6 - 1 + 0*x**4 - x**2 + 4/3*x**3. Factor o(n).
2*n*(n - 1)**3*(n + 1)
Let k(c) = -c**3 + 0*c**2 - 3*c**3 + 16*c**2 - 2*c - 10*c. Let s(z) = -z**2 + 1. Let a(h) = k(h) + 4*s(h). Factor a(r).
-4*(r - 1)**3
Let y(v) = -19*v + 34. Let i be y(4). Let p be i/(-132) - (-4)/22. Solve 0*t**2 + p*t**3 + 0*t + 1/2*t**5 + 0 - t**4 = 0 for t.
0, 1
Let f(a) = -5*a**3 - 74*a**2 - 322*a - 244. Let c(t) = 65*t**3 + 960*t**2 + 4185*t + 3170. Let m(u) = 3*c(u) + 40*f(u). Factor m(q).
-5*(q + 1)*(q + 5)*(q + 10)
Suppose 9*z + 4 = 4. Let h(i) be the second derivative of z*i**2 - 3*i + 0 + 1/16*i**4 - 1/8*i**3. Factor h(s).
3*s*(s - 1)/4
Let h = 865 - 865. Let k(f) be the second derivative of 1/11*f**2 + f + 0 + h*f**3 - 1/66*f**4. Factor k(u).
-2*(u - 1)*(u + 1)/11
Determine s, given that 16 + 192*s**2 - 578*s**2 + 195*s**2 - 10*s + 192*s**2 = 0.
2, 8
Let s(f) be the first derivative of 0*f**2 + 15 - 2*f**3 + 3*f**5 + 0*f + 9/4*f**4. Factor s(h).
3*h**2*(h + 1)*(5*h - 2)
Let s(a) be the second derivative of a**7/7560 + a**6/3240 - 7*a**3 - 16*a. Let v(d) be the second derivative of s(d). Factor v(l).
l**2*(l + 1)/9
Let g(l) be the first derivative of 4*l**5/5 + l**4 - 16*l**3/3 - 8*l**2 - 628. Factor g(s).
4*s*(s - 2)*(s + 1)*(s + 2)
Let s(j) be the first derivative of -j**6/60 + j**5/40 + j**4/12 + 36*j - 3. Let r(i) be the first derivative of s(i). Factor r(m).
-m**2*(m - 2)*(m + 1)/2
Let w be (-8)/(-36) - 10/45. Let t(a) be the third derivative of -1/20*a**5 + 1/2*a**4 + w*a + 0 + 1/2*a**3 + 3*a**2 - 1/10*a**6. What is g in t(g) = 0?
-1, -1/4, 1
Let b(q) = 27*q**2 - q - 1. Let z be b(-2). Let y = z - 543/5. Suppose -8/5*p - 2/5 - 12/5*p**2 - 8/5*p**3 - y*p**4 = 0. Calculate p.
-1
Determine m so that -8/3*m - 8/3*m**2 + 0 + 2/3*m**3 + 2/3*m**4 = 0.
-2, -1, 0, 2
Let s(o) be the third derivative of o**6/20 + o**5/6 + 7*o**4/36 + o**3/9 + 239*o**2. Suppose s(u) = 0. What is u?
-1, -1/3
Let p(z) be the second derivative of z**9/3780 + z**8/560 + z**7/630 - z**6/60 - z**5/15 + z**4 + 15*z. Let f(n) be the third derivative of p(n). Factor f(w).
4*(w - 1)*(w + 1)**2*(w + 2)
Let d(g) = 3*g**2 + 11*g + 8. Let j(v) = -v**2 - 5*v - 4. Let o(q) = -4*d(q) - 10*j(q). Find x, given that o(x) = 0.
-1, 4
Let m(y) be the first derivative of y**5/20 - y**3/12 - 237. Factor m(r).
r**2*(r - 1)*(r + 1)/4
Determine s, given that 3 - 3/2*s**3 + 9/2*s + 0*s**2 = 0.
-1, 2
Let u(h) be the second derivative of -14*h + 0*h**3 + 1/50*h**5 + 0*h**2 + 0 + 1/150*h**6 + 0*h**4. What is z in u(z) = 0?
-2, 0
Suppose -5*n + 20 = 5*y, 1 = 2*y + 5*n - 13. Factor 60*f + 10*f**2 + 22*f**y + 3*f**2 - 20.
5*(f + 2)*(7*f - 2)
Let i(b) be the first derivative of -16 - 2*b**2 - 6*b - 2/9*b**3. Suppose i(c) = 0. Calculate c.
-3
Let s = 15 - 2. Let h be (108/(-48))/(s/(-8)). Factor -h*k**2 - 2/13*k**3 - 54/13 - 54/13*k.
-2*(k + 3)**3/13
Let a(b) be the first derivative of -5*b**4/3 + 46*b**3/9 - 2*b**2 - 196. Factor a(o).
-2*o*(o - 2)*(10*o - 3)/3
Let o be (6 - 10)*(-5)/2. Let i = -5 + o. Factor -2*g**3 - 9*g**2 + 2*g + 6*g**2 - 2 + i*g**2.
-2*(g - 1)**2*(g + 1)
Find d such that 40 - 2*d**3 - 242*d - 1055*d**2 + 320*d + 1091*d**2 = 0.
-1, 20
Let i(r) be the first derivative of 1/6*r**6 - 8 + r**4 - 5/2*r**2 - 2*r - 2/3*r**3 + 4/5*r**5. Solve i(x) = 0 for x.
-2, -1, 1
Let u be 7/4 + ((-266)/(-56))/19. Find n such that -12/5 - 9/5*n**3 + 9*n - 24/5*n**u = 0.
-4, 1/3, 1
Let g be (1 + 3/42)/((-14040)/(-420)). Let r(u) be the third derivative of -g*u**4 - 7*u**2 + 1/780*u**6 + 0 + 0*u - 1/13*u**3 - 1/390*u**5. Factor r(z).
2*(z - 3)*(z + 1)**2/13
Determine n so that -15*