n(f) be the third derivative of f**7/945 - f**6/540 - f**5/90 + 5*f**4/108 - 2*f**3/27 + 15*f**2. Factor n(o).
2*(o - 1)**3*(o + 2)/9
Let b(j) = -j**3 + 10*j**2 - 14*j + 10. Let c be b(9). Let n = -31 - c. Factor 0 + 8/3*q**4 - 2/3*q**5 + 8/3*q**2 - 2/3*q - n*q**3.
-2*q*(q - 1)**4/3
Suppose i - 10 = -2*u, -i - u + 1 = -2*u. Let p(d) be the third derivative of -1/6*d**5 + 0*d + 1/6*d**i + 0*d**3 + 0 - 2*d**2. Find t, given that p(t) = 0.
0, 2/5
Let r(l) be the first derivative of l**4/16 + l**3/6 + l**2/8 - 30. Factor r(c).
c*(c + 1)**2/4
Suppose 2*g = -j + 12, -13*g = j - 16*g + 13. Determine y, given that -1/4*y + 1/4*y**j + 0 = 0.
0, 1
Let v(f) = f**3 - 3*f**2 - 14*f - 4. Let j be v(6). Suppose -3*d - 2*d = -j. Factor 0*a + 2/7*a**d + 0 - 4/7*a**3 + 2/7*a**2.
2*a**2*(a - 1)**2/7
Let d(v) be the third derivative of 4*v**2 + 1/48*v**4 + 0*v + 0 + 1/240*v**5 + 0*v**3. Factor d(k).
k*(k + 2)/4
Let w(x) be the third derivative of x**7/2520 - x**6/360 + x**5/120 - x**4/12 + 6*x**2. Let b(t) be the second derivative of w(t). Factor b(k).
(k - 1)**2
Let j(v) be the third derivative of v**2 + 2/105*v**7 + 0*v**3 - 1/15*v**5 + 0*v**6 + 1/168*v**8 - 1/12*v**4 + 0*v + 0. Solve j(t) = 0.
-1, 0, 1
Suppose 2*z**4 - 2 + 3/2*z**5 - 1/2*z + 12*z**2 - 13*z**3 = 0. What is z?
-4, -1/3, 1
Let b(p) be the third derivative of p**8/5040 - p**6/540 + p**4/72 - 5*p**3/6 + p**2. Let s(o) be the first derivative of b(o). Solve s(q) = 0.
-1, 1
Suppose 3*q - 4*r + r = 0, -r + 2 = 0. Let b(f) be the first derivative of -2*f + 0*f**3 + f**4 + q - 2*f**2 + 2/5*f**5. What is k in b(k) = 0?
-1, 1
Determine f, given that -8/7 + 2/7*f**3 - 8/7*f + 2/7*f**2 = 0.
-2, -1, 2
Suppose l + 2*l - 9 = 0. Factor c**2 + l*c**3 + 21*c**4 - c**2 + 24*c**3 + 6*c**2.
3*c**2*(c + 1)*(7*c + 2)
Let w(m) = 2*m - 10. Let f be w(6). Let b(g) be the first derivative of g**2 - 4/3*g**3 + 1/2*g**4 + 0*g + f. Suppose b(x) = 0. What is x?
0, 1
Let x(u) = -43*u**4 - 67*u**3 - 32*u**2 - 8*u. Let w(p) = -44*p**4 - 68*p**3 - 31*p**2 - 7*p. Let a(o) = -5*w(o) + 4*x(o). Solve a(d) = 0.
-1, -1/4, 0
Let g(j) be the second derivative of j**5/4 - 5*j**3/2 + 5*j**2 - 4*j. Suppose g(s) = 0. What is s?
-2, 1
Let w(g) be the first derivative of -g**5/5 + 3*g**4/4 + g**3/3 - 3*g**2/2 - 40. Suppose w(k) = 0. Calculate k.
-1, 0, 1, 3
Let j(s) be the third derivative of s**7/210 - s**6/30 - s**5/30 + s**4/2 + 3*s**3/2 - 2*s**2. Factor j(i).
(i - 3)**2*(i + 1)**2
Let t(z) be the third derivative of 1/24*z**4 + 1/120*z**6 + 0*z + 0 + 0*z**3 + 1/30*z**5 + 3*z**2. Determine d so that t(d) = 0.
-1, 0
Let j(f) be the second derivative of -f**6/180 + f**5/15 - f**4/3 + f**3 - 4*f. Let d(p) be the second derivative of j(p). Suppose d(t) = 0. Calculate t.
2
Let u be 33/(-9) + (-12)/(-3). Find h, given that 0*h + 1/3*h**2 + 0 - u*h**4 + 0*h**3 = 0.
-1, 0, 1
Let g(j) be the third derivative of j**11/110880 - j**10/25200 + j**8/3360 - j**7/1680 - j**5/60 - j**2. Let n(a) be the third derivative of g(a). Factor n(p).
3*p*(p - 1)**3*(p + 1)
Suppose 2*i - 1 = -o, 2*o - 2*i - 2*i = 10. Determine r, given that -3*r + o*r + 2*r**4 + 6*r**3 - 10*r**3 = 0.
0, 2
Let d(m) = -3*m**5 + m**4. Let q(a) = -4*a**5 + a**4. Let f(s) = -3*d(s) + 2*q(s). Find y such that f(y) = 0.
0, 1
Let j be (1 + -10 - -4) + 4 + 1. Factor 0*d + j + 0*d**2 - 1/4*d**3.
-d**3/4
Let u(p) be the first derivative of p**6/150 - p**5/30 + p**4/30 - p**2/2 - 8. Let s(r) be the second derivative of u(r). Determine d so that s(d) = 0.
0, 1/2, 2
Let d = 10 - 7. Let j = 2 + 0. Factor j*t - t**2 - d*t + 2*t**2.
t*(t - 1)
Let d(u) be the third derivative of 1/75*u**5 - 1/60*u**4 + 0*u**3 - 1/300*u**6 + 0*u + 0 - 5*u**2. Find k, given that d(k) = 0.
0, 1
Factor 1/3 - 2/3*z + 1/3*z**2.
(z - 1)**2/3
Let g(w) = -w**3 - w**2 + 3*w + 1. Let k be g(-2). Let h = 3 - k. Let 0*b + 0 + 1/5*b**3 + 4/5*b**h - 3/5*b**5 - 2/5*b**2 = 0. What is b?
-2/3, 0, 1
Let b(p) be the second derivative of -p**9/3024 + p**7/420 - p**5/120 - p**3/2 + 4*p. Let x(w) be the second derivative of b(w). Find q such that x(q) = 0.
-1, 0, 1
Let b(m) be the second derivative of -1/30*m**6 + 0*m**5 + 0*m**2 + m + 0*m**4 + 0*m**3 + 0 - 1/42*m**7. Solve b(c) = 0 for c.
-1, 0
Let g be ((-2)/4)/(2/(-2)). Factor 1/4*k**2 + g - 3/4*k.
(k - 2)*(k - 1)/4
Let u be ((-46)/6 + 6)/(-5). What is f in 2/3 - 5/3*f**2 - 1/3*f**3 + f**4 + u*f = 0?
-1, -2/3, 1
Let l be ((-10)/(-6))/(5/15). Factor -f**4 + 0 + f**2 + 0*f - 1/2*f**3 + 1/2*f**l.
f**2*(f - 2)*(f - 1)*(f + 1)/2
Let y(w) = -w**3 + 6*w**2 - 6*w + 4. Let v be y(4). Solve -11*o**2 + 0*o + 2*o + v*o**2 = 0 for o.
-2, 0
Let l = -54/5 - -2273/210. Let f(d) be the second derivative of 0*d**2 + 0*d**3 + d + 0 + 0*d**4 + l*d**7 + 0*d**6 - 1/20*d**5. Let f(i) = 0. What is i?
-1, 0, 1
Let r(d) be the third derivative of -d**8/20160 - d**7/3780 + d**6/2160 + d**5/180 + d**4/12 + 6*d**2. Let l(g) be the second derivative of r(g). Factor l(b).
-(b - 1)*(b + 1)*(b + 2)/3
Let l(u) be the second derivative of 3*u**5/40 - u**4/4 + u**3/4 - 6*u. Factor l(h).
3*h*(h - 1)**2/2
Determine i so that -58 + i - 55 - i**3 + 113 = 0.
-1, 0, 1
Let d(k) be the first derivative of k**4/60 + k**3/30 - 3*k - 2. Let h(l) be the first derivative of d(l). Find g such that h(g) = 0.
-1, 0
Factor 0*y + 0*y**2 + 0 - 2/5*y**3.
-2*y**3/5
Let c be 3/(-3) - (-5)/((-15)/(-9)). Let q(i) be the first derivative of 2*i - c*i**2 + 2 + 2/3*i**3. Let q(b) = 0. What is b?
1
Let q(k) be the first derivative of k**6/12 + k**5/5 + k**4/8 - 1. Let q(d) = 0. Calculate d.
-1, 0
Suppose h + 20 = 5*n, h + 9 - 1 = n. Suppose 3*g - j = -0*j + 15, 0 = -n*g - 4*j. Let 0 - 4/5*d + 2/5*d**2 + 16/5*d**3 + 2*d**g = 0. Calculate d.
-1, 0, 2/5
Let s(o) be the first derivative of -o**8/5040 - o**7/504 - o**6/135 - o**5/90 + 5*o**3/3 + 3. Let p(g) be the third derivative of s(g). Factor p(q).
-q*(q + 1)*(q + 2)**2/3
Let n(o) be the second derivative of -3*o**5/80 + o**4/8 + o**3/8 - 3*o**2/4 - 2*o. Factor n(i).
-3*(i - 2)*(i - 1)*(i + 1)/4
Factor 2/23*b**2 + 2/23*b + 0.
2*b*(b + 1)/23
Let a(o) be the first derivative of 2*o**6/21 + 3*o**5/35 - 5*o**4/28 - o**3/7 + o**2/14 - 20. Solve a(d) = 0 for d.
-1, 0, 1/4, 1
Let a be -2*10*3/12. Let c(g) = -g - 3. Let v be c(a). Suppose -5*q**3 + 2*q**2 + v*q**3 + q**3 = 0. Calculate q.
0, 1
Let y(z) be the second derivative of 0 + 0*z**3 + 3*z + 2/21*z**7 - 1/30*z**6 - 1/5*z**5 + 0*z**2 + 1/12*z**4. Factor y(p).
p**2*(p - 1)*(p + 1)*(4*p - 1)
Let -22/7*x**2 - 12/7*x**4 + 34/7*x**3 + 4/7*x + 0 = 0. Calculate x.
0, 1/3, 1/2, 2
Let y = 8 + -6. Factor -4*f + 2*f**3 - 2*f**y + 2*f**3 - 2*f**3.
2*f*(f - 2)*(f + 1)
Suppose -2*c + 8*c + 2*c**3 - c**4 - 15*c**2 + 10*c**3 - 2*c**4 = 0. What is c?
0, 1, 2
Let n(k) = -2*k**3 + 12*k**2 - 16*k + 6. Let i(h) = 4*h**3 - 25*h**2 + 32*h - 11. Let u(x) = 2*i(x) + 5*n(x). Determine b so that u(b) = 0.
1, 2
Let t(j) be the second derivative of -j**4/21 + 2*j**3/21 - 34*j. Solve t(g) = 0 for g.
0, 1
Let m(r) be the first derivative of r**3/18 - r**2/12 - 19. What is u in m(u) = 0?
0, 1
Let x(n) be the second derivative of 0 + 1/2*n**5 + 4/3*n**3 + 0*n**2 - 4*n + 1/15*n**6 + 4/3*n**4. Solve x(g) = 0 for g.
-2, -1, 0
Let n = -10 + 12. Factor 3*k + 2*k - n*k - 3*k**2 + 6.
-3*(k - 2)*(k + 1)
Let k(c) = -2*c**2 - 4*c + 2. Suppose 2*q + 9 = -q. Let l(m) = 2*m**2 + 4*m - 1. Let i(x) = q*k(x) - 4*l(x). Factor i(p).
-2*(p + 1)**2
Let q(t) = t**3 - 6*t**2 - t + 8. Let d be q(6). Solve 2*k - d*k**2 - 3*k + 5*k = 0.
0, 2
Let u(d) = -d + 8. Let i be u(5). Let q(k) be the third derivative of 1/12*k**4 - 3*k**2 + 0*k**i + 0 + 0*k - 1/60*k**5. Factor q(h).
-h*(h - 2)
Let y(a) be the first derivative of a**5/5 - 5*a**4/4 + 4*a**3/3 + 71. Solve y(l) = 0 for l.
0, 1, 4
Let g be 3/5 + (-132)/20. Let m(k) = -k**2 + 7*k - 6. Let a = 2 + -3. Let b(j) = -j + 1. Let c(t) = a*m(t) + g*b(t). Factor c(u).
u*(u - 1)
Let w(p) = -p**3 - p**2 - p - 4. Let j be w(-2). Factor 0*b + 10/7*b**5 - j*b**4 + 0 + 0*b**2 + 4/7*b**3.
2*b**3*(b - 1)*(5*b - 2)/7
Let y be (1 - 4/(-2)) + 0. Suppose 5*p**4 - p**4 - 2*p**y - p**4 - p**3 = 0. Calculate p.
0, 1
Let b(i) be the second derivative of -5*i**4/12 - 20*i**3 - 360*i**2 - 5*i - 1. Factor b(j).
-5*(j + 12)**2
Suppose -2*z + 5*z = 0, 5*r - 25 = 3*z. Let y(s) be the f