 2)/9
Let l(g) be the second derivative of g**4/4 - 4*g**3 + 24*g**2 + 2*g. Find o such that l(o) = 0.
4
Let n(j) be the first derivative of 2*j**5/105 - 2*j**4/21 - 22*j**3/63 - 2*j**2/7 + 65. Determine t, given that n(t) = 0.
-1, 0, 6
Suppose -1/4*c**2 + 0 + c = 0. What is c?
0, 4
Let c = 2758 + -13863/5. Let w = 15 + c. Find y, given that 0*y + 0*y**2 + w*y**4 + 2/5*y**3 + 0 = 0.
-1, 0
Let o(y) be the second derivative of y**3/6 - y**2 - 2*y. Let q be o(4). Solve -9/2*j**4 + 21/2*j**3 + 2*j + 0 - 8*j**q = 0 for j.
0, 2/3, 1
Let m be (1 - -5)*4/12. Let a(u) be the second derivative of -m*u + 0*u**3 + 0 - u**2 + 1/6*u**4. Determine z, given that a(z) = 0.
-1, 1
Let c(d) be the second derivative of -d**7/2520 + d**6/720 - d**4/12 - 3*d. Let y(w) be the third derivative of c(w). Let y(g) = 0. What is g?
0, 1
Let s(p) be the second derivative of 2/21*p**4 - 1/7*p**2 + 0 + 1/7*p**3 - 2*p. Let s(j) = 0. Calculate j.
-1, 1/4
Let s(w) be the third derivative of -4*w**2 + 0*w + 0 - 1/9*w**3 - 1/180*w**5 + 1/24*w**4. Factor s(b).
-(b - 2)*(b - 1)/3
Let x be -54*(0 - (-153)/42). Let k = 197 + x. Suppose -2/7*a**2 + k*a**4 - 2/7*a**5 + 2/7*a**3 + 0*a + 0 = 0. What is a?
-1, 0, 1
Let o(i) be the second derivative of -i**4/3 + 10*i**3/3 - 8*i**2 - 19*i. Determine g, given that o(g) = 0.
1, 4
Let o be 4 + (-156)/28 + 3. Determine h, given that 2/7*h**4 + 6/7*h**3 + 4/7*h - o*h**2 - 2/7*h**5 + 0 = 0.
-2, 0, 1
Let c be (0 + -1)*(1 - 2). Suppose -5 - c = -3*a. Factor -1/3*n**4 - 2/3*n**3 - 1/3*n**a + 0 + 0*n.
-n**2*(n + 1)**2/3
Let i(l) be the third derivative of l**8/20160 + l**5/60 - l**2. Let w(y) be the third derivative of i(y). Determine k, given that w(k) = 0.
0
Find o, given that -5*o**2 - o**2 + 2 + 4*o**2 = 0.
-1, 1
Suppose -4/3*h**3 + 2/3 - 14/3*h**2 + 4*h**4 + 7/3*h**5 - h = 0. Calculate h.
-1, 2/7, 1
Let q be (-4)/(-6)*(-36)/(-8). Determine a so that q - 3*a**2 + 6*a**3 + 10*a - 13*a - 3*a**3 = 0.
-1, 1
Let t be 120/32 + (-1)/4. Let x = t + -3. Factor -7/2*w**3 - 9/2*w**5 - x*w**2 - 15/2*w**4 + 0*w + 0.
-w**2*(w + 1)*(3*w + 1)**2/2
Let o be (-9)/(-3) - (1 + 0). Suppose -o*y + 7*y = 0. Factor y*a**2 + 0*a + 0 - 4/7*a**3 - 6/7*a**5 + 10/7*a**4.
-2*a**3*(a - 1)*(3*a - 2)/7
Let a(d) = -d**2 + 5*d - 2. Let n = -7 + 11. Let k be a(n). Factor 4 + 6*l**2 - 4*l - 2*l**2 - 3*l**k.
(l - 2)**2
Suppose -7 + 19 = 4*l. Let 0*g - 6/7*g**4 - 2/7*g**2 + 0 - 2/7*g**5 - 6/7*g**l = 0. Calculate g.
-1, 0
Suppose 2 = 18*w - 17*w. Factor x**w + 3*x**3 + 5*x**2 - 13*x + 4*x.
3*x*(x - 1)*(x + 3)
Let x(z) be the third derivative of z**5/180 - 2*z**3/9 - 6*z**2. Factor x(u).
(u - 2)*(u + 2)/3
Let y(x) be the first derivative of -x**4/8 + x**2/4 + 5. Suppose y(o) = 0. What is o?
-1, 0, 1
Let v = -176 - -176. Suppose -7/3*l**4 + 0 + 0*l + 2/3*l**3 + v*l**2 = 0. Calculate l.
0, 2/7
Let k be ((-385)/44 - (-3 - 3)) + 3. Factor -3/4 + k*j**2 + 1/2*j.
(j - 1)*(j + 3)/4
Let b(n) be the first derivative of -n**9/1512 + n**8/840 + n**7/420 - n**6/180 - n**3 - 4. Let x(f) be the third derivative of b(f). Solve x(s) = 0.
-1, 0, 1
Suppose -5*k + 4 = -3*h + 1, -4*h + 19 = k. Let 4*i**k + i**2 - i**3 + i**2 - i**3 = 0. What is i?
-1, 0
Let d = -163 + 491/3. Let 4/3*p**4 + 2/3*p**3 + 0 - 4/3*p**2 - d*p = 0. What is p?
-1, -1/2, 0, 1
Suppose -4*w - 18 = 2*g, 0*w - 8 = 2*w. Let t(a) = -a + 1. Let x(d) = 7*d**2 - 15*d - 1. Let c(y) = g*x(y) + 3*t(y). Let c(v) = 0. What is v?
-2/7, 2
Let b(x) be the second derivative of x**8/20160 - x**7/1260 + x**6/180 - x**5/45 - x**4/4 + 6*x. Let g(d) be the third derivative of b(d). Factor g(u).
(u - 2)**3/3
Let c(s) be the first derivative of 2*s**4 + 26*s**3/3 - 13*s**2 - 8*s + 7. Find l, given that c(l) = 0.
-4, -1/4, 1
Let x(s) be the first derivative of 39/2*s**2 + 5*s**3 - 5 - 18*s. Solve x(m) = 0.
-3, 2/5
Let v = 18 - 18. Suppose 0 = x - r + 3 - 9, v = x - 4*r - 12. Factor 0 - 1/3*b**4 - x*b**2 + 2*b**3 + 8/3*b.
-b*(b - 2)**3/3
Let s(n) be the first derivative of -7*n**4/18 - 74*n**3/27 - 38*n**2/9 - 16*n/9 - 23. What is f in s(f) = 0?
-4, -1, -2/7
Suppose -v = -3*g - 19, 2*v + g = 6*v - 21. Let n(w) be the first derivative of -6/35*w**5 - 1 - 10/21*w**3 + 0*w + 1/2*w**v + 1/7*w**2. Factor n(h).
-2*h*(h - 1)**2*(3*h - 1)/7
Factor 0 - 13/4*z**2 - 3/2*z + 5/4*z**3.
z*(z - 3)*(5*z + 2)/4
Let l(j) be the first derivative of -j**3/24 + 7*j**2/16 + j - 29. Factor l(t).
-(t - 8)*(t + 1)/8
Let u(t) = t - 1. Let h be u(3). Factor -2*p - p**3 + 4 - 3*p**h + 2*p.
-(p - 1)*(p + 2)**2
Let f(g) = g**2 + 6*g + 5. Let m be f(-5). Let r be (-55)/(-30) - 1/(-6). What is p in m - 2/9*p**3 - 4/9*p**r - 2/9*p = 0?
-1, 0
Let w = 56/93 - -2/31. Let j(h) be the first derivative of 2*h**3 + 2*h**2 - 3 + w*h. What is s in j(s) = 0?
-1/3
Suppose -2*l + 4 = 3*t - t, 0 = -t + 2*l - 4. Let i = 21/2 + -10. What is s in i*s - 1/2*s**3 + t*s**2 - 1/4*s**4 + 1/4 = 0?
-1, 1
Let x be 3*(10/5)/2. Find d, given that 0 + 1/5*d**x + 1/5*d + 2/5*d**2 = 0.
-1, 0
Let s(r) = r - 29. Let o be s(14). Let a be 6/o - 140/(-225). What is g in -4/9*g**2 + 0 + a*g**3 + 2/9*g = 0?
0, 1
Let r(t) be the second derivative of t**4/54 - t**3/27 - 9*t. Let r(l) = 0. What is l?
0, 1
Let b(i) be the first derivative of 2/3*i**3 + 0*i**2 - 1 + 1/2*i**4 + 0*i. Factor b(h).
2*h**2*(h + 1)
Let b(o) be the second derivative of o**4/12 - 5*o**3/6 + 2*o**2 - 32*o. Factor b(j).
(j - 4)*(j - 1)
Let v(k) = k - 1. Let h be v(1). Suppose 3*d = -2*z + 3, 4*d + 2*z = -h*z + 6. Find p, given that -p**d + 1/2*p**2 + 0*p + 0 + 1/2*p**4 = 0.
0, 1
Let m(d) be the second derivative of d**4/4 - 3*d**2/2 - 5*d. Factor m(v).
3*(v - 1)*(v + 1)
Let n(p) = p + 9. Let i be n(-8). Let j = i - -1. What is k in 2/7*k**j + 4/7*k + 2/7 = 0?
-1
Let c = 14/71 - -1009/284. Let z(j) be the first derivative of 1 - 6*j**3 - 3/5*j**5 + 24*j + c*j**4 - 6*j**2. Factor z(n).
-3*(n - 2)**3*(n + 1)
Let z(q) = -q**3 - 5*q**2 + 6*q + 4. Let b be z(-6). Let o(n) be the third derivative of -1/18*n**3 + 0*n + 2*n**2 - 4/45*n**5 + 0 + 1/9*n**b. Factor o(f).
-(4*f - 1)**2/3
Let r(h) = 2*h + 15. Let k be r(-9). Let d be ((-7)/k + -2)/1. Factor d*s**2 - 1/3*s + 2/3*s**3 + 0.
s*(s + 1)*(2*s - 1)/3
Let f = -909 - -913. Factor -10/7*s**f + 2/7*s**5 + 4/7*s + 18/7*s**3 - 2*s**2 + 0.
2*s*(s - 2)*(s - 1)**3/7
Let z(l) = -l**4 - 5*l**4 + 6*l + 4*l**4 - 4*l**3 + 6 + 0. Let g(u) = 6*u**4 + 11*u**3 - u**2 - 18*u - 19. Let n(a) = 4*g(a) + 14*z(a). Factor n(i).
-4*(i - 1)*(i + 1)**2*(i + 2)
Let v be (-8)/(-6) + 10/15. Find b such that 10*b**2 - 2*b**4 + 3*b**v + 9*b**2 + 6*b**5 - 4*b**2 - 4*b - 18*b**3 = 0.
-2, 0, 1/3, 1
Let z(s) = s**3 + 4*s**2 + s + 4. Let p be z(-3). Factor -11*a + 0*a**2 + p*a + a**2.
a*(a - 1)
Let c = 22 - 12. Let h be (-30)/(-56) + c/(-35). Factor -1/2*d - h*d**2 + 0.
-d*(d + 2)/4
Let d(w) be the third derivative of -w**8/840 + w**7/168 - w**6/360 - w**5/60 + 7*w**3/6 + 5*w**2. Let j(m) be the first derivative of d(m). Factor j(u).
-u*(u - 2)*(u - 1)*(2*u + 1)
Let d(a) be the second derivative of -a**5/50 + a**3/15 - 21*a. Determine t, given that d(t) = 0.
-1, 0, 1
Let g(q) be the third derivative of 1/150*q**5 - 1/60*q**4 + 9*q**2 - 2/15*q**3 + 0 + 0*q. Let g(n) = 0. Calculate n.
-1, 2
Let y(t) be the first derivative of t**5/120 - t**3/12 - t**2 + 8. Let v(n) be the second derivative of y(n). Factor v(d).
(d - 1)*(d + 1)/2
Let h(t) = -12*t**4 + 5*t**3 + 25*t**2 + 6*t. Let j(m) = 47*m**4 - 21*m**3 - 101*m**2 - 24*m. Let p(k) = -9*h(k) - 2*j(k). Factor p(y).
y*(y + 1)*(2*y - 3)*(7*y + 2)
Suppose 3*p - 11 = -5. Let j be 112/160*(5/(-7) + 1). Determine s so that -1/5*s**p + 1/5 - j*s**3 + 1/5*s = 0.
-1, 1
Suppose 4*q - 8 = 3*m, -4*m = -2*m. Let a(t) be the first derivative of -1/4*t**4 - 6*t**2 + 8*t + q*t**3 + 1. Factor a(k).
-(k - 2)**3
Let i(h) be the second derivative of h**6/360 + h**3/3 - 3*h. Let f(r) be the second derivative of i(r). Determine p, given that f(p) = 0.
0
Let i(v) = v**2 + v + 1. Let h(x) = -x**3 - 7*x**2 - 6*x - 7. Let s(k) = 5*h(k) + 35*i(k). Factor s(n).
-5*n*(n - 1)*(n + 1)
Let b be (-324)/91 - 4/14 - -4. Determine t so that b*t**3 + 4/13 - 4/13*t**2 - 2/13*t = 0.
-1, 1, 2
Let z(k) = -2*k + 15. Let n be z(0). Let c = -12 + n. Let 0 + 8/3*y**5 - 2*y**c - 8/3*y**4 - 2/3*y + 8/3*y**2 = 0. What is y?
-1, 0, 1/2, 1
Suppose -4*