be the second derivative of -16*f**7/189 + 104*f**6/135 - 193*f**5/90 + 13*f**4/9 - f**3/3 + 8*f. Factor z(k).
-2*k*(k - 3)**2*(4*k - 1)**2/9
Let t = 31/162 - 2/81. Let y(c) be the second derivative of 3*c - t*c**4 + 0 + 1/20*c**5 + 0*c**2 + 1/6*c**3. Factor y(q).
q*(q - 1)**2
Let a(v) be the second derivative of v + 0*v**5 + 0*v**2 + 1/30*v**6 + 0 + 0*v**3 - 1/12*v**4. Factor a(d).
d**2*(d - 1)*(d + 1)
Let y(s) be the second derivative of -s**7/6300 - s**6/900 - s**5/300 - s**4/4 + s. Let a(t) be the third derivative of y(t). Factor a(o).
-2*(o + 1)**2/5
Suppose -5*g + 4*z = -0*z, 5*g = 2*z. Suppose 2*f + 2*w + 8 = 0, f + g*w - 16 = 3*w. Factor -d + f + 1/4*d**2.
(d - 2)**2/4
Let u(g) be the first derivative of -4/3*g**3 + 0*g - 2/5*g**5 - 3/2*g**4 + 3 + 0*g**2. Factor u(p).
-2*p**2*(p + 1)*(p + 2)
Let j(q) be the first derivative of -q**6/12 - 2*q**5/5 - q**4/2 + q**3/3 + 5*q**2/4 + q + 8. Factor j(f).
-(f - 1)*(f + 1)**3*(f + 2)/2
Let v = 21 - 62/3. Let -1/3 - v*w**3 - w**2 - w = 0. Calculate w.
-1
Let u(j) be the first derivative of 0*j**3 + 1/24*j**4 + 2*j**2 - 1/60*j**5 - 3 + 0*j. Let s(i) be the second derivative of u(i). Let s(y) = 0. Calculate y.
0, 1
Let x be ((-78)/(-72) - (-9)/(-12))*1. Factor -1/3*m**2 + x*m**3 - 1/3*m + 1/3.
(m - 1)**2*(m + 1)/3
Let a = 0 + 2. Let f(c) be the first derivative of 0*c + 2/27*c**3 + 1/9*c**a - 2. Determine l so that f(l) = 0.
-1, 0
Factor 1/3*v - 1/6*v**2 + 1/2.
-(v - 3)*(v + 1)/6
Factor 27/2 + 33*i**2 + 3/2*i**4 - 36*i - 12*i**3.
3*(i - 3)**2*(i - 1)**2/2
Let s(w) be the third derivative of w**8/110880 + w**7/9240 + w**6/1980 + w**5/20 - 3*w**2. Let t(i) be the third derivative of s(i). Solve t(k) = 0 for k.
-2, -1
Let b be (4/(-3))/(4/(-6)). Suppose -10*a**4 + 10*a**2 - 4*a**3 + 4*a**3 - b*a**3 + 6*a**5 - 4*a + 0*a**5 = 0. What is a?
-1, 0, 2/3, 1
Let k(w) = -7*w**3 + w**2 - w - 1. Let q be k(-1). Let u be q/6 - 11/11. Factor 1/3*v**2 + u*v - 2/3.
(v - 1)*(v + 2)/3
Let g(v) be the first derivative of -1/60*v**5 - 1/360*v**6 + v**3 - 1/24*v**4 + 1 + 0*v**2 + 0*v. Let y(u) be the third derivative of g(u). Factor y(a).
-(a + 1)**2
Let v = 369 - 44279/120. Let l(f) be the third derivative of 3*f**2 + 0*f**3 + 1/48*f**4 + 0 + 0*f - v*f**5. Solve l(i) = 0.
0, 1
Let a(f) = -f**2 - 12*f. Let l be a(-12). Let t(j) be the third derivative of -1/66*j**4 + 0 - 1/330*j**5 + j**2 - 1/33*j**3 + l*j. Suppose t(i) = 0. What is i?
-1
Determine k, given that -8/5 - 22/3*k**2 - 10/3*k**3 + 112/15*k = 0.
-3, 2/5
Let k(o) be the second derivative of -o**7/2520 + o**6/240 - o**5/60 - o**4/3 - 2*o. Let a(w) be the third derivative of k(w). Factor a(r).
-(r - 2)*(r - 1)
Let p(t) = -2 + 2 - t**3 + t**2 - 4*t**2. Let i be p(-3). Factor i - 2/5*h**3 + 0*h - 2/5*h**2.
-2*h**2*(h + 1)/5
Let t be (-358)/(-14) + (-54)/(-126). Let q = 105/4 - t. Factor -1 - q*n**2 - n.
-(n + 2)**2/4
Let x(o) be the first derivative of 4*o**5/5 + 2*o**4 + 4*o**3/3 + 47. Solve x(h) = 0 for h.
-1, 0
Let u(v) be the first derivative of 1 - 1/12*v**3 - 1/8*v**2 + 0*v. Determine a, given that u(a) = 0.
-1, 0
Let q(y) be the third derivative of -y**6/60 + 2*y**5/5 - 4*y**4 + 64*y**3/3 - 6*y**2. Determine o, given that q(o) = 0.
4
Let j = 13/20 - 2/5. Factor 0*h**2 + 0 + 1/4*h**3 + j*h**4 + 0*h.
h**3*(h + 1)/4
Let x(j) = -5*j + 1. Let y be x(-1). Factor -a**4 + 0*a + 0*a**2 - y*a**2 + 6*a**3 - a**4 + 2*a.
-2*a*(a - 1)**3
Let t(d) = -d. Let c be t(-1). Factor -13/4*z**2 + 3/4*z**3 + 4*z - c.
(z - 2)**2*(3*z - 1)/4
Let u be (-10)/(-55) + 442/(-132). Let j = 35/6 + u. Factor -2/3*r - 4*r**3 + 0 + j*r**2 + 8/3*r**4 - 2/3*r**5.
-2*r*(r - 1)**4/3
Let o(y) = -y**3 - 3*y**2 - 2*y + 2. Let u be o(-2). Let p = -18 - -21. Suppose 2/3*s**p + 2/3*s + 4/3*s**u + 0 = 0. What is s?
-1, 0
Let i = 173/4 - 43. Let t(b) be the first derivative of -i*b**2 - 1/6*b**3 - 3 + 0*b. Determine c, given that t(c) = 0.
-1, 0
Factor 0 + 3/2*u**2 + 15/2*u.
3*u*(u + 5)/2
Let r = 42/11 + -40/11. Determine c so that 0*c**4 + 4/11*c**3 + 0*c**2 + 0 - r*c**5 - 2/11*c = 0.
-1, 0, 1
Let m(x) = 3*x - 33. Let y be m(11). Let d(w) be the second derivative of 0 + y*w**3 - 1/45*w**6 + 0*w**5 + w + 0*w**2 + 1/18*w**4. Factor d(f).
-2*f**2*(f - 1)*(f + 1)/3
Let g = -1 - -6. Suppose 0*b = -b + g*z + 2, -4*b = z - 8. Factor -10/9*c - 8/9*c**b - 2/9.
-2*(c + 1)*(4*c + 1)/9
Let v(q) = -7*q**3 - 19*q**2 - 11. Let w(s) = 4*s**3 + 10*s**2 + 6. Let g(f) = 6*v(f) + 11*w(f). Solve g(p) = 0 for p.
0, 2
Factor -134/5*q**3 + 32/5*q - 98/5*q**5 - 46/5*q**2 + 238/5*q**4 + 8/5.
-2*(q - 1)**3*(7*q + 2)**2/5
Let t(d) be the second derivative of -d**7/126 - d**6/90 + d**5/20 + d**4/36 - d**3/9 + 2*d. Find i, given that t(i) = 0.
-2, -1, 0, 1
Suppose 4*w - 16 = 0, 4*t = 3*t - 3*w + 15. Factor 0 - 3/2*p**t + 0*p - p**2 - 1/2*p**4.
-p**2*(p + 1)*(p + 2)/2
Let c(l) be the second derivative of 0*l**2 - 1/240*l**5 - 1/720*l**6 + 0 - 2/3*l**3 + 0*l**4 + l. Let w(s) be the second derivative of c(s). Solve w(d) = 0.
-1, 0
Let l(z) = z**3 - 1. Let a(m) = -m**4 - m**3 + 3*m**2 + 2*m + 1. Let d(i) = a(i) + l(i). Factor d(n).
-n*(n - 2)*(n + 1)**2
Let v be ((-15)/12)/(2/(-8)). Find j such that -v*j + 2*j**3 + 5*j + j**3 = 0.
0
Let c(h) be the third derivative of 2/21*h**3 + 0*h - 1/210*h**5 - 1/84*h**4 + 0 - 2*h**2. Factor c(i).
-2*(i - 1)*(i + 2)/7
Let z(g) be the third derivative of g**8/560 - g**7/350 - g**6/200 + g**5/100 + g**2. Find t such that z(t) = 0.
-1, 0, 1
Let u(y) be the first derivative of -2*y**3/21 + 3*y**2/7 - 4*y/7 + 4. Determine a, given that u(a) = 0.
1, 2
Let s be -4*(13/(-4) - -2). Let g(p) = -6*p**2 - 6*p + 12. Let q(y) = 4*y**2 + 4*y - 8. Let z(r) = s*g(r) + 7*q(r). Determine m so that z(m) = 0.
-2, 1
Let z be 0/(3 + -7 - (-3)/1). Find o such that 0 + 1/2*o**2 + z*o + 1/2*o**3 = 0.
-1, 0
Suppose -4*d + 7 = 2*g - 13, -5*g = 5*d - 35. Suppose -5 - g = -3*c. Let 10*v**4 - 10*v + 4/3 - 82/3*v**c + 26*v**2 = 0. Calculate v.
1/3, 2/5, 1
Factor 10/9*m**2 - 2*m - 4/9.
2*(m - 2)*(5*m + 1)/9
Factor -1/2*l + 1/2*l**3 - 1/2*l**2 + 1/2.
(l - 1)**2*(l + 1)/2
Let y(u) be the third derivative of -u**7/735 - u**6/210 + 11*u**5/210 + u**4/7 + u**2 + 5*u. Factor y(w).
-2*w*(w - 3)*(w + 1)*(w + 4)/7
Suppose 0 + 4 = 4*u. Let t be u*(-1 - -2) - -2. Find l, given that l**t - l + l = 0.
0
Let x(r) be the third derivative of r**10/75600 + r**9/30240 - r**8/5040 + r**5/10 - 7*r**2. Let g(c) be the third derivative of x(c). Factor g(i).
2*i**2*(i - 1)*(i + 2)
Let m be (-12)/27*(-423)/6. Let u = m - 31. Find w, given that 2/3*w - u*w**2 - 1/3 = 0.
1
Let n(s) = -s**3 - 2*s**2. Let c be 6/(-4)*(-4)/(-3). Let r be n(c). What is j in 2 + r - 10*j**2 - 2*j**3 - j - 2*j**3 + 8*j**4 + 5*j**5 = 0?
-1, 2/5, 1
Suppose -2*c + 4*b = 14, c + 6 = b + 2. Let p = 5 + c. Factor 0*s + 0*s**2 - 1/3*s**3 + 0 + 2/3*s**p - 1/3*s**5.
-s**3*(s - 1)**2/3
Suppose -i + 4*f = -21, -4*f = -5*i - 9*f + 5. Suppose 0*v - i*v = 0. Factor 0 + v*k + 1/4*k**3 - 1/4*k**2.
k**2*(k - 1)/4
Let i(h) = -h**3 - 8*h**2 - h - 2. Let a be i(-8). Suppose 0 = -4*s + a - 2. Factor -c**2 - 3*c - s + 5*c + 0*c.
-(c - 1)**2
Let y(o) = o**4 + o**3 - 2*o**2 + 2*o - 2. Let q(l) = 2*l**4 + 2*l**3 - 5*l**2 + 5*l - 5. Let d(a) = -2*q(a) + 5*y(a). What is z in d(z) = 0?
-1, 0
Let f(s) = 5*s + 32. Let a be f(-6). Factor 1/4*x + 1/4*x**a + 0 - 1/4*x**4 - 1/4*x**3.
-x*(x - 1)*(x + 1)**2/4
Let x be -3 + 2 + 2 - 29. Let k be x/(-80) - 1/(-4). Factor -6/5*n + k + 3/5*n**2.
3*(n - 1)**2/5
Let a(t) be the second derivative of 2*t - 1/21*t**3 - 3/70*t**5 + 0*t**2 + 1/105*t**6 + 1/14*t**4 + 0. Factor a(g).
2*g*(g - 1)**3/7
Suppose 0 + 9/8*u**3 + 3/8*u**4 + 0*u**2 + 0*u = 0. Calculate u.
-3, 0
Let q(b) be the third derivative of b**8/20160 + b**4/8 - 8*b**2. Let i(x) be the second derivative of q(x). Suppose i(d) = 0. What is d?
0
Determine h, given that 3/4*h**2 - 15/4*h**4 + 3 - 3/4*h**5 - 21/4*h**3 + 6*h = 0.
-2, -1, 1
Let f(j) be the third derivative of -j**7/2100 + j**6/900 - 5*j**4/24 + 5*j**2. Let i(s) be the second derivative of f(s). Suppose i(y) = 0. What is y?
0, 2/3
Let b be -41 - -41 - (-2)/9. Let -2/3*v**5 + 0 - 4/3*v**3 + b*v + 16/9*v**4 + 0*v**2 = 0. Calculate v.
-1/3, 0, 1
Suppose 0*v + 11 = -v - s, v + 3*s + 7 = 0. Let r = v - -17. Factor 0*t**2 + 0 + 2/3*t**5 + 2/3*t**r + 0*t + 