Let x = 2/167 - y. Determine h, given that 0*h + 2/7*h**4 - x*h**3 + 0*h**2 + 0 = 0.
0, 1
Let m(p) be the third derivative of 0*p + 0 - 2/945*p**7 - 1/540*p**6 - 1/1512*p**8 + 0*p**4 + 0*p**5 + 0*p**3 - 4*p**2. Solve m(k) = 0.
-1, 0
Let y(l) be the third derivative of 0*l + 0*l**3 + 3*l**2 + 0 + 1/315*l**7 + 0*l**5 + 0*l**4 + 1/180*l**6. Solve y(p) = 0 for p.
-1, 0
Let s(k) = 2*k + 4. Let i be s(-6). Let g be (i/20)/((-2)/10). Factor 2*d**3 - 3*d**2 + d**2 + 2*d**g.
2*d**3
Let b(h) be the third derivative of -h**7/210 - h**6/40 - h**5/60 + h**4/8 + h**3/3 + 19*h**2. Factor b(x).
-(x - 1)*(x + 1)**2*(x + 2)
Let x(f) = f**3 - 2*f**2 - 2*f + 2. Let s be x(3). Suppose -s*z = -3*m + 32, -3*z = m - 2*z. Find q, given that 4*q + 2 + q**m - 4 - q**3 + q - 3*q**2 = 0.
-2, 1
Let m(y) = -7*y**4 + 3*y**2 + 3*y. Let r(k) = -20*k**4 + 8*k**2 + 8*k. Let c(d) = -8*m(d) + 3*r(d). Factor c(n).
-4*n**4
Let u = -7929/5 + 1620. Let b = -1529/45 + u. Factor b*q + 0 - 2/9*q**2.
-2*q*(q - 1)/9
Determine g, given that -8/5 - 4/5*g + 4/5*g**3 + 8/5*g**2 = 0.
-2, -1, 1
Suppose -4 + 14 = 2*n. Let c(f) be the third derivative of 0*f + 1/120*f**n - 1/48*f**4 + 0 + 3*f**2 + 0*f**3. Factor c(q).
q*(q - 1)/2
Let b(i) be the second derivative of i**6/70 - 3*i**5/35 + 3*i**4/28 + 6*i. Factor b(v).
3*v**2*(v - 3)*(v - 1)/7
Let w(b) = -71*b**5 - 16*b**4 + 41*b**3 - 6*b**2 - 4*b - 4. Let k(y) = -y**5 - y**4 + y**3 - y**2 + y + 1. Let q(t) = 4*k(t) + w(t). What is r in q(r) = 0?
-1, 0, 1/3, 2/5
Determine g, given that 0*g**2 - 3*g**2 + 0*g**2 - 2*g**4 + 5*g**4 = 0.
-1, 0, 1
Let r(j) be the third derivative of -3*j**8/896 - 11*j**7/560 - 3*j**6/80 - j**5/40 - 22*j**2. Find b, given that r(b) = 0.
-2, -1, -2/3, 0
Let v = 2/179 - -348/895. Suppose 0 - v*d - 2/5*d**2 = 0. Calculate d.
-1, 0
Let w = 92 + -27. Let x = -453/7 + w. Suppose -x + 6/7*a**2 + 2/7*a + 4/7*a**4 - 10/7*a**3 = 0. What is a?
-1/2, 1
Let n be (-45)/10*(-3)/(-18)*-2. Let c(x) be the first derivative of 1/3*x**3 + 3 + 2*x - n*x**2. Factor c(b).
(b - 2)*(b - 1)
Let c be 6/(-27) - 146/(-9). Find f such that 4*f**2 - c + 6 + 4*f + 2 = 0.
-2, 1
Let h = 143 + -141. Determine k, given that -1/2 + 1/4*k**h + 1/4*k = 0.
-2, 1
Let c = 6 - 4. Suppose -c*u = -u. Factor -b**3 + u*b - 2*b**2 + 2*b**2 - b**2 + b + 1.
-(b - 1)*(b + 1)**2
Let d(i) be the second derivative of -i**6/255 - i**5/34 - 5*i**4/102 + 5*i**3/51 + 6*i**2/17 + 37*i. Let d(v) = 0. What is v?
-3, -2, -1, 1
Let l(j) = j**3 + j + 7. Let m be l(0). Factor 6*a**2 + 4*a**3 - a - m*a**3 + 3*a - 5*a.
-3*a*(a - 1)**2
Let a = 2989/1990 + -2/995. Factor -15/4*f**3 - 3*f**4 - a*f**2 + 0*f + 0 - 3/4*f**5.
-3*f**2*(f + 1)**2*(f + 2)/4
Let w(p) be the second derivative of -p**5/110 + 2*p**4/33 - 5*p**3/33 + 2*p**2/11 - 3*p. Factor w(x).
-2*(x - 2)*(x - 1)**2/11
Let p(i) be the second derivative of -1/8*i**3 + 1/40*i**5 - 1/8*i**2 + 5*i + 1/168*i**7 + 1/40*i**6 - 1/24*i**4 + 0. What is s in p(s) = 0?
-1, 1
Let r be 2/(-3) - (-4)/3. Let d = -2693/6 - -899/2. Solve 4/3 - r*u**2 - d*u = 0.
-2, 1
Let f(r) be the first derivative of 0*r - 9/2*r**2 + r**3 - 4. Factor f(l).
3*l*(l - 3)
Let f(p) be the second derivative of 0*p**2 - 1/24*p**4 + 0 - 1/80*p**5 - 1/2*p**3 - 1/720*p**6 - 2*p. Let i(v) be the second derivative of f(v). Factor i(c).
-(c + 1)*(c + 2)/2
Let f(r) be the first derivative of -r**6/15 - 2*r**5/25 + r**4/10 + 2*r**3/15 - 10. Factor f(p).
-2*p**2*(p - 1)*(p + 1)**2/5
Let h(r) be the second derivative of 1/66*r**4 + 0*r**2 + 0 - r + 2/33*r**3. Factor h(g).
2*g*(g + 2)/11
Suppose 0 = 2*u + 6, 2*f = u + 4 + 5. Determine c so that -5*c**2 + 0*c + c**2 - c**3 - f*c = 0.
-3, -1, 0
Let r = 53 + -18. Let q = r + -33. Factor 0 - 2/11*h - 2/11*h**q.
-2*h*(h + 1)/11
Factor p**2 + 3/2 - 13/4*p + 3/4*p**3.
(p - 1)*(p + 3)*(3*p - 2)/4
Let d(h) be the second derivative of h**7/504 + h**6/540 - h**5/72 - h**4/36 + h**3/6 - 2*h. Let f(z) be the second derivative of d(z). Solve f(y) = 0.
-1, -2/5, 1
Let q be -4 - 9941/(-1267) - 3. Let j = 2/181 + q. Solve -16/7*v**2 - 8/7*v + j*v**3 + 0 + 18/7*v**4 = 0 for v.
-2/3, 0, 1
Let q(i) = -2*i - 1 - 5*i + 0*i - i**2. Let p(l) = 6*l**2 + 36*l + 6. Let h be (1 + 0)/((-1)/(-3)). Let w(o) = h*p(o) + 16*q(o). Factor w(t).
2*(t - 1)**2
Suppose 5*g = 35 - 5. Let c(s) = 10*s**3 + 10*s**2 + 22*s + 6. Let k(v) = -9*v**3 - 11*v**2 - 21*v - 5. Let q(y) = g*k(y) + 5*c(y). Factor q(u).
-4*u*(u + 2)**2
Let d(n) be the second derivative of -n - 1/18*n**3 + 0 - 1/36*n**4 + 1/3*n**2. Factor d(h).
-(h - 1)*(h + 2)/3
Suppose -14*a**2 - 18*a**3 - 2*a**5 - 6*a + 0*a**5 + 0*a + 2*a - 10*a**4 = 0. Calculate a.
-2, -1, 0
Let t = -1800 + 9054/5. Factor t*y - 54/5 - 18/5*y**2 + 2/5*y**3.
2*(y - 3)**3/5
Let b be (0 - (-1)/(-7))/(-120). Let c(h) be the third derivative of 0*h**6 + 0*h**5 + 1/336*h**8 + 0*h**3 + b*h**7 - 2*h**2 + 0*h**4 + 0*h + 0. Factor c(u).
u**4*(4*u + 1)/4
Let a(k) be the first derivative of -2*k**3/15 - 8*k**2/5 - 32*k/5 + 4. Let a(i) = 0. Calculate i.
-4
Let h = 3862/3 - 1286. Factor -4/3*z**3 + 0 + 0*z - h*z**4 + 8/3*z**2.
-4*z**2*(z - 1)*(z + 2)/3
Solve 8/5 + 14/5*u**4 + 38/5*u**3 + 32/5*u + 2/5*u**5 + 10*u**2 = 0 for u.
-2, -1
Let n(b) be the second derivative of 4*b + 0 - 3/4*b**5 + 0*b**2 + 3/4*b**4 + 9/2*b**3 + 1/10*b**6. Let n(k) = 0. What is k?
-1, 0, 3
Factor -11*j**4 + 9 + 5*j**4 - 6*j**3 + 24*j**2 - 21*j - 3 + 3*j**5.
3*(j - 1)**4*(j + 2)
Let p(r) = -3*r**2 - 30*r - 77. Let s(u) = -6*u**2 - 60*u - 155. Let h(b) = -5*p(b) + 2*s(b). Find l, given that h(l) = 0.
-5
Let g(p) be the first derivative of 0*p**3 - 1/8*p**2 + 1 + 0*p + 1/16*p**4. Determine f so that g(f) = 0.
-1, 0, 1
Determine c, given that -16/3 + 24*c**2 + 32/3*c + 7/3*c**4 + 40/3*c**3 = 0.
-2, 2/7
Let k(d) = -7*d**3 + 6*d**2 - 3*d. Let p = -31 - -58. Let f(b) = 48*b**3 - 42*b**2 + 21*b. Let w(o) = p*k(o) + 4*f(o). Solve w(t) = 0 for t.
0, 1
Suppose 0 = -8*n + 13*n. Factor n + 0*q**2 + 0*q - 2/3*q**4 + 2/3*q**3.
-2*q**3*(q - 1)/3
Let k be ((-13)/4)/(49/(-28)) - 1. Factor k*o + 2/7 + 2/7*o**3 + 6/7*o**2.
2*(o + 1)**3/7
Let a(t) be the first derivative of 7/3*t**3 + 1/6*t**6 - 4*t - 1/4*t**4 + 0*t**2 - 3/5*t**5 + 1. Factor a(s).
(s - 2)**2*(s - 1)*(s + 1)**2
Let a(z) = 5*z**3 - 7*z**2 - 7*z + 5. Let m(c) = 15*c**3 - 22*c**2 - 22*c + 15. Let t(q) = -7*a(q) + 2*m(q). Let t(f) = 0. Calculate f.
-1, 1
Let t(y) be the second derivative of y**5/30 + y**4/18 - 11*y. Factor t(n).
2*n**2*(n + 1)/3
Let b = 211/2 - 105. Let x = 7 - 5. Factor -1/2*k**5 + 1/2*k**4 + 0*k + b*k**3 + 0 - 1/2*k**x.
-k**2*(k - 1)**2*(k + 1)/2
Let h(t) = t**3 - 26*t**2 + 70*t - 23. Let p be h(23). Solve 1/2*x**4 - 1/2*x**2 + 0 - 1/4*x**5 + 1/4*x + p*x**3 = 0 for x.
-1, 0, 1
Factor -1/6 + s**3 + 3/2*s**4 - 4/3*s**2 - s.
(s - 1)*(s + 1)*(3*s + 1)**2/6
Let z(u) be the third derivative of u**6/30 + u**5/3 + 4*u**4/3 + 8*u**3/3 - 3*u**2. Factor z(x).
4*(x + 1)*(x + 2)**2
Suppose -3*p - 1 = r, 2*p + 0 = -2*r + 2. Factor 0*i + 2/9*i**r + 2/9*i**3 + 0.
2*i**2*(i + 1)/9
Let k(l) be the second derivative of -l**7/56 + l**6/20 - 3*l**5/80 - 3*l. Suppose k(p) = 0. Calculate p.
0, 1
Let w(x) be the first derivative of 2*x**3/21 - 2*x**2/7 + 5. Solve w(c) = 0 for c.
0, 2
Let f(q) be the second derivative of -q**9/22680 - q**8/10080 + q**7/3780 + q**6/1080 + q**4/4 - q. Let g(w) be the third derivative of f(w). Factor g(n).
-2*n*(n - 1)*(n + 1)**2/3
Solve 2/3*g**3 + 0 + 4/3*g + 2*g**2 = 0 for g.
-2, -1, 0
Let d(j) = -3*j - 3. Let i be d(-4). Suppose u + 14 = 16. Determine k so that 9*k**4 - i*k**4 - 2*k**5 - k + k**5 + u*k**3 = 0.
-1, 0, 1
Let h(b) be the third derivative of b**8/16 - 4*b**7/7 + 11*b**6/10 + 29*b**5/10 - 51*b**4/8 - 9*b**3 + 32*b**2. Let h(u) = 0. Calculate u.
-1, -2/7, 1, 3
Suppose -5*x + 4 = -6. Let o be (-3 - (-87)/21) + x. Let 8/7*n**3 - 4/7 - 4*n**2 + 32/7*n**4 - o*n + 2*n**5 = 0. What is n?
-1, -2/7, 1
Suppose -5*x + 13 = -12. Let i be 12/4 + (-1)/x. Factor 11/5*w + 24/5*w**2 + i*w**4 + 2/5 + 26/5*w**3 + 3/5*w**5.
(w + 1)**4*(3*w + 2)/5
Let i(v) be the third derivative of -v**5/330 - 5*v**4/66 - 25*v**3/33 - 16*v**2. Factor i(m).
-2*(m + 5)**2/11
Factor 3/2*z + 5/4 + 1/4*z**2.
(z + 1)*(z + 5)/4
Let p(o) be the third derivative of -o**7/210 + o**6/120 + o**5/20 - o**4/24 - o**3/3 + 5*o**2. Factor p(h).
