ative of -b**6/150 - b**5/100 + b**4/60 + b**3/30 - 9*b. Find r such that u(r) = 0.
-1, 0, 1
Let s be (-2)/(-4)*1*0/(-5). Let y(h) be the third derivative of 0 + s*h + 1/30*h**3 - 1/12*h**4 + 1/12*h**5 + 2*h**2. Find b, given that y(b) = 0.
1/5
Let r(w) = -w - 2. Let x be r(3). Let i = -3 - x. Determine g, given that 2/5 - 4/5*g - 6/5*g**i = 0.
-1, 1/3
Let a = 636/2177 + -2/311. Let v(n) be the second derivative of 1/42*n**4 + 0 - n - 1/7*n**3 + a*n**2. Factor v(p).
2*(p - 2)*(p - 1)/7
Let c(v) be the first derivative of 3*v**4/2 - 3*v**3 + 3*v - 2. Factor c(y).
3*(y - 1)**2*(2*y + 1)
Suppose 1/3*m**3 + 1 - 5/3*m + 1/3*m**2 = 0. Calculate m.
-3, 1
Let p(c) be the third derivative of 0 + 0*c - 1/180*c**6 + 4*c**2 - 1/9*c**3 + 1/90*c**5 + 1/36*c**4. Find n such that p(n) = 0.
-1, 1
Let g = -13 + 7. Let r be 0*(g/(-9))/(-2). Factor -2*p**4 + p**3 + 2*p**5 - p**5 + r*p**4.
p**3*(p - 1)**2
Let j(g) be the first derivative of -g**4/24 + 7*g**3/6 - 49*g**2/4 + 343*g/6 - 9. Solve j(a) = 0 for a.
7
Let a(y) be the third derivative of -y**8/168 + 3*y**7/35 - y**6/2 + 23*y**5/15 - 11*y**4/4 + 3*y**3 - 19*y**2 - y. Factor a(g).
-2*(g - 3)**2*(g - 1)**3
Let q be 87/15 - 2/(-10). Suppose 20*g + 3*g**3 - 5*g - 6 - 6*g**2 - q*g**2 = 0. Calculate g.
1, 2
Let h(r) be the second derivative of r**4/42 + r**3/21 - 2*r**2/7 - 14*r. Factor h(k).
2*(k - 1)*(k + 2)/7
Let w(a) be the second derivative of -5*a - 1/60*a**4 + 0*a**2 + 0*a**3 + 0 - 1/100*a**5. Suppose w(h) = 0. Calculate h.
-1, 0
Let s(h) = 10*h**3 + 24*h**2 + 14*h. Let u(x) = -20*x**3 - 49*x**2 - 28*x + 1. Let o(p) = -5*s(p) - 2*u(p). Suppose o(y) = 0. What is y?
-1, -1/5
Let k(u) = 36*u**2 + u. Let v be k(-1). Suppose 3*g - o - 4*o = v, 3*g - 19 = o. Find y such that y**2 + 2*y**3 - y**4 + y**3 - 2*y**3 - y**g = 0.
-1, 0, 1
Factor 8*u**3 - 7*u**3 + u**2 + u**4 + u**3.
u**2*(u + 1)**2
Find j, given that -6*j**3 - 24/5*j**4 + 0*j + 0 - 12/5*j**2 - 6/5*j**5 = 0.
-2, -1, 0
Factor -9*g**3 + 24*g**4 - 2*g**5 - 28*g**4 + 10*g**3 + 5*g**3.
-2*g**3*(g - 1)*(g + 3)
Let -60*r**2 - 2*r**3 + 2*r**4 - 40*r - 38*r**3 - 7*r**4 + 10*r**3 = 0. Calculate r.
-2, 0
Let g(s) = -4*s**3 - 5*s**2 - 3*s + 3. Let a(p) = -5*p**3 - 6*p**2 - 4*p + 4. Let o(q) = -3*a(q) + 4*g(q). Suppose o(m) = 0. What is m?
-2, 0
Factor -4*k**2 - 2/3*k**3 - 16/3 - 8*k.
-2*(k + 2)**3/3
Let r = 164 - 301/2. Determine u so that 0*u - r*u**3 + 3*u**2 + 0 = 0.
0, 2/9
Let d(m) = 19*m**3 + 23*m**2 + 7*m + 3. Let p(a) = -37*a**3 - 45*a**2 - 13*a - 5. Let q(v) = 5*d(v) + 3*p(v). Factor q(t).
-4*t*(t + 1)*(4*t + 1)
Suppose 0*t - 13 = t - 4*d, 0 = 5*t + 3*d - 27. Factor k**2 - 1/2*k + 0 - 1/2*k**t.
-k*(k - 1)**2/2
Let c = -1/78 - -20/39. Factor -c + 1/2*p**2 + 0*p.
(p - 1)*(p + 1)/2
Let w(h) be the first derivative of h**3/3 + 9*h**2/2 - 6. Let k be w(-9). Let 106/5*l**2 + 0*l - 8/5 + k*l**3 - 98/5*l**4 = 0. What is l?
-1, -2/7, 2/7, 1
Let k(z) be the third derivative of z**8/1344 - z**7/840 - z**6/160 + z**5/48 - z**4/48 + 15*z**2. Factor k(y).
y*(y - 1)**3*(y + 2)/4
Let s(c) be the first derivative of c**7/840 - c**6/180 + c**5/120 - c**3/3 - 2. Let u(o) be the third derivative of s(o). Determine d, given that u(d) = 0.
0, 1
Let o(s) = s + 12. Let i be o(0). Let q(r) = -2*r + 26. Let c be q(i). Suppose 6 + 63/2*b**c - 30*b = 0. What is b?
2/7, 2/3
Let f(y) be the second derivative of -1/30*y**4 + 0*y**2 - 1/50*y**5 + 2/15*y**3 + 0 - y. Factor f(w).
-2*w*(w - 1)*(w + 2)/5
Let v = -4 + 8. Suppose -4*o**4 - o**4 + 2*o**v + 3*o**2 = 0. What is o?
-1, 0, 1
Let l(i) = 7*i**2 - 2*i - 9. Let r(z) = 4*z**2 - z - 5. Suppose 2*m - 6*m = -24. Let a(u) = m*l(u) - 11*r(u). Factor a(q).
-(q + 1)*(2*q - 1)
Suppose 40 = -5*g - 0*g. Let z be (g/(-10))/((-9)/(-45)). Factor -4/5*o**2 - 2/5*o + 4/5*o**3 - 2/5*o**5 + 2/5 + 2/5*o**z.
-2*(o - 1)**3*(o + 1)**2/5
Let x(r) = r**2 - 4*r - 1. Let u be x(4). Let f be (-2)/(-14)*(3 + u). What is y in -4/7*y**3 + 2/7 + 2/7*y + f*y**4 - 4/7*y**2 + 2/7*y**5 = 0?
-1, 1
Factor -3/2*j**3 + 13/4*j**2 - 1 + 0*j.
-(j - 2)*(2*j + 1)*(3*j - 2)/4
Let x(f) = f. Let l(c) = c**2 - 7*c - 5. Let j(h) = -l(h) - 3*x(h). Let j(k) = 0. Calculate k.
-1, 5
Let d(q) be the third derivative of q**9/120960 + q**8/80640 - q**7/10080 - q**6/2880 - q**5/30 + q**2. Let p(u) be the third derivative of d(u). Factor p(b).
(b - 1)*(b + 1)*(2*b + 1)/4
Suppose 2*y = -3*y + 25. Let i(g) be the third derivative of 0*g - 1/21*g**3 + 1/210*g**y - g**2 + 0*g**4 + 0. Determine w so that i(w) = 0.
-1, 1
Let l(i) = 3*i**2 + 7*i - 2. Let f(u) = 24*u**2 + 57*u - 15. Let h(v) = 4*f(v) - 33*l(v). Determine r, given that h(r) = 0.
-2, 1
Let a(z) be the third derivative of z**7/210 - z**5/30 + z**3/6 + 5*z**2. Let a(m) = 0. What is m?
-1, 1
Factor 3*q - 4*q**3 + q**3 - 3*q.
-3*q**3
Let h(l) = l**3 + 3*l**2 - 7*l - 9. Let p be h(-4). Let f(r) be the first derivative of 1 - 4/3*r + 2/9*r**p - 1/3*r**2. Factor f(z).
2*(z - 2)*(z + 1)/3
Let o be 1/3 + (-56)/420. Find l such that -1/5*l**2 + 0*l + o = 0.
-1, 1
Suppose 3/5*v + 0*v**3 + 0 + 6/5*v**4 - 3/5*v**5 - 6/5*v**2 = 0. Calculate v.
-1, 0, 1
Let u(y) be the second derivative of -2*y**6/15 + 18*y**5/5 - 36*y**4 + 144*y**3 - 51*y. Suppose u(o) = 0. What is o?
0, 6
Let z be (-50)/(-9) + (-21)/7 + 3. Let w(h) be the first derivative of z*h**3 + 2/3*h + 10/3*h**2 - 1. Solve w(n) = 0 for n.
-1/5
Let p = -1 + 4. Factor 0*z**2 - 2*z**p - 6*z**2 + z - 5*z.
-2*z*(z + 1)*(z + 2)
Let u be (-2)/(6/9) + 13. Let t = u - 5. Factor -14*a**2 - a - a**3 + t*a - 3*a**3 + 14*a**4.
2*a*(a - 1)*(a + 1)*(7*a - 2)
Let q(l) = -50*l**2 + 15*l - 2. Suppose 14 = 2*h - j, -6 - 1 = -3*h - 2*j. Let i(x) = -x. Let s(v) = h*i(v) - q(v). Factor s(z).
2*(5*z - 1)**2
Let n(y) = 2*y - 6. Let a be n(3). Let u(g) be the first derivative of 0*g**3 - 12/5*g**5 - 3/2*g**6 + 0*g + a*g**2 - g**4 + 1. Suppose u(r) = 0. Calculate r.
-2/3, 0
Factor -z + 0 - 23 + 5*z**3 - 19*z - 17 - 5*z**4 + 30*z**2.
-5*(z - 2)**2*(z + 1)*(z + 2)
Let v be (-14)/14*(-1 - -2)*-4. Determine x so that 0 - 1/2*x**v + 0*x + 1/2*x**3 + 0*x**2 = 0.
0, 1
Let l(m) = 12*m**5 - 15*m**2. Let u(o) = o**5 - o**2. Let w(y) = l(y) - 15*u(y). Solve w(z) = 0 for z.
0
Let r(g) = g**2 + 2*g - 3. Let b(s) = 3*s**2 + 5*s - 7. Let t(i) = -4*b(i) + 9*r(i). Suppose t(w) = 0. Calculate w.
-1, 1/3
Let c(u) = -u**2 + 9*u. Let f be c(7). Suppose 8 = h + 2. Find z, given that -4*z**3 + 29*z**3 - f*z**2 + 3*z + 47*z**3 - h + 80*z**2 = 0.
-2/3, -1/2, 1/4
Determine g so that 9/5*g**2 + 0 + 3/5*g**3 + 6/5*g = 0.
-2, -1, 0
Let x(s) be the second derivative of -s**8/4480 - s**7/1680 + s**6/240 - 7*s**4/12 - 9*s. Let r(g) be the third derivative of x(g). Factor r(p).
-3*p*(p - 1)*(p + 2)/2
Let b(j) be the second derivative of j**5/90 + j**4/6 + j**3 + 5*j**2/2 - 7*j. Let l(v) be the first derivative of b(v). Factor l(w).
2*(w + 3)**2/3
Let y be (74/(-8))/((-1)/8). Let q be (-10)/35 + y/14. Factor -3*s**2 - 5*s**2 + 9 + q*s**2 + 6*s.
-3*(s - 3)*(s + 1)
Let t be (-4)/(-8) + (-21)/6. Let y be (4/3)/((-14)/t). Factor 4/7 + y*h**2 - 6/7*h.
2*(h - 2)*(h - 1)/7
Let p be (-2)/(-6) - 13/3. Let r = 17/4 + p. Solve 0 + 0*h - r*h**3 + 0*h**2 = 0 for h.
0
Let k(v) be the third derivative of -v**6/100 + 3*v**5/50 + v**4/20 - 3*v**3/5 - 15*v**2. Factor k(d).
-6*(d - 3)*(d - 1)*(d + 1)/5
Suppose 3*k = 2*k - 5*r, r = -4*k. Let c(i) be the second derivative of 2/3*i**4 - 5/3*i**3 + 2*i**2 - 1/10*i**5 + i + k. Find l such that c(l) = 0.
1, 2
Factor 9/5*z**2 + 3/5*z**3 + 6/5*z + 0.
3*z*(z + 1)*(z + 2)/5
Suppose -34 = 18*l - 70. Suppose 3*v = -1 + 13. Suppose 0*i + l*i**2 + 0*i**3 - 1/4*i**4 - v = 0. Calculate i.
-2, 2
Let l(m) = 3*m**2 - 3*m. Let i(q) = 2*q**2 - 2*q + 6. Let n(j) = 1. Let k(g) = i(g) - 6*n(g). Let t(w) = 5*k(w) - 4*l(w). Determine c so that t(c) = 0.
0, 1
Determine h, given that 6 + 3*h**5 - 12*h**2 - 6*h**3 + 32*h + 6*h**4 + 0*h**3 - 29*h = 0.
-2, -1, 1
Suppose i + 3*m = -14, -i + 4*m + 16 = -5*i. Let u be i - (-2 + 4)/2. Determine z so that 3*z - 2*z**3 + u*z**3 - 2*z**2 + 2*z**4 - z = 0.
-1, 0, 1
Factor 1/3*s - 5/6*s**2 + 1/6*s**4 - 1/6*s**5 + 1/2*s**3 + 0.
-s*(s - 1)**3*(s + 2)/6
Let t(k) = -3 - k - 3*k**2 + 0*k - 1 + 5*k. Let s(i) = -i**3 + 7*i**2 - 9*i + 9. Let r(w) = 4*s(w) + 9*t(w). What is c in r(c) = 0?
0, 1/4
Let s = 944 + -942