- 14 = 2*p + w, -20 = -5*p - w. Factor -9/5*g**4 - 2/5 + 29/5*g**3 + p*g - 33/5*g**2.
-(g - 1)**3*(9*g - 2)/5
Factor 4/5*b**2 - 12/5*b - 16/5.
4*(b - 4)*(b + 1)/5
Let c(j) be the second derivative of 11*j**6/60 - j**5/20 - 11*j**4/24 + j**3/6 + 2*j. Factor c(y).
y*(y - 1)*(y + 1)*(11*y - 2)/2
Suppose 0 = -0*l + 4*l - 4. Let f(g) be the first derivative of -l + 0*g**4 - 6/25*g**5 + 0*g + 2/15*g**6 + 2/15*g**3 + 0*g**2. Factor f(p).
2*p**2*(p - 1)**2*(2*p + 1)/5
Let x = -9 + 27. Factor 16*o - o - x - 2*o**2 - 3*o.
-2*(o - 3)**2
Let f(t) be the second derivative of 0 - 1/12*t**3 - 4*t + 0*t**2 - 1/24*t**4. Find s, given that f(s) = 0.
-1, 0
Let j = -144 + 579/4. Solve -1/4*b**4 - 3/4*b**3 + 0 - j*b**2 - 1/4*b = 0 for b.
-1, 0
Let k(o) = 95*o**5 - 205*o**4 + 205*o**3 + 35*o**2 - 35*o. Let p(z) = 8*z**5 - 17*z**4 + 17*z**3 + 3*z**2 - 3*z. Let m(v) = 3*k(v) - 35*p(v). Factor m(x).
5*x**3*(x - 2)**2
Suppose y - 8 + 6 = 0. Determine h, given that 0 - 2*h**5 + 4/7*h**y + 0*h - 22/7*h**3 + 32/7*h**4 = 0.
0, 2/7, 1
Let c(j) = 7*j**2 + 3*j + 2. Let b be c(-1). Suppose -5*l + b = -4. Solve -2/5*h**l + 2/5*h + 0 = 0.
0, 1
Let t(v) = -v**3 + v**2 - v + 2. Let l be t(0). Let g = 6 + 2. Factor 2*q**3 - 8*q + g*q**2 + 4 - l*q - 4*q**3.
-2*(q - 2)*(q - 1)**2
Let o(t) be the first derivative of -289*t**3/6 + 17*t**2 - 2*t - 23. What is d in o(d) = 0?
2/17
Suppose 4*c + 6 = -2*t, 0 = c - t - 0 + 9. Let d = 4 + c. Factor -12/5*s**2 - 4*s**4 - 2/5*s + d - 24/5*s**3 - 6/5*s**5.
-2*s*(s + 1)**3*(3*s + 1)/5
Let r be 2*28/21 + 2/(-3). Let d(i) be the first derivative of 2/21*i**3 - 1 + 1/14*i**4 + 0*i - 2/7*i**r. Factor d(h).
2*h*(h - 1)*(h + 2)/7
Let h(k) be the third derivative of k**8/294 - k**7/147 - k**6/210 + k**5/70 - 17*k**2. Find a such that h(a) = 0.
-3/4, 0, 1
Let g(u) be the first derivative of 3*u**4/16 - 9*u**3/4 + 9*u**2 - 12*u + 7. Let g(z) = 0. What is z?
1, 4
Let j(k) = -4*k - 57. Let w be j(-15). Suppose -2*f = -4*h + 2*f + 8, -h + 4*f - 4 = 0. Find a, given that -a**4 + 6*a**2 - 6*a**h + a**4 - w*a + 3*a**5 = 0.
-1, 0, 1
Let q(y) = y**5 - y**3 + y - 1. Let v(f) = -5*f**5 + 14*f**3 - 6*f**2 - 11*f + 8. Let s(t) = -2*q(t) - v(t). Factor s(g).
3*(g - 1)**3*(g + 1)*(g + 2)
Let m(y) = -3*y + 42. Let n be m(14). Factor n*s**4 + 0*s + 0*s**2 - 2/3*s**3 + 0 + 2/3*s**5.
2*s**3*(s - 1)*(s + 1)/3
Determine j, given that 2/5*j**4 + 2/5*j**3 + 0 - 2/5*j**2 - 2/5*j = 0.
-1, 0, 1
Let g = -1/65 + 133/195. Let s(c) be the first derivative of 1 + 4/3*c - 1/3*c**2 - g*c**3. What is h in s(h) = 0?
-1, 2/3
Let s(l) be the second derivative of -1/63*l**7 + 0 - 3*l - 1/3*l**2 - 1/3*l**5 - 5/9*l**4 - 1/9*l**6 - 5/9*l**3. Solve s(p) = 0 for p.
-1
Suppose 4*d + 5*i = -0 - 5, 2*d - 4*i - 4 = 0. Suppose -4 = -2*m - d. What is n in 0*n - 2/3 + 2/3*n**m = 0?
-1, 1
Let w(o) be the first derivative of o**3/9 + o**2 + 5*o/3 + 7. Factor w(s).
(s + 1)*(s + 5)/3
Factor -l**3 - 13 + l**2 + 13.
-l**2*(l - 1)
Let o(s) = -6*s - 8. Let m be o(-2). Factor 0*d**m + 0 - 2/7*d + 4/7*d**3 + 0*d**2 - 2/7*d**5.
-2*d*(d - 1)**2*(d + 1)**2/7
Let g be 3/6 + 15/6. Solve -2*r**2 + 4*r**3 - 7*r**g - 2*r**4 - r**3 = 0 for r.
-1, 0
Let u(d) = 2 + d**2 - d + 3 - 5. Let j be u(3). Factor -3*g**4 - 6*g**4 - 2*g**3 + 3*g**4 + j*g**2 + 2*g.
-2*g*(g - 1)*(g + 1)*(3*g + 1)
Let o = -684/49 + 21793/294. Let y = o - 60. Suppose -1/6*m**3 + 1/6 - 1/6*m**2 + y*m = 0. Calculate m.
-1, 1
Factor 84*f**2 - 84*f**2 - 4*f**3.
-4*f**3
Let j(o) = o**2 + 9*o + 9. Let i be j(-8). Let n = 2 + i. Factor -12*f - 20*f**2 - 1 - 64*f**n - 10*f**2 - 18*f**2.
-(4*f + 1)**3
Let j(t) = 6*t**4 - 30*t**3 + 36*t**2 + 24*t - 56. Let d(b) = -2*b**4 + 10*b**3 - 12*b**2 - 8*b + 19. Let i(u) = -8*d(u) - 3*j(u). Solve i(l) = 0.
-1, 2
Let q(m) be the first derivative of m**3/3 - 7*m**2/12 + m/6 + 26. Determine c, given that q(c) = 0.
1/6, 1
Let p be 2 - (-2 + (-20)/(-8)). Let j be 8/(-12) + 24/9. Find h, given that -3/2*h**j - p*h**3 + 0*h + 0 = 0.
-1, 0
Suppose 4*a + 2946 = 1182. Let s be (-21)/a - 2/(-7). Factor 1/3*c**2 - 2/3 + s*c.
(c - 1)*(c + 2)/3
Let z(h) be the first derivative of 3*h**4/4 - h**3 - 3*h**2/2 + 3*h - 7. Factor z(d).
3*(d - 1)**2*(d + 1)
Let y(p) = -12*p + 6. Let z(t) = t**2 + 1. Let k(s) = y(s) + 3*z(s). Determine b so that k(b) = 0.
1, 3
Let w(m) be the first derivative of -m**5/60 + m**3/18 - 2*m - 4. Let o(l) be the first derivative of w(l). Factor o(h).
-h*(h - 1)*(h + 1)/3
Let s(l) = -27*l**3 + 185*l**2 - 198*l + 47. Let w(n) = 26*n**3 - 185*n**2 + 199*n - 46. Let v(q) = -6*s(q) - 7*w(q). Factor v(b).
-5*(b - 8)*(b - 1)*(4*b - 1)
Let d(o) be the second derivative of o**3/3 - o**2 + 7*o. Let w be d(1). Suppose -1/2*g**2 + 1/2*g**3 - 1/2*g**5 + w + 1/2*g**4 + 0*g = 0. Calculate g.
-1, 0, 1
Let d be 3 - ((-856)/(-360) - 6/(-27)). Let -6/5*z**3 + d*z + 8/5*z**2 - 4/5 = 0. Calculate z.
-2/3, 1
Let n(r) be the second derivative of -r**4/60 + r**3/5 - r**2/2 - 34*r. Factor n(v).
-(v - 5)*(v - 1)/5
Let c(x) = 5*x**2 + 12*x + 6. Let s(o) = -o**2 - o - 1. Let p(d) = -c(d) - 6*s(d). Find y such that p(y) = 0.
0, 6
Let f = 2 + 1. Suppose -2*h = -3*o + 3, 0 = -5*o + 2*o + f*h. Let -u + 5*u**4 - 5*u**2 - u**5 - 3*u**o + 2*u**4 + 5*u**5 - 2*u**4 = 0. Calculate u.
-1, -1/4, 0, 1
Let s(x) be the second derivative of x**7/21 - x**6/15 - 3*x**5/5 - x**4/3 + 5*x**3/3 + 3*x**2 - 12*x. What is r in s(r) = 0?
-1, 1, 3
Suppose 0*k - 2*k = -4*t - 28, 31 = 4*k - 3*t. Factor 3*h**2 - k*h + 2*h**2 - 3*h**2 + 2*h**2 - 8.
4*(h - 2)*(h + 1)
Suppose 48/13*v**2 + 20/13*v**3 + 2/13*v**4 - 64/13*v - 256/13 = 0. What is v?
-4, 2
Let s(u) = 3*u - 43. Let o be s(15). Factor 6/7*m**3 + 2*m**o + 10/7*m + 2/7.
2*(m + 1)**2*(3*m + 1)/7
Factor 16/9*l + 0 - 52/9*l**3 - 14/9*l**4 - 40/9*l**2.
-2*l*(l + 2)**2*(7*l - 2)/9
Let u(f) be the first derivative of 0*f**2 + 1/180*f**6 + 1/12*f**4 - 1/30*f**5 - 1/3*f**3 + 0*f - 1. Let p(l) be the third derivative of u(l). Solve p(a) = 0.
1
Let k = -10 + 12. Let n = k - 0. Factor -9/2*i**4 + 6*i**n + 27/2*i**5 - 12*i**3 + 0*i + 0.
3*i**2*(i + 1)*(3*i - 2)**2/2
Let y(f) be the third derivative of -f**6/240 - f**5/60 - 3*f**2. Factor y(p).
-p**2*(p + 2)/2
Let m(x) = 2*x**2 + 2*x - 1. Let h be m(-2). Factor 0*r**h + 7*r**3 + 2*r - r**3 + 2*r**4 + 6*r**2.
2*r*(r + 1)**3
Let j(c) be the third derivative of c**6/30 + c**5/3 + 7*c**4/6 + 2*c**3 - 4*c**2. Factor j(b).
4*(b + 1)**2*(b + 3)
Let i be 0 + (3/(-3) - -3). Let 16*c**2 + 4*c**3 + 10*c + 10*c**i + 38*c - 2*c**2 + 32 = 0. Calculate c.
-2
Let y(q) = -q**5 + q**4 - q**2. Let p(d) = d**5 - d**4 - 30*d**3 + 66*d**2 - 55*d + 15. Let l(t) = -p(t) + 4*y(t). Determine u so that l(u) = 0.
-3, 1
Let j = 5 - 7. Let p be j/(-9) - (-16)/9. Find i such that -3/2*i**p + 3/2*i - 1/2 + 1/2*i**3 = 0.
1
Let j = 15 - 13. Solve 8/7*l**5 + 0*l + 0*l**j + 2/7*l**3 + 0 - 10/7*l**4 = 0.
0, 1/4, 1
Let x be 3/(-12) - (-75)/12. Let p be x - (0 + (3 - 1)). Factor -5*j**4 - 6*j**3 + 5*j**4 - 4 - 4*j**4 + 11*j**2 + 4*j - 5*j**p.
-(j + 1)**2*(3*j - 2)**2
Let b(p) be the first derivative of -5*p**4/4 - 5*p**3 - 2. Factor b(r).
-5*r**2*(r + 3)
Let j(t) = -t**2 + 10*t - 9. Let d be (-2)/4 + 76/8. Let f be j(d). Factor 0 + 1/4*o - 1/4*o**3 + f*o**2.
-o*(o - 1)*(o + 1)/4
Factor 2/11*d**3 + 2/11*d**2 - 4/11*d + 0.
2*d*(d - 1)*(d + 2)/11
Let z(u) = -u**2 + 5*u. Let q = -3 + 8. Let w be z(q). Factor -1/4*o + w - 1/4*o**2.
-o*(o + 1)/4
Let t(o) = -3*o**2 - 11*o - 3. Let v(g) = 2*g**2 + 10*g + 4. Let u(j) = -4*t(j) - 5*v(j). Determine i, given that u(i) = 0.
-1, 4
Suppose 0 - 4/5*w**2 - 1/5*w**3 - 4/5*w = 0. What is w?
-2, 0
Let l(i) be the second derivative of i**5/5 - 2*i**3 + 4*i**2 + 13*i. Let l(k) = 0. What is k?
-2, 1
Let f(w) = -w**3 - 9*w**2 - 8*w + 3. Let d be f(-8). Solve 2*z + 4*z - 5*z - z**2 + 0*z + z**4 - z**d = 0.
-1, 0, 1
Let k(q) = -3*q**4 - q**3 - 1. Let o(a) = a**4 + a**3 + 1. Let x(p) = k(p) + o(p). Factor x(s).
-2*s**4
Let h = -1 - -5. Solve -h*s + 3*s**2 - 3*s**2 + 2 + 2*s**2 = 0.
1
Let l(w) = w**3 + w**2 - w - 1. Let n(p) = 2*p**3 + 4*p**2 - 2*p - 4. Let r(q) = 3*l(q) - n(q). Factor r(a).
(a - 1)**2*(a + 1)
Let h(x) be the second derivative of 3/20*x**5 + 0*x**4 - 3*x + 0*x**2 + 0 + 0*x**3. Factor h(u).
3*u**3
Let r(y) be the second derivative of -y**7/294 - 2*y**6/105 + 13*y**5/70 - 11*y*