 = 0.
-2, 0, 2/3
Let b(l) be the first derivative of -2*l**5/35 + l**4/14 + 2*l**3/21 - l**2/7 + 14. Factor b(j).
-2*j*(j - 1)**2*(j + 1)/7
Let k = -9/10 - -37/30. Factor k*t**2 - 1/3 + 0*t.
(t - 1)*(t + 1)/3
Let f(a) be the second derivative of a**7/210 + a**6/120 - a**5/120 + 2*a**3/3 + a. Let i(v) be the second derivative of f(v). Solve i(g) = 0.
-1, 0, 1/4
Let f(v) be the second derivative of -v**6/6 + 3*v**5/4 - 5*v**4/12 - 5*v**3/2 + 5*v**2 - 17*v. Factor f(b).
-5*(b - 2)*(b - 1)**2*(b + 1)
Suppose -2*d - 58 = -4. Let j be (6/(-21))/(d/21). Suppose -4/9 + 2/3*o - j*o**3 + 0*o**2 = 0. What is o?
-2, 1
Let c(y) = y**3 - y**2 + y - 1. Let x(p) = 11*p**3 + 19*p**2 + 13*p - 7. Let f(b) = -3*c(b) + x(b). Determine t, given that f(t) = 0.
-2, -1, 1/4
Let k(v) = -67*v + 337. Let q be k(5). Factor -27/5 + 27/5*x + 1/5*x**3 - 9/5*x**q.
(x - 3)**3/5
Let z(w) = -w**2 - 5*w**3 + 2*w - 3 - w**4 + 3*w**4 + 0*w**4 - 5*w. Let o(a) = 9*a**4 - 21*a**3 - 4*a**2 - 13*a - 13. Let h(u) = -6*o(u) + 26*z(u). Factor h(q).
-2*q**2*(q + 1)**2
Let a(b) be the first derivative of 1/6*b**2 - 1 + 0*b - 1/12*b**4 + 1/9*b**3 - 1/15*b**5. Solve a(x) = 0.
-1, 0, 1
Let z(r) = r**2 + 3*r - 7. Let w be z(-5). Suppose -w*j = -5*j - i + 9, -3*i = j - 17. Factor -2*q + 0*q**2 + q**3 + q**j + 0*q.
q*(q - 1)*(q + 2)
Factor 49/5 + 14/5*m + 1/5*m**2.
(m + 7)**2/5
Suppose -4*i - j = 0, 4*i + 2*j = 6*i. Factor -8*b**2 - b - 4 + 2*b**3 + 3*b + i + 8*b.
2*(b - 2)*(b - 1)**2
Let m = -20 - -26. Factor 50*k + 0*k**4 - 46*k + 4*k**3 + m*k**2 + k**4 + 1.
(k + 1)**4
Let j = 15 + -11. Let z be (0 - 1)*1*-3. Solve 3*n**3 + 6*n**4 - 3 + 1 + 5*n**z - j*n**2 - 8*n = 0.
-1, -1/3, 1
Let c(v) be the first derivative of 9*v**4/4 - 13*v**3 + 39*v**2/2 - 9*v - 13. Suppose c(p) = 0. Calculate p.
1/3, 1, 3
Let z(n) be the second derivative of n**9/45360 - n**8/10080 + n**4/2 - 7*n. Let b(f) be the third derivative of z(f). Factor b(a).
a**3*(a - 2)/3
Let n(j) = -5*j + 5*j + 2 + j**3 + 2*j**2. Let g be n(-2). Factor 1/3*w**4 + w**g + 1/3*w + 0 + w**3.
w*(w + 1)**3/3
Let m(d) = d**3 - d**2 + d + 1. Let x(s) = 4*s**3 - 7*s**2 + 8*s + 1. Let a(n) = 3*m(n) - x(n). Determine z, given that a(z) = 0.
1, 2
Suppose -8 = n - 3*h + 5, 0 = -4*h + 20. Let y(d) = -d - 3. Let p be y(-5). Factor b**3 + 3*b**2 + 2*b**3 - n*b - 5*b**p - b**3 + 2.
2*(b - 1)**2*(b + 1)
Suppose 3*r = 2*t - 7, -t - r - r = 0. Find o, given that o - 1/2 - 1/2*o**t = 0.
1
Let g be 4/5*(19 + -4). Determine w so that 2 - 2 + 3*w**2 + 12*w + g = 0.
-2
Let b be (-26)/39 - 11/(-3). Let u be (3 - (-15)/(-6))*0. Factor -2/3*m - m**2 - 1/3*m**b + u.
-m*(m + 1)*(m + 2)/3
Let a(b) = -5*b**2 + 1. Let x be a(1). Let d be ((-63)/(-30))/((-2)/x). Let 0 + 3/5*j + 36/5*j**3 + d*j**2 = 0. Calculate j.
-1/3, -1/4, 0
Let x be (-30 + 19)*(-26)/(-10). Let q = x - -29. Factor 0*k**2 + 6/5*k**3 + 0 - 8/5*k - q*k**4.
-2*k*(k - 2)**2*(k + 1)/5
Let r be (-84)/56 + (-4)/6*-3. Determine f, given that -r + 1/2*f**2 + 0*f = 0.
-1, 1
Let m(c) = 5*c**3 + 5*c**2 - 10*c - 15. Let g(y) = -5*y**3 - 4*y**2 + 11*y + 16. Let a(w) = 5*g(w) + 6*m(w). Let a(n) = 0. What is n?
-2, -1, 1
Let c(d) = 6*d**2 - 2*d - 2. Let j be c(2). Let u(b) = 19*b**2 + 45*b - 1. Let q(o) = 5*o**2 + 11*o. Let a(g) = j*q(g) - 4*u(g). Find r such that a(r) = 0.
-1, -2/7
Let z(s) be the third derivative of s**6/30 - s**5/5 - 3*s**4/2 - 10*s**3/3 + 8*s**2. Suppose z(d) = 0. What is d?
-1, 5
Factor -2/3*y**2 - 4/3*y - 2/3.
-2*(y + 1)**2/3
Let d(b) be the second derivative of 2*b**7/21 + 4*b**6/15 - 3*b**5/5 - 8*b**4/3 - 8*b**3/3 + 9*b. Find f, given that d(f) = 0.
-2, -1, 0, 2
Let w = -381/2 - -194. Suppose w*h**2 + 0 + h + 5/2*h**3 = 0. Calculate h.
-1, -2/5, 0
Suppose 4*x - 9*x = -20. Solve 1/3*f + f**3 + 0 - f**2 - 1/3*f**x = 0.
0, 1
Let q(f) be the second derivative of -2/3*f**4 + 3*f + 6*f**2 + 10/3*f**3 + 0. Let q(u) = 0. Calculate u.
-1/2, 3
Let d be -3 - (-115)/10*4/8. Factor -3/2*n - d*n**2 + 5/4*n**4 + 0 + 3*n**3.
n*(n - 1)*(n + 3)*(5*n + 2)/4
Suppose 7*s - 4*s = 0. Suppose 5*a + 16 = -2*x, 3*a - 12 = -4*x + 4*a. Determine p, given that 0 + 1/4*p + s*p**x - 1/4*p**3 = 0.
-1, 0, 1
Suppose 4*f = -f + 10. Suppose f*t**2 + 3 + 9 - t - 4 - 7*t = 0. Calculate t.
2
Let x(z) = 2*z**5 + 13*z**4 + 10*z**3 + 9*z**2 - 5. Let r(w) = 2*w**5 + 14*w**4 + 10*w**3 + 10*w**2 - 6. Let h(m) = -5*r(m) + 6*x(m). Let h(j) = 0. What is j?
-2, -1, 0
Let g(j) be the first derivative of -5/18*j**4 + 0*j**2 + 3 + 0*j - 4/27*j**3 + 2/15*j**5. Find d such that g(d) = 0.
-1/3, 0, 2
Let t be 19/8 - (-9)/72. Let i(j) be the first derivative of -j + t*j**2 - 2 - 4/3*j**3. Factor i(g).
-(g - 1)*(4*g - 1)
Let p = -68 + 71. Let 0*c + 2/3*c**2 + 2/3*c**4 + 0 + 4/3*c**p = 0. What is c?
-1, 0
Let o = -45 - -136/3. Let l(a) be the third derivative of -o*a**3 - 2*a**2 + 0 + 1/5*a**5 + 0*a + 1/12*a**4. Find j such that l(j) = 0.
-1/2, 1/3
Suppose -3*p + 4 = -5. Suppose p*z = 5*h - 15, -3*h + 9 = 5*z - 0*h. Factor 2/7*f**2 + 0*f + z + 2/7*f**3.
2*f**2*(f + 1)/7
Let r = 75 + -45. Suppose -2*q + r = 4*q. Factor 0*t - q*t**4 - 4/3 - 5/3*t**3 + 3*t**5 + 5*t**2.
(t - 1)**3*(3*t + 2)**2/3
Factor -84*u**3 - 50*u + 5*u**4 + 39*u**3 + 15*u + 75*u**2.
5*u*(u - 7)*(u - 1)**2
Factor -g**4 - 1/2*g**5 + g**2 + 0 + 0*g**3 + 1/2*g.
-g*(g - 1)*(g + 1)**3/2
Let s(l) = 2*l**3 + 5*l**2 + 4*l - 5. Let i be s(-4). Let z = i + 346/5. What is d in -1/5*d - 2/5 + z*d**2 = 0?
-1, 2
Let b(o) = o**2 - 5*o - 5. Let v be b(7). Factor -21*s**4 + v*s**3 - 10*s**4 - 6*s + 10*s**4 + 9*s**2 + 9*s**5.
3*s*(s - 1)**3*(3*s + 2)
Let n = -22856/45 + 508. Let b(q) be the third derivative of n*q**5 + 1/9*q**3 + 0 - 7/36*q**4 + 4/45*q**6 + q**2 + 0*q. Let b(v) = 0. What is v?
-1, 1/4
Factor -24 - 34*g - g**2 + 28*g + 4*g**2.
3*(g - 4)*(g + 2)
Find l such that 0*l**5 - 16*l**4 - 7*l**5 - 16 - 50*l**3 - 76*l**2 + 2*l**5 + 3*l**5 - 56*l = 0.
-2, -1
Let f(o) = -5*o**3 - 11*o**2 + 2. Let t(q) = 39*q**3 + 89*q**2 - q - 17. Let i(x) = -51*f(x) - 6*t(x). Factor i(y).
3*y*(y + 1)*(7*y + 2)
Let p be 24/7 + 3/(-7). Let s + 2 - 5*s**p + s**2 - 3*s**2 + 4*s + 0 = 0. What is s?
-1, -2/5, 1
Let i = -8 + 11. Solve u**2 - i + 2*u**2 - 3*u**4 + 3*u**2 = 0 for u.
-1, 1
Let m(j) be the second derivative of j**4/8 - j**3 + 3*j**2 - 11*j. Factor m(x).
3*(x - 2)**2/2
Let i(y) = -y**3 - 1. Let q be i(-1). Suppose f + 5 - 10 = q. Solve 1160/3*k**3 - 650/3*k**4 + 125/3*k**f + 272/3*k - 32/3 - 848/3*k**2 = 0.
2/5, 2
Let x = -138 + 415/3. Solve x - 1/3*u**5 - 1/3*u - 2/3*u**2 + 2/3*u**3 + 1/3*u**4 = 0 for u.
-1, 1
Suppose -2/5*j**4 + 1/5*j - 2/5 + 1/5*j**5 - 2/5*j**3 + 4/5*j**2 = 0. What is j?
-1, 1, 2
What is f in -4/3 + 2*f + 10/3*f**2 = 0?
-1, 2/5
Let -22*o**2 + 70*o + 8*o**3 - 173 + 123 - 6*o**3 = 0. What is o?
1, 5
Find x such that 111*x + 40*x**2 - 34*x**3 + 36*x**3 + 89*x = 0.
-10, 0
Let i be -6*1*(-1)/3. Let l(o) = o. Let s be l(i). Factor -2 + 4 + 2*n**s - 4*n**2.
-2*(n - 1)*(n + 1)
Let p(j) be the third derivative of -j**5/130 - 5*j**4/156 + 2*j**3/39 + 6*j**2. Determine c, given that p(c) = 0.
-2, 1/3
Factor 2/7*p**2 + 0*p + 2/7*p**4 + 0 + 4/7*p**3.
2*p**2*(p + 1)**2/7
Factor 43*k**2 + 36 + 138*k + 7/2*k**3.
(k + 6)**2*(7*k + 2)/2
Let y(n) = -n**3 + 29*n**2 + 33*n - 87. Let v be y(30). Find u, given that 9/2*u**3 + v*u**2 + 3/2*u**4 + 0 + 0*u = 0.
-2, -1, 0
Factor 20*i**2 + 20*i**4 - 132*i**3 - 3*i**5 - 2*i**5 - 5*i + 102*i**3.
-5*i*(i - 1)**4
Let w(l) = 2*l**2 + 18*l + 2. Let n be w(-9). Let c(t) be the second derivative of -n*t + 1/24*t**4 + 0*t**2 + 0 - 1/12*t**3. Factor c(y).
y*(y - 1)/2
Let k = 20 - 17. Let z be 2/k + 2/(-12). Factor n**2 + z + 5/4*n + 1/4*n**3.
(n + 1)**2*(n + 2)/4
Suppose -j = -4*x + 11, -7*x + 2*x = j - 16. Factor 2*h**2 - 5 - 3*h**5 + 6*h**x - h**4 - 3*h + 4*h**2 + 2 - 2*h**4.
-3*(h - 1)**2*(h + 1)**3
Let v = 26 - 18. Let -a + 11 - a**2 - v - 3 = 0. What is a?
-1, 0
Let f(q) = -3*q**4 - 6*q**3 - 6*q**2 - 3*q + 3. Let p(l) = -3*l**4 - 7*l**3 - 6*l**2 - 2*l + 2. Let m(x) = 2*f(x) - 3*p(x). Solve m(z) = 0 for z.
-2, -1, 0
Let l(c) be the first derivative of -6 + 8/3*c**3 + 0*c**2 + 0*c - 3*c**4 + 4/5*c**5. Find f, given that l(f) = 0.
0, 1, 2
Let t(u) be the second derivative of u**5/150 - u**4/30 + u**3/15 - u**2/15 + 3*u. Suppose t(l) = 0. What is l?
1
Let x = 2013/7 - 444859/