= 0.
-3/8
Let g(x) be the first derivative of -6*x**5 - 5*x**4/4 + 30*x**3 + 75*x**2/2 + 10*x - 71. Find o, given that g(o) = 0.
-1, -1/6, 2
Suppose 6 = 2*w - 8*m + 4*m, w - 1 = 4*m. Factor 7*x**2 + w*x**2 - 13*x**2.
-x**2
Factor -39/2*k + 5 - 2*k**2.
-(k + 10)*(4*k - 1)/2
Let w = 17 + -13. Let -85*g**2 - 6*g**w + 4*g**5 - 2*g**4 + 93*g**2 - 4*g = 0. What is g?
-1, 0, 1
Let y(q) = q - 1. Let l(u) = 3*u**2 - 6*u - 3. Suppose 4*z + 2 = 2*z. Let w(o) = z*l(o) - 3*y(o). Solve w(a) = 0 for a.
-1, 2
Suppose -2*g + 4*i = 0, -2*g = 3*g + 5*i + 30. Let s be 3/(-2)*g/21. Factor s*z**2 + 4/7*z + 2/7.
2*(z + 1)**2/7
Suppose 0 = 5*f - 17 - 8. Factor 3*o - f*o**2 + 1 + o**3 + 2*o**2 - 2 + 0*o**2.
(o - 1)**3
Let t(n) be the third derivative of n**7/840 + n**6/240 - n**4/48 - n**3/24 - 10*n**2. Factor t(p).
(p - 1)*(p + 1)**3/4
Suppose 0 = b - 3*q - 5, -4*b - 4 = -5*q - 52. Suppose -2*u = t - b - 6, 0 = 5*u - 3*t - 63. Factor 2*s + 9 + 15 + 2*s**3 + u*s**2 - 8 + 22*s.
2*(s + 2)**3
Suppose 0 = -5*s + o - 10 + 24, -2*s - 12 = 4*o. Suppose 3*u - s*z - 2 = 6, 5*u + 3*z - 7 = 0. What is g in -6*g**2 + 0*g - u*g**4 + 4*g**3 - 2*g - 10*g**3 = 0?
-1, 0
Let k(d) be the first derivative of 5*d**3/3 + 20*d**2 + 80*d - 9. Factor k(i).
5*(i + 4)**2
Let s = 19 - 17. Let a(j) be the second derivative of 2*j - 1/3*j**s - 1/18*j**3 + 0 + 1/12*j**4. Determine m, given that a(m) = 0.
-2/3, 1
Suppose 3*v = 1 + 5. Factor 0*x**v - 6*x**3 + 0*x**2 + 2*x + 4*x**3.
-2*x*(x - 1)*(x + 1)
Suppose 2*t + 3*d = -3, -3*d - 9 = 4*t + 12. Let a be t/(-2) + 27/(-18). Solve -2/11*u**a + 6/11*u - 4/11 + 0*u**2 = 0.
-2, 1
Let b(z) be the second derivative of -z**6/12 + z**5/8 + 5*z**4/12 - 28*z. Suppose b(g) = 0. What is g?
-1, 0, 2
Let g be -5*(28/(-10) - -2) + -4. Let q(c) be the second derivative of g*c**4 + 0 + 0*c**3 + 0*c**2 - 3/20*c**5 + 1/5*c**6 - c. Solve q(o) = 0.
0, 1/2
Let j(r) be the second derivative of r**5/2 + r**4/3 - 5*r**3/3 - 2*r**2 - 7*r. Determine k so that j(k) = 0.
-1, -2/5, 1
Find f, given that 12 + 8*f**2 + 15*f**3 + 12*f - 15*f**2 - 32*f**2 = 0.
-2/5, 1, 2
Let u(k) be the second derivative of 0*k**5 + 0 + 1/18*k**3 - 1/126*k**7 + 0*k**2 - 1/18*k**4 + 1/45*k**6 - 4*k. Determine t, given that u(t) = 0.
-1, 0, 1
Factor 6/7*j + 0 - 2/7*j**3 - 4/7*j**2.
-2*j*(j - 1)*(j + 3)/7
Let h(r) = -r**2 - r. Let v(z) = z**2 - 3*z + 1. Let y be v(6). Let s = y - 13. Let i(x) = -x**3 - 4*x**2 - 7*x. Let w(j) = s*h(j) - i(j). Factor w(u).
u*(u - 1)**2
Let q(t) be the second derivative of -t**6/180 + t**4/24 + t**3/18 - 5*t. Solve q(k) = 0 for k.
-1, 0, 2
Let q(f) = 1. Let z(d) = d**2 - 2*d + 7. Let s(x) = 6*q(x) - z(x). Factor s(r).
-(r - 1)**2
Let b(j) be the third derivative of -j**8/420 + j**6/150 - 11*j**2. Factor b(o).
-4*o**3*(o - 1)*(o + 1)/5
Let m(v) = v**2 - 5*v + 2. Let k be m(5). Let t(f) be the first derivative of 0*f**3 + 0*f**2 - 1/2*f**4 + 0*f + k + 2/5*f**5. Factor t(i).
2*i**3*(i - 1)
Suppose 3*r - 4*t - 13 = 0, 5*r - 1 = -4*t + 10. Factor 4/5*d**4 + 0*d + 2/5*d**2 + 6/5*d**r + 0.
2*d**2*(d + 1)*(2*d + 1)/5
Let n(q) be the second derivative of 0 - 4*q + 0*q**2 + 1/24*q**4 - 1/12*q**3. Factor n(y).
y*(y - 1)/2
Let j = 3/5608 - 3336769/16824. Let o = j - -201. Solve 8/3*a**5 - 2/3*a**2 + 0*a + 0 - 2/3*a**3 + o*a**4 = 0 for a.
-1, -1/2, 0, 1/2
Let x(a) be the first derivative of -a**5/50 - a**4/40 + a**3/6 - 3*a**2/20 + 34. Determine o so that x(o) = 0.
-3, 0, 1
Suppose -19*q + 18*q = -2*i + 2, -17 = -2*q - 3*i. Factor 1/2*l**q + 2*l + 0*l**2 - 3/2*l**3 + 0.
l*(l - 2)**2*(l + 1)/2
Let w(y) be the third derivative of -y**7/245 - y**6/70 + y**4/14 + y**3/7 - 2*y**2 + 9. Factor w(o).
-6*(o - 1)*(o + 1)**3/7
Let a(l) = l**3 + 5*l**2 + l + 5. Let z be a(-5). Let m(o) be the first derivative of 7/2*o**4 - 4/3*o**3 + 0*o**2 + 1 + z*o. Factor m(f).
2*f**2*(7*f - 2)
Let r(w) be the first derivative of w**6/90 - w**5/60 - w**4/18 - 3*w + 2. Let a(n) be the first derivative of r(n). Suppose a(f) = 0. Calculate f.
-1, 0, 2
Let k be 14 + -1 - (1 - 0). Let x be (-1)/((-2 - 1)/k). What is v in -5*v**2 - x + 8*v**2 + 1 = 0?
-1, 1
Factor 1/3*g**4 - 7/3*g**3 + 8/3 + 6*g**2 - 20/3*g.
(g - 2)**3*(g - 1)/3
Let x(m) be the second derivative of -5*m**4/3 + 2*m**3 + 4*m**2 - 6*m. Solve x(c) = 0.
-2/5, 1
Let j = -4 - -12. Suppose 0 = j*h - 3*h. Let 0 + 4/5*m**3 - 2/5*m**5 - 2/5*m + 0*m**4 + h*m**2 = 0. Calculate m.
-1, 0, 1
Factor 1/2*x**5 - 1/2*x - x**2 + x**4 + 0*x**3 + 0.
x*(x - 1)*(x + 1)**3/2
Let w(l) = 2*l**4 - 18*l**3 + 18*l**2 - 2*l + 3. Let z(t) = 3*t**4 - 17*t**3 + 17*t**2 - 3*t + 2. Let a(v) = 2*w(v) - 3*z(v). Suppose a(r) = 0. What is r?
0, 1
Suppose -2*m = 2*y - 0*m - 12, -5*m = 2*y - 24. Let d(n) be the first derivative of 0*n**2 - 1/6*n**3 - y + 0*n. Solve d(x) = 0 for x.
0
Let z be (-6)/8*(15 - -5). Let d(r) = 3*r**2 - 9*r + 15. Let m(h) = -h**2 + 2*h - 4. Let v(p) = z*m(p) - 4*d(p). Factor v(g).
3*g*(g + 2)
Let v = 3/94 + 304/47. Solve 7/4*s**4 + 27/4*s**2 + s + v*s**3 - 1 = 0.
-2, -1, 2/7
Let y = -587 - -589. Let -1/6 - 1/2*o**y - 1/2*o - 1/6*o**3 = 0. What is o?
-1
Let r(u) be the second derivative of u**4/8 - u**3/4 + 13*u. Factor r(v).
3*v*(v - 1)/2
Let q be 0 - -5 - (2 + -1). Suppose 18 = -c - 5*i, -3*c - c - 3*i - q = 0. Factor 2*p - 4/3*p**3 - c*p**4 - 2/3*p**5 + 2/3 + 4/3*p**2.
-2*(p - 1)*(p + 1)**4/3
Let g(r) be the third derivative of -r**6/1080 - r**5/180 + r**3 - 5*r**2. Let h(c) be the first derivative of g(c). Factor h(t).
-t*(t + 2)/3
Let m(z) = -4 + 8 - 3*z + 0*z + z**2. Let c be m(3). Factor 7*g**2 - 22*g + 2 + c + 17*g**2 - 2.
2*(3*g - 2)*(4*g - 1)
Let b(o) be the third derivative of -o**8/20160 + o**6/720 + o**5/30 + 6*o**2. Let x(m) be the third derivative of b(m). Suppose x(w) = 0. Calculate w.
-1, 1
Factor -4*q + 13*q + 3*q**2 - 3 + 7*q**2 + 2*q**2.
3*(q + 1)*(4*q - 1)
Let a = -8034866/11 - -730982. Let u = 540 - a. Suppose 2/11*v**2 + u*v + 2/11 = 0. Calculate v.
-1
Suppose y = 3*y. Let 18*p**5 + 3*p**2 + y*p**3 + 18*p**4 + 0*p**2 - 2*p**3 - 5*p**2 = 0. What is p?
-1, -1/3, 0, 1/3
Let c be 4/20 - 1/5. Factor 2 + c + n**2 + 2*n + 0*n**2 + n.
(n + 1)*(n + 2)
Let u(l) be the first derivative of 3*l**5/5 - l**3 + 8. Suppose u(s) = 0. What is s?
-1, 0, 1
Let l be 1*-4*(-10)/25. Factor 0*u + 2/5*u**3 + 6/5*u**2 - l.
2*(u - 1)*(u + 2)**2/5
Find g, given that 14 - 3*g**3 + 7*g**2 + 4*g**2 - 2 + 7*g**2 - 27*g = 0.
1, 4
Let g(k) = k + 20. Let y be g(-16). Factor 2*r**4 - 7*r - y*r**2 + 6*r + r + 2.
2*(r - 1)**2*(r + 1)**2
Let w(k) = -k**3 + 5*k**2 - 2*k - 4. Let r be w(4). Suppose -r*n + 3*h = -6, 0*h = -2*n - h - 2. Solve 0*d - d**2 - d**3 + n*d = 0 for d.
-1, 0
Let g(z) = -z + 5. Let l be g(4). Let s(y) = 4*y**3 + 2*y**2 - 2*y + 1. Let r be s(l). Factor 2*f**r + 16*f**3 + 0 - 9*f**4 + 2 + 6*f - 3 - 14*f**2.
(f - 1)**4*(2*f - 1)
Solve 2/5*v**3 - 2/5*v + 0 - 2/5*v**4 + 2/5*v**2 = 0 for v.
-1, 0, 1
Solve 0 + 7/2*z + 1/4*z**2 = 0 for z.
-14, 0
Suppose 20*b**2 - 28*b**3 + 9 + 7 - 32*b + 24*b**3 = 0. Calculate b.
1, 2
Let i(a) be the third derivative of a**7/10080 + a**6/2880 - a**4/8 + 3*a**2. Let r(z) be the second derivative of i(z). Factor r(b).
b*(b + 1)/4
Let r(k) = 2*k**2 - 15*k + 7. Let a(g) = g**2 - 8*g + 4. Let m(s) = 5*a(s) - 3*r(s). Let y be m(4). Factor -5*z**3 + 2*z**2 + 5*z**y - 5*z**3.
-z**2*(5*z - 2)
Determine y, given that 0 - 4/3*y**3 - 16/3*y - 16/3*y**2 = 0.
-2, 0
Let y(f) be the first derivative of -f**4/18 + 2*f**3/27 + f**2/9 - 2*f/9 + 12. Determine u so that y(u) = 0.
-1, 1
Let q(r) be the first derivative of 3*r**4/4 + 4*r**3 + 6*r**2 - 2. Determine o, given that q(o) = 0.
-2, 0
Suppose -2*v - 20 = -7*v. Suppose 37 = 3*u - 5*a, 3*u - v = -a + 3. Determine n, given that -u*n**2 - 3*n**5 + 7*n**5 - 6*n + 6*n**4 + 4*n**3 - 2*n**5 - 2 = 0.
-1, 1
Let i(c) be the first derivative of -c**3/3 + 7*c**2/2 - 7*c + 12. Let g be i(5). Determine s, given that 0*s + 0 - s**g - 3/5*s**4 - 2/5*s**2 = 0.
-1, -2/3, 0
Let t(v) = -9*v + 1. Let p be t(0). Factor 1/3*n**2 - p - 2/3*n.
(n - 3)*(n + 1)/3
Let m(j) = 2*j**4 - 3*j**3 - 8*j**2 - 3*j + 3. Let d(y) = -5*y**4 + 10*y**3 + 25*y**2 + 10*y - 10. Let w(o) = -3*d(o) - 10*m(o). Suppose w(k) = 0. What is k?
-1, 0, 1
Suppose -9 = -2*q + 5*f, -3*f + 2 = 5. Factor 51 + 3*n**q - 63 - 2*n + 2*n.
3*(n - 2)*(n + 2)
Let b =