1)
Let q(j) be the first derivative of -j**3/9 + 11*j**2/6 - 10*j/3 - 27. Let q(t) = 0. What is t?
1, 10
Suppose -4*y + 15 - 7 = 0. Let o(c) be the first derivative of 1/6*c**2 + 2/9*c**3 - y + 1/12*c**4 + 0*c. Factor o(a).
a*(a + 1)**2/3
Let c be -2 + 12*(-8)/(-6). Let z be (c/(-21))/((-2)/12). Find s such that 1/3*s**2 + 0*s - 1/3*s**z + 0*s**3 + 0 = 0.
-1, 0, 1
Let g be 2 + -1 - 1/(-5). Suppose -12/5*c**2 - g + 3/5*c**3 + 3*c = 0. Calculate c.
1, 2
Let o = 6 - 11. Let b(p) = -2*p**3 - 6*p**2 + 3*p. Let r(x) = x**3. Let d(y) = o*r(y) - b(y). Factor d(c).
-3*c*(c - 1)**2
Let g(q) = -2*q**4 + 7*q**3 + 13*q**2 - 9*q. Let v(j) = -j**4 + 3*j**3 + 6*j**2 - 4*j. Suppose 13 = -2*p + 31. Let m(f) = p*v(f) - 4*g(f). Factor m(c).
-c**2*(c - 1)*(c + 2)
Let a(p) be the first derivative of p**6/72 - p**5/90 - 3*p**2/2 + 2. Let k(o) be the second derivative of a(o). Factor k(x).
x**2*(5*x - 2)/3
Let t(o) = -o**3 + 6*o**2 + 6*o. Let w(k) = -2*k**3 + 11*k**2 + 11*k. Suppose -y - 30 + 10 = 4*c, -3*c - 26 = -2*y. Let s(f) = c*w(f) + 11*t(f). Solve s(b) = 0.
0
Let j(b) = -5*b**2 - 10*b + 15. Let w(v) = v**3 + 6*v**2 + 9*v - 16. Let y(x) = 6*j(x) + 5*w(x). Factor y(r).
5*(r - 1)**2*(r + 2)
Suppose a = -4*a + 15. Suppose 0 = -a*q - 5*s, -q = -0*q - 2*s. What is v in q*v**3 + 2*v**3 + v + v - 4*v**2 = 0?
0, 1
Let t be 2 - 5/3 - (-3)/9. Let 0*v**2 + 0 - t*v**3 + 2/3*v = 0. What is v?
-1, 0, 1
Factor 0 - 5/6*u**4 - 17/6*u**3 - 2/3*u - 8/3*u**2.
-u*(u + 1)*(u + 2)*(5*u + 2)/6
Let l(m) be the third derivative of 0*m**3 - 9*m**2 - 1/48*m**4 + 0 - 1/240*m**6 + 1/60*m**5 + 0*m. Let l(g) = 0. Calculate g.
0, 1
Let t be (-416)/(-156)*(-1 - (-46)/40). Suppose 2/5*g**2 - t*g**5 + 0*g + 0 - 2/5*g**4 + 2/5*g**3 = 0. Calculate g.
-1, 0, 1
Solve 0*a**4 - 8/7*a**3 + 4/7*a**5 + 0 + 4/7*a + 0*a**2 = 0 for a.
-1, 0, 1
Let j(g) be the third derivative of 0*g**4 + 0*g**6 - 4/735*g**7 - 1/588*g**8 + 0*g**3 + 10*g**2 + 0*g + 0 + 0*g**5. Let j(w) = 0. What is w?
-2, 0
Let y(t) be the second derivative of 2*t**7/21 - 3*t**5/5 + 2*t**4/3 - 14*t. Find g, given that y(g) = 0.
-2, 0, 1
Suppose -2/13*k + 2/13*k**3 + 4/13 - 4/13*k**2 = 0. Calculate k.
-1, 1, 2
Let x(c) be the second derivative of -c**7/21 - c**6/3 - 3*c**5/5 + c**4/3 + 7*c**3/3 + 3*c**2 - 56*c. Factor x(d).
-2*(d - 1)*(d + 1)**3*(d + 3)
Suppose g - 2*m + 1 = 0, 2*m - 6 = -3*g + 7. Suppose -3*j + t = 6*t - 35, 5*j - 13 = g*t. Factor a**j - 5*a**4 + 2*a**4 + 2*a**4.
a**4*(a - 1)
Let f = 2 - 0. Let v be ((-8)/(-10))/(f/5). Factor -3*a + 5*a**v - 3 + 1 + a**2 - 1.
3*(a - 1)*(2*a + 1)
Let y(j) be the third derivative of 1/210*j**5 + 0 + 0*j**4 + 0*j**3 - 2*j**2 + 0*j. Factor y(o).
2*o**2/7
Let y = 23 + -19. Let f(q) be the second derivative of 0 + 1/5*q**5 + 0*q**y - 2/3*q**3 + 1/15*q**6 - q**2 + q. Determine k so that f(k) = 0.
-1, 1
Let f(t) be the first derivative of 0*t + 1/21*t**6 - 1/7*t**4 + 0*t**3 + 0*t**5 + 3 + 1/7*t**2. Find x such that f(x) = 0.
-1, 0, 1
Suppose 0 = -33*t + 35*t. Factor 0 + 1/6*k**2 - 1/3*k**3 + t*k + 1/6*k**4.
k**2*(k - 1)**2/6
Factor -2*p**3 - 13/3*p**2 - 1/3*p**4 - 4/3 - 4*p.
-(p + 1)**2*(p + 2)**2/3
Let o be (-1 + 0)/((-3)/9). Factor -2*y**2 + 3*y**4 - 3*y**3 + 0*y**o - y**2 + 3*y.
3*y*(y - 1)**2*(y + 1)
Let r(g) be the third derivative of g**9/181440 + g**8/30240 + g**7/15120 + g**5/20 + 2*g**2. Let k(p) be the third derivative of r(p). Factor k(b).
b*(b + 1)**2/3
Let f(u) be the first derivative of 2*u**5/5 + u**4/2 - 2*u**3 - u**2 + 4*u - 5. Suppose f(a) = 0. Calculate a.
-2, -1, 1
Determine h, given that -132*h + 12 + 21*h**3 - 22 + 46 + 15*h**2 = 0.
-3, 2/7, 2
Let n = 132 - 129. Determine f so that 3/2*f**2 + 0*f + 0*f**n + 0 - 3/2*f**4 = 0.
-1, 0, 1
Let g = -7 + 5. Let z(k) = -3*k - 1. Let y be z(g). Factor f**2 + 1 - 3*f**2 + f + f**y + 3*f**4 - f**3 - f**3 - 2*f**4.
(f - 1)**2*(f + 1)**3
Let v(k) = 3*k**2 - 21*k - 18. Let s(z) = -z**2. Let y(h) = -6*s(h) + v(h). Factor y(d).
3*(d - 3)*(3*d + 2)
Let q(n) = -n**3 - 5*n**2 - 4*n + 3. Let m be q(-4). Suppose -g**2 + 3*g**2 + 4*g - g**2 - m*g = 0. Calculate g.
-1, 0
Let f(y) = 9*y**3 - 54*y**2 - 80*y - 17. Let x(j) = 3*j**3 - 18*j**2 - 27*j - 6. Let u(r) = 6*f(r) - 17*x(r). Factor u(k).
3*k*(k - 7)*(k + 1)
What is v in -41*v**3 + 3*v**5 - 19*v**4 - 18*v**5 + 3*v**2 - 34*v**3 + 88*v**4 + 18*v = 0?
-2/5, 0, 1, 3
Let q = -1 - -8. Let i(b) = b**2 - 7*b + 2. Let s be i(q). Solve -4*u + 11*u**2 + 6*u**5 - s*u**3 - 2*u**2 - 10*u**4 + u**2 = 0.
-1, 0, 2/3, 1
Let g = 658 + -5920/9. Suppose -4/9*j - g*j**2 - 2/9 = 0. What is j?
-1
Let b(j) be the second derivative of 0 - 2/9*j**3 + 2/3*j**2 - 3*j + 1/36*j**4. Factor b(h).
(h - 2)**2/3
Solve 0 + 1/2*g**2 + 0*g - 1/4*g**3 = 0 for g.
0, 2
Let i(b) be the second derivative of 0 - 3*b - 1/12*b**4 + b**2 + 1/6*b**3. Solve i(d) = 0 for d.
-1, 2
Let w(c) = 11*c**5 + 29*c**4 + 33*c**3 + 14*c**2 + 2*c. Let d(o) = -32*o**5 - 86*o**4 - 98*o**3 - 42*o**2 - 6*o. Let t(f) = -3*d(f) - 8*w(f). Solve t(l) = 0.
-1, -1/4, 0
Let v(u) = 21*u**3 - 13*u**2 - 12*u + 1. Let o(m) = 127*m**3 - 77*m**2 - 72*m + 5. Let c(f) = -6*o(f) + 34*v(f). Factor c(g).
-4*(g - 1)*(3*g + 1)*(4*g + 1)
Let o(b) = b**2 + b. Let j be o(-1). Let y be (2/8)/((21/(-30))/(-7)). What is d in 3/2*d**3 + d**2 - y*d**4 + 0 + j*d = 0?
-2/5, 0, 1
Factor t**2 + 4 + t**2 - t**3 + 0*t**3 - 5*t**2.
-(t - 1)*(t + 2)**2
Let q(u) be the third derivative of 1/84*u**4 - 1/1260*u**6 + 0*u**5 - 2*u**2 - 1/2*u**3 + 0*u + 0. Let m(h) be the first derivative of q(h). Solve m(t) = 0.
-1, 1
Let q(m) be the third derivative of m**8/26880 - m**7/10080 + m**4/12 + 4*m**2. Let w(j) be the second derivative of q(j). Find i, given that w(i) = 0.
0, 1
Let z be (-866)/5*40/(-28). Let r = 248 - z. Let 0*v**4 + r*v**3 - 2/7*v**5 - 2/7*v + 0*v**2 + 0 = 0. Calculate v.
-1, 0, 1
Factor 2/3*p**2 - 2/3*p**4 + 0 - 2/3*p**3 + 2/3*p**5 + 0*p.
2*p**2*(p - 1)**2*(p + 1)/3
Let w = 29 - 27. Factor 1/3 + 2/3*g + 0*g**w - 2/3*g**3 - 1/3*g**4.
-(g - 1)*(g + 1)**3/3
Suppose -32/9*l + 98/9*l**5 - 238/9*l**4 + 134/9*l**3 - 8/9 + 46/9*l**2 = 0. What is l?
-2/7, 1
Factor 5*w**2 + 47 - 8*w**2 - 49 - 9*w**2 + 14*w.
-2*(w - 1)*(6*w - 1)
Let t(l) be the first derivative of -1/3*l**2 + 1/3*l - 1 + 1/9*l**3. Solve t(r) = 0.
1
Let g(y) be the second derivative of y**5/15 - y**4/6 - 4*y**3/3 - y**2/2 - 6*y. Let s(x) be the first derivative of g(x). Factor s(z).
4*(z - 2)*(z + 1)
Let o(l) be the third derivative of -l**7/1680 + l**6/720 + l**5/240 - l**4/48 + l**3/6 + l**2. Let r(n) be the first derivative of o(n). Factor r(v).
-(v - 1)**2*(v + 1)/2
Let g(v) be the first derivative of 0*v**3 + 1/24*v**4 - v**2 + 1/60*v**5 + 0*v - 2. Let o(b) be the second derivative of g(b). Determine d so that o(d) = 0.
-1, 0
Let u(x) be the second derivative of x**7/105 - x**6/20 + x**5/15 + 3*x**2/2 + 4*x. Let d(n) be the first derivative of u(n). Factor d(c).
2*c**2*(c - 2)*(c - 1)
Let z(h) be the first derivative of -h**7/168 + h**6/20 - 13*h**5/80 + h**4/4 - h**3/6 + 3*h - 1. Let x(o) be the first derivative of z(o). Factor x(t).
-t*(t - 2)**2*(t - 1)**2/4
Suppose 0 = -h + 3*l + 7, -4*l - 24 = -5*h - 0*l. Let w = -7 + 12. What is k in k**5 - h*k**3 - 3*k + 5*k + k**w = 0?
-1, 0, 1
Suppose -2*s + 1 = -3*s. Let b(m) = -3*m - 1. Let q be b(s). Solve -4/3 + 2/3*y + 2/3*y**q = 0.
-2, 1
Let v(x) be the third derivative of x**7/840 + x**6/90 + x**5/24 + x**4/12 + x**3/3 - 3*x**2. Let u(r) be the first derivative of v(r). Factor u(d).
(d + 1)**2*(d + 2)
Let v(z) be the third derivative of 0*z + 0 + 0*z**3 - 1/735*z**7 - 3*z**2 - 1/1176*z**8 + 1/210*z**5 + 1/420*z**6 + 0*z**4. Factor v(k).
-2*k**2*(k - 1)*(k + 1)**2/7
Let d = 4 - -6. Let -6*t**4 - 6*t**5 - d*t**2 + 12*t**3 + 2 + 6*t**2 + 8*t**4 - 6*t = 0. What is t?
-1, 1/3, 1
Let y be (-24)/(-14)*(344/(-40) - -10). Find k such that 0 + 8/5*k**2 + 4/5*k - y*k**3 = 0.
-1/3, 0, 1
Solve a**3 - 277*a + 272*a - 10*a**2 + 4*a**3 + 10*a**4 = 0 for a.
-1, -1/2, 0, 1
Let b(c) be the second derivative of c**4/14 - 2*c**3/21 - c**2/7 + 27*c. Factor b(h).
2*(h - 1)*(3*h + 1)/7
Solve 1/2*m**5 + 5/2*m + 5*m**3 - 5*m**2 - 5/2*m**4 - 1/2 = 0.
1
Let a(g) be the third derivative of -g**9/30240 + g**8/3360 - g**7/1260 - 3*g**4/8 - 2*g**2. Let r(n) be the second derivative of a(n). Factor r(j).
-j**2*(