
0, 1
Let h(v) = -v**2 - 16*v + 9. Let y(t) = t**2 - 1. Let j(s) = 5*h(s) + 30*y(s). Suppose j(n) = 0. What is n?
1/5, 3
Let m(k) be the first derivative of -k**5/5 - 5*k**4/2 - 12*k**3 - 27*k**2 - 27*k - 30. Factor m(x).
-(x + 1)*(x + 3)**3
Suppose -5*d - 21 = -l - 3*l, -3 = -d - l. Let g be d/(-6) - 6/(-18). Factor 0 + 1/2*x**3 + 0*x**4 + 0*x**2 - g*x**5 + 0*x.
-x**3*(x - 1)*(x + 1)/2
Let z(g) be the third derivative of -g**6/360 + g**5/90 - g**4/72 + 8*g**2. Determine r so that z(r) = 0.
0, 1
Factor -8*w**3 + 0*w - 10*w**2 + 10*w - 8*w - 4*w.
-2*w*(w + 1)*(4*w + 1)
Let f be 8/2 + 0 + (-14)/4. Factor -r**2 + 1 - 1/2*r + f*r**3.
(r - 2)*(r - 1)*(r + 1)/2
Let j(w) be the third derivative of 0*w + 1/135*w**5 - 1/945*w**7 - 1/54*w**4 - 1/756*w**8 - 1/27*w**3 - w**2 + 0 + 1/135*w**6. Find y such that j(y) = 0.
-1, -1/2, 1
Let t = 9 + -7. Let o(l) = -6*l**3 - 5*l**2 + l + 7. Let q(a) = 2*a**3 + 2*a**2 - 2. Let v(h) = t*o(h) + 7*q(h). Suppose v(c) = 0. What is c?
-1, 0
Let b(a) = -21*a**3 - 15*a - 15. Let g be (18/12)/((-2)/20). Let p(x) = 3*x**3 + 2*x + 2. Let i(t) = g*p(t) - 2*b(t). Solve i(s) = 0 for s.
0
Let 749*n - n**2 + 5*n**2 - 741*n = 0. Calculate n.
-2, 0
Suppose 2*q = 6*q - 8. Let n(v) be the third derivative of 0*v + 2/9*v**3 + 0 + 1/3*v**4 + 5/72*v**6 + 1/4*v**5 + 2*v**q. Factor n(s).
(s + 1)*(5*s + 2)**2/3
Let q(r) be the first derivative of 8 - 1/2*r**3 + 1/8*r**4 + 1/2*r**2 + 0*r. Find p such that q(p) = 0.
0, 1, 2
Suppose -6 = 4*a - 14. Suppose 6*x = a*x + 8. Solve -2/5*c**x - 1/5*c**3 - 1/5*c + 0 = 0 for c.
-1, 0
Let j(w) = 3*w**3 - w + 2. Let f be j(1). Let 3/4*p**5 + 9/4*p**3 + 0 + 0*p - 3/4*p**2 - 9/4*p**f = 0. Calculate p.
0, 1
Let p(o) = 20*o**2 + 14*o - 6. Let j be 44/16 + 1/4. Let i(n) = -4*n**2 - 3*n + 1. Let y(a) = j*p(a) + 16*i(a). Solve y(g) = 0 for g.
-1, -1/2
What is n in -4*n**2 - n**3 + 0*n**3 - 4*n**4 + 0*n**3 + 9*n**3 = 0?
0, 1
Let b(t) = 5*t**5 - 8*t**4 + 2*t**3 + 4*t**2 - 7*t + 4. Let j(i) = i**5 - i**4 - i**3 + i**2. Let o(z) = b(z) - 6*j(z). Suppose o(m) = 0. What is m?
-4, -1, 1
Let d(o) be the first derivative of o**4/24 - o**3/18 - 5*o**2/12 - o/2 + 20. Let d(u) = 0. What is u?
-1, 3
Suppose -4*r - 3 + 15 = 0. Factor c**2 + 3*c**3 + c**4 - 2*c**3 + 0*c**2 - r*c**3.
c**2*(c - 1)**2
Let 4/3*a + 40/3*a**4 + 0 - 10/3*a**2 - 34/3*a**3 = 0. What is a?
-2/5, 0, 1/4, 1
Let a(n) be the second derivative of n**7/3 - 53*n**6/25 + 253*n**5/50 - 173*n**4/30 + 16*n**3/5 - 4*n**2/5 + 7*n - 1. What is r in a(r) = 0?
1/7, 2/5, 1, 2
Suppose -2*m - 4*k = 1 + 5, 4*m = -3*k + 13. Suppose z = -4 + m. Factor 2*g**2 - 1 - 7 + 5*g - 4*g**2 + z*g.
-2*(g - 2)**2
Factor 11*y + 5 - 5 - 3*y**2 - 17*y.
-3*y*(y + 2)
Let z(j) be the third derivative of 0 + 3*j**2 - 1/24*j**4 + 0*j**3 + 1/30*j**5 - 1/120*j**6 + 0*j. Factor z(v).
-v*(v - 1)**2
Let y(u) be the third derivative of -1/3*u**3 + 1/6*u**4 + 0 + 2*u**2 - 1/30*u**5 + 0*u. Suppose y(j) = 0. Calculate j.
1
Let m(o) be the first derivative of -o**5/90 + o**4/36 - 2*o**2 + 4. Let j(t) be the second derivative of m(t). Suppose j(v) = 0. What is v?
0, 1
Let b(d) = -9*d**3 - 12*d**2 + 3*d - 6. Let f = -17 - -29. Let o(w) = -w**3 - w. Let m(r) = f*o(r) - b(r). Factor m(k).
-3*(k - 2)*(k - 1)**2
Let h(p) = p**3 + 3*p**2. Let t be h(-3). Suppose -1/2*w**2 - w**3 + t + 0*w - 1/2*w**4 = 0. What is w?
-1, 0
Suppose 3*f + 1 = 4*p + 10, 0 = 5*p. Solve 0*n**2 - 2/5 + 2/5*n**4 + 4/5*n - 4/5*n**f = 0.
-1, 1
Let w(s) = s**2 - 12*s. Let u be w(12). Let t(r) be the first derivative of 1/7*r**2 - 1 + 4/21*r**3 + u*r + 1/14*r**4. Factor t(b).
2*b*(b + 1)**2/7
Let s(x) be the third derivative of -x**8/10080 - x**7/3780 + x**4/24 + 3*x**2. Let k(m) be the second derivative of s(m). Let k(v) = 0. Calculate v.
-1, 0
Let t(f) be the third derivative of 0*f + 0*f**3 + 1/50*f**5 + 1/525*f**7 - 1/100*f**6 + 0 - 4*f**2 - 1/60*f**4. Solve t(a) = 0 for a.
0, 1
Let n(k) be the third derivative of 7*k**8/12 - 151*k**6/30 - 98*k**5/15 + 2*k**4 + 16*k**3/3 + 5*k**2. Suppose n(t) = 0. What is t?
-1, -2/7, 2/7, 2
Let g(l) be the third derivative of -l**8/1680 - l**7/525 - l**6/600 + 3*l**2. Suppose g(d) = 0. What is d?
-1, 0
Let y(w) = -5*w**2 + 40*w + 3. Let u be y(8). Let 10/11*s - 14/11*s**2 + 6/11*s**u - 2/11 = 0. What is s?
1/3, 1
Let g(y) = 9*y**4 - 6*y - 3. Let x(o) = o**4 - o**3. Let w be (-15)/6*(-12)/5. Let j(a) = w*x(a) - g(a). Factor j(d).
-3*(d - 1)*(d + 1)**3
Let x be (-1612)/(-336) - 5 - (-2)/7. Let j(n) be the third derivative of 1/210*n**7 + 0*n + 0 + 1/18*n**3 + n**2 + 1/36*n**6 + x*n**4 + 1/15*n**5. Factor j(b).
(b + 1)**3*(3*b + 1)/3
Let o(h) = h**4 + h**3 + h. Let i be 20/6*(-54)/(-30). Let c(l) = l**4 + 3*l**3 + 2*l. Let s(y) = i*o(y) - 3*c(y). Solve s(j) = 0 for j.
0, 1
Factor 26/3*r - 4 + 2/3*r**3 - 16/3*r**2.
2*(r - 6)*(r - 1)**2/3
Let u(o) be the second derivative of 1/4*o**2 - o + 0 + 5/48*o**4 - 7/24*o**3. Factor u(p).
(p - 1)*(5*p - 2)/4
Let z be (3 + -1)*2/(10 + -2). Solve 0*t + z*t**2 - 1/4*t**4 + 0 - 1/4*t**3 = 0 for t.
-2, 0, 1
Solve 0 + 2/3*p - 1/3*p**2 = 0.
0, 2
Let n(c) be the first derivative of -9/8*c**4 + 0*c + 3 - 1/2*c**3 + 3/2*c**2. Factor n(h).
-3*h*(h + 1)*(3*h - 2)/2
Factor 17*a**2 + 5 + a**3 + 2 + 2 + 15*a - 10*a**2.
(a + 1)*(a + 3)**2
Let n(w) be the third derivative of 0*w**3 + 0*w**4 + 0 - 1/60*w**5 + 0*w - 1/80*w**6 - 1/420*w**7 - 4*w**2. Suppose n(v) = 0. What is v?
-2, -1, 0
Let r(c) be the second derivative of -c**6/840 + c**5/280 + 2*c**3/3 - 2*c. Let p(q) be the second derivative of r(q). Factor p(m).
-3*m*(m - 1)/7
Let p(d) be the first derivative of 2*d**2 - 1 - 1/3*d**3 - 4*d. Solve p(t) = 0.
2
Let f(b) be the first derivative of b**7/336 - 7*b**6/720 + b**5/120 + 5*b**3/3 - 1. Let h(c) be the third derivative of f(c). Factor h(j).
j*(j - 1)*(5*j - 2)/2
Let t(d) = -d**5 + 2*d**3 - d + 1. Let y(j) = -j**4 - j**3 + j**2 + j - 1. Let z(l) = -t(l) - y(l). What is v in z(v) = 0?
-1, 0, 1
Let i(h) = 2*h**2 - 2*h. Let j(d) = 2*d**2 - 11*d + 2*d**2 + 7*d**2. Suppose 0 = 4*f + 4*s - 144, f + s = -4*s + 44. Let k(a) = f*i(a) - 6*j(a). Factor k(r).
2*r*(r - 1)
Let v = 68 + -65. Factor v*d + 5/4*d**2 + 1.
(d + 2)*(5*d + 2)/4
Let v = 62/3 + -20. Factor 2/3 + 4*m**2 - 8/3*m + v*m**4 - 8/3*m**3.
2*(m - 1)**4/3
Let d = 29521/564 + -13/141. Let u = d - 52. Solve -1/2*g + u*g**4 + 1/2*g**3 + 0*g**2 - 1/4 = 0 for g.
-1, 1
Let g = 14 + -11. Factor 2*b**2 - 2*b**4 - g*b**4 + b**4 + 2*b**2.
-4*b**2*(b - 1)*(b + 1)
Let q(r) be the third derivative of -2*r**7/105 - r**6/15 + r**5/5 + 2*r**4/3 - 8*r**3/3 - 2*r**2 - 3*r. Factor q(x).
-4*(x - 1)**2*(x + 2)**2
Let g(b) = -b**3 - 7*b**2 + 2*b + 6. Let h be g(-6). Let m be (-1 + 5)*(-7)/h. Factor -4/3*w + m + 2/3*w**2.
2*(w - 1)**2/3
Let k = 56 - 29. Let t be -1*(k/(-12))/3. Solve 0*p + 3/4*p**3 + 0 - t*p**2 = 0 for p.
0, 1
Suppose 15 = 5*q, -7*q + 11*q + 8 = 4*r. Solve 0*i**4 + 2/5*i + 0*i**2 + 2/5*i**r + 0 - 4/5*i**3 = 0 for i.
-1, 0, 1
Let k(f) = -125*f**3 - 855*f**2 - 335*f. Let d(m) = 9*m**3 + 61*m**2 + 24*m. Let a(c) = -85*d(c) - 6*k(c). Factor a(n).
-5*n*(n + 3)*(3*n + 2)
Let t = -10 + 17. Let c(u) = t*u**2 + 4*u**3 + 3*u**3 - 2*u**3 - u - 3. Let l(k) = -11*k**3 - 15*k**2 + 3*k + 7. Let o(w) = 9*c(w) + 4*l(w). Factor o(r).
(r + 1)**3
Let o(j) be the third derivative of 19/90*j**6 - 2*j**2 - 1/3*j**5 + 0*j + 0 + 1/18*j**4 + 4/9*j**3 - 2/45*j**7. Factor o(w).
-4*(w - 1)**3*(7*w + 2)/3
Let f(j) be the third derivative of -j**8/672 + j**7/420 + j**6/120 - j**5/60 - j**4/48 + j**3/12 - 7*j**2. Factor f(z).
-(z - 1)**3*(z + 1)**2/2
Let x(f) = -3*f - 7. Let h be x(-3). Let w be 1*6 + -1 + -2. Suppose h*b**2 + 2*b**4 - 2*b**w - b + 3*b - 4*b**2 = 0. What is b?
-1, 0, 1
Let f(t) = -125*t**2 + 1765*t - 11885. Let n(z) = -9*z**2 + 126*z - 849. Let o(a) = 4*f(a) - 55*n(a). Factor o(g).
-5*(g - 13)**2
Let y(c) be the first derivative of -5*c**4 + 5*c**3/3 + 40*c**2 - 20*c + 57. Factor y(i).
-5*(i - 2)*(i + 2)*(4*i - 1)
Let h(y) be the third derivative of -1/30*y**5 + 0 - 1/18*y**4 + 0*y - 1/18*y**3 - 1/90*y**6 - 1/630*y**7 - 8*y**2. Factor h(r).
-(r + 1)**4/3
Let d(n) be the first derivative of 5*n**3/3 - 35*n**2/2 + 30*n + 17. Suppose d(r) = 0. What is r?
1, 6
Solve -2/7*a**3 + 0 + 4/7*a**2 - 2/7*a = 0 for a.
0, 1
Let f(j) = -j**3 + 3*j**2 + 4.