)/5
Let b(p) be the third derivative of p**2 + 0*p**4 + 0*p**3 - 1/105*p**7 + 1/60*p**6 + 0*p + 0 + 0*p**5. Let b(g) = 0. What is g?
0, 1
Let p(x) be the first derivative of 7/18*x**4 - 4/3*x**2 + 8/9*x + 5 - 2/3*x**3. Factor p(k).
2*(k - 2)*(k + 1)*(7*k - 2)/9
Solve -3/2*h**3 - 1/2*h**2 - 1/2*h**4 + 1 + 3/2*h = 0 for h.
-2, -1, 1
Find j, given that 0*j**4 + 0*j + 0 + 2/11*j**5 - 6/11*j**3 - 4/11*j**2 = 0.
-1, 0, 2
Let c = 27 - 7. Determine d so that -12*d**2 + d**4 - 4 - 3*d**3 + 15*d**4 - 17*d**3 + c*d = 0.
-1, 1/4, 1
Suppose 0 = -11*d + 3*d. Solve -u - 5/2*u**3 - 7/2*u**2 + d = 0.
-1, -2/5, 0
Let b be (-4)/(-5)*(-15)/(-6). What is x in 8*x**3 - 8*x - 4*x**2 + 10*x**4 + 0*x**2 + 0 - b - 4*x**4 = 0?
-1, -1/3, 1
Let f be (-2)/(-6) - 69/(-9). What is b in -2*b**2 - 14*b**5 - 2*b**2 + 16*b**4 - 6*b**3 + f*b**4 = 0?
-2/7, 0, 1
Let q(k) = 3*k**3 + 60*k**2 - 39*k - 42. Let s(z) = z**3 + 17*z**2 - 11*z - 12. Let r(y) = -5*q(y) + 18*s(y). Factor r(d).
3*(d - 1)*(d + 1)*(d + 2)
Suppose 4/3*s**3 - 2/3*s - 2*s**4 - 2/3*s**5 - 2 + 4*s**2 = 0. What is s?
-3, -1, 1
Let h(v) = -5*v**2 + 32*v - 27. Let f(o) = -2*o**2 + 15*o - 13. Let t(k) = -14*f(k) + 6*h(k). Factor t(p).
-2*(p - 1)*(p + 10)
Let x(c) be the third derivative of c**9/90720 - c**8/10080 + c**7/2520 - c**6/1080 - 7*c**5/60 + 4*c**2. Let k(s) be the third derivative of x(s). Factor k(u).
2*(u - 1)**3/3
Find s such that -2*s**3 + 14/3*s**2 - 4/3 + 2*s - 10/3*s**4 = 0.
-1, 2/5, 1
Let z = 11 + -2. Let y be 6/18 + 1/z. What is x in -y*x**2 - 2/9 - 2/3*x = 0?
-1, -1/2
Let u(i) be the first derivative of 1/8*i**4 + 1/12*i**6 + 0*i**2 + 0*i - 1/5*i**5 + 0*i**3 - 1. Solve u(s) = 0.
0, 1
Let d(x) = -x**4 - x**2 - 1. Let n(h) = 2*h**3 - h**2 - 2*h - 2. Suppose -5*r = -b - 7, 16 = -5*b + 6. Let o(s) = r*d(s) - n(s). Suppose o(f) = 0. Calculate f.
-1, 1
Let p(d) be the first derivative of 2*d**5/45 + d**4/9 + 2*d**3/27 - 8. Factor p(z).
2*z**2*(z + 1)**2/9
Let s = -4 + 5. Let o = s + 1. Let -4*d**o + 2 - 2*d**2 + 3*d + 4 - 3*d**3 = 0. Calculate d.
-2, -1, 1
Suppose 0 = 2*p - 4. Let t(u) be the second derivative of -1/6*u**3 + 1/15*u**6 + 0 + 1/20*u**5 + 0*u**2 - 1/6*u**4 - p*u. Determine d so that t(d) = 0.
-1, -1/2, 0, 1
Let v(s) be the second derivative of s**7/1680 + s**6/240 - s**4/12 + s**3/2 + 2*s. Let n(y) be the second derivative of v(y). Find w such that n(w) = 0.
-2, 1
Let u(f) be the second derivative of -3*f + 0 + 1/12*f**5 + 1/90*f**6 - 4/9*f**3 - 1/36*f**4 - 1/126*f**7 - 2/3*f**2. Suppose u(h) = 0. What is h?
-1, 2
Suppose -3*v + 15 = -0*v. Find k, given that -3*k**2 + k + 2*k**3 + 3*k**v - 6*k**3 + k**2 + 2*k**4 = 0.
-1, 0, 1/3, 1
Let q be 32/60 + (-1)/5. Let k(p) be the second derivative of 0 + 1/10*p**5 + 0*p**4 + 0*p**2 + 2*p - q*p**3. Suppose k(o) = 0. What is o?
-1, 0, 1
Let i(f) be the first derivative of 2*f**3/15 - 2*f**2/5 + 38. Factor i(p).
2*p*(p - 2)/5
Let a(q) = -q**4 + q**3 + q - 1. Let l(s) = -5*s**4 + 2*s**3 + 6*s**2 + 2*s - 5. Let u(m) = -30*a(m) + 5*l(m). Factor u(n).
5*(n - 1)**4
Let x(s) = s**4 - s**3 - 1. Let u(d) = -8*d**4 - 6*d**2 - 2*d + 6. Let q(o) = -o + 7. Let v be q(6). Let t(l) = v*u(l) + 6*x(l). Suppose t(i) = 0. What is i?
-1, 0
Let x(y) = -3*y - 6. Let g be x(-4). Suppose o + g*q - 2*q = 3, 4*q - 12 = -4*o. Let 0*u**3 + u**4 - 3*u**o + 0*u**2 + 3*u**2 - u = 0. What is u?
0, 1
Let j(u) be the second derivative of u**7/350 + u**6/100 - u**5/100 - u**4/20 - u**2/2 + 5*u. Let k(a) be the first derivative of j(a). Let k(s) = 0. What is s?
-2, -1, 0, 1
Let j(i) be the third derivative of 8*i**7/105 + i**6/6 + i**5/15 - 12*i**2. What is b in j(b) = 0?
-1, -1/4, 0
Let p be 17 + (-32)/4 - 9. Solve 1/2*b**2 + p + 0*b + 0*b**3 - 1/2*b**4 = 0 for b.
-1, 0, 1
Factor 1/7 - 2/7*j**2 + 1/7*j.
-(j - 1)*(2*j + 1)/7
Let n(j) be the third derivative of j**5/270 + j**4/108 - 8*j**2. Suppose n(u) = 0. Calculate u.
-1, 0
Let m(v) be the second derivative of v**7/63 + v**6/15 - v**5/30 - 7*v**4/18 + 4*v**2/3 + 8*v. Determine p so that m(p) = 0.
-2, -1, 1
Factor -4/5*y**5 + 0*y**2 + 0*y**3 - 8/5*y**4 + 0 + 0*y.
-4*y**4*(y + 2)/5
Let l(y) be the first derivative of y**7/4200 - y**6/450 + y**5/120 - y**4/60 + y**3 - 2. Let n(g) be the third derivative of l(g). Factor n(m).
(m - 2)*(m - 1)**2/5
Suppose 29 = 4*m + 9. Suppose -r = -4*u + 37, -2*u = -u + m*r - 4. Suppose -2*f**3 - 3*f + 3*f**3 + 6*f**2 + 2 + u*f + f**3 = 0. What is f?
-1
Suppose 3*j = -0*j - 15. Let h be j*(18/15 + -2). What is u in -h*u**2 + 2*u**2 + u**2 + 1 = 0?
-1, 1
Let j(l) = -13*l**3 + 17*l**2 + 5*l + 9. Let k(h) = 0*h**2 + 4*h - 4*h**2 + 2*h**3 - 5*h + h**3 - 2. Let w(z) = -2*j(z) - 9*k(z). Factor w(s).
-s*(s - 1)**2
Let o(g) be the first derivative of -5*g**5/3 + 65*g**4/12 - 5*g**3 - 5*g**2/6 + 10*g/3 - 13. Factor o(a).
-5*(a - 1)**3*(5*a + 2)/3
Suppose -9 = 2*j - 7*j - z, 0 = 5*j + 5*z - 5. Suppose -3*k + 12 = -2*p + 4*p, -11 = -5*p + j*k. Find b, given that -2/7*b**4 + 0*b + 2/7*b**p + 0*b**2 + 0 = 0.
0, 1
Let w be 6/(5*2/5). Factor -8*z**2 + 8 + 2*z + 8*z - 6*z - 4*z**w.
-4*(z - 1)*(z + 1)*(z + 2)
Let t(n) = n**2 + 4*n + 2. Let l(b) be the first derivative of 8*b**3/3 + 16*b**2 + 15*b + 1. Let k(r) = 6*l(r) - 51*t(r). Determine y, given that k(y) = 0.
-2
Determine p so that 128/7 - 128/7*p - 4/7*p**4 - 24/7*p**2 + 4*p**3 = 0.
-2, 1, 4
Solve -1/4 - 1/2*n**4 - 9/4*n**2 + 7/4*n**3 + 5/4*n = 0.
1/2, 1
Let s(q) = -17*q**2 - 12*q - 17. Let l(y) = -6*y**2 - 4*y - 6. Let t(g) = 11*l(g) - 4*s(g). Determine u so that t(u) = 0.
-1
Let b = 1 - -1. Let t(p) = 3*p - 1. Let m be t(1). What is i in 2 + 2 - b*i**m + 0 + 2*i = 0?
-1, 2
Factor -10*d - 2*d**3 + 9*d - 4 + 7*d.
-2*(d - 1)**2*(d + 2)
Factor 1/4*u**2 - u + 3/4.
(u - 3)*(u - 1)/4
Let m(r) be the third derivative of r**7/525 + r**6/300 + 7*r**2. Let m(z) = 0. What is z?
-1, 0
Let g(n) be the first derivative of -2*n**5/15 - n**4/2 - 4*n**3/9 - 17. Factor g(i).
-2*i**2*(i + 1)*(i + 2)/3
Let s(l) = -l**3 - 25*l**2 + l + 27. Let c be s(-25). Suppose -2/3*j - 1/3*j**c + 0 = 0. What is j?
-2, 0
Let f(p) = p**3 - p + 1. Let n(u) = 3*u**3 + 17*u**2 + 15*u + 20. Let j(b) = -2*f(b) + n(b). Let l be j(-16). Factor 3/2*i**l - 1 - 1/2*i.
(i - 1)*(3*i + 2)/2
Suppose 0*b = -5*b. Let r(p) be the second derivative of -1/3*p**3 - 1/21*p**7 + 0 + 3*p + b*p**4 + 0*p**2 + 1/5*p**5 + 0*p**6. Let r(c) = 0. What is c?
-1, 0, 1
Let p be (-2)/11 + (-186)/(-297). Let r be 2*2/6*3. What is o in -p*o - 2/9 - 2/9*o**r = 0?
-1
Let f be (161/(-28))/(-1 - -4) + 2. Let y(j) be the first derivative of 0*j**3 - f*j**4 - 2/3*j + 1/2*j**2 - 2. Find b, given that y(b) = 0.
-2, 1
Factor x**2 + 1/2 + 5/4*x + 1/4*x**3.
(x + 1)**2*(x + 2)/4
Let t(u) = -5*u**2 + 58*u - 178. Let h(i) = -35*i**2 + 405*i - 1245. Let p(o) = 2*h(o) - 15*t(o). Let p(w) = 0. Calculate w.
6
Let k(a) be the third derivative of 0*a + 0*a**6 + 0*a**3 + 4*a**2 + 1/120*a**5 + 0 + 0*a**4 - 1/420*a**7. Suppose k(z) = 0. Calculate z.
-1, 0, 1
Let v(u) = -3*u**3 - 3*u**2 - 3*u - 8. Let j(d) = 2*d**3 + 2*d**2 + d + 4. Let i(q) = 5*j(q) + 3*v(q). Suppose i(l) = 0. What is l?
-2, -1, 2
Factor 0 + 1/3*y**2 - 1/3*y**4 + 1/6*y + 0*y**3 - 1/6*y**5.
-y*(y - 1)*(y + 1)**3/6
Let b be (1 - 0) + 6 + (-136)/20. Factor -1/5*q**3 + b - 1/5*q**2 + 1/5*q.
-(q - 1)*(q + 1)**2/5
Let b(x) be the second derivative of 0 - 1/15*x**6 + x + 0*x**5 + 0*x**4 + 0*x**2 + 0*x**3. Determine a so that b(a) = 0.
0
Factor -8/3*z**2 + 3/2*z**3 + 5/6*z + 1/3.
(z - 1)**2*(9*z + 2)/6
Let l(i) be the first derivative of 4/3*i**3 - 3/2*i**4 + 4 + 1/3*i**6 + 0*i**5 + 0*i + 0*i**2. Solve l(j) = 0 for j.
-2, 0, 1
Let p(g) be the second derivative of 4*g + 1/60*g**4 + 0 - 1/15*g**3 + 1/10*g**2. Suppose p(m) = 0. What is m?
1
Suppose -5*v + 3*s + 3 = 0, v - 29 = -2*v - 5*s. Let j(p) be the first derivative of -1/8*p**4 + 1/4*p**2 + 0*p + 1/6*p**v - 1/10*p**5 + 1. Factor j(x).
-x*(x - 1)*(x + 1)**2/2
Let y(i) be the first derivative of -9*i**4/2 + i**3 + 9*i**2 - 3*i - 10. Factor y(h).
-3*(h - 1)*(h + 1)*(6*h - 1)
Let p(m) be the second derivative of -m**4/34 + 5*m**3/51 + 2*m**2/17 - m. Let p(k) = 0. Calculate k.
-1/3, 2
Let 4*l**3 - 10*l**2 - 3*l**4 + 8*l**4 + 2*l**3 - 11*l**3 = 0. What is l?
-1, 0, 2
Let p(r) = -3*r**4 - 3*r**3 + 6*r**2 + 3*r + 3. Let o(g) = 9*g**4 + 9*g**3 - 17*g**2 