 1
Let p(v) be the second derivative of -v**6/30 - v**5/10 - v**4/12 + 6*v. Determine f so that p(f) = 0.
-1, 0
Let m(v) = v**2 - 3*v - 2. Suppose 0 = 5*o + 2*q - 12, -4*o + 9*o + q = 16. Let g be m(o). Find d such that d + 3*d - d**g - 3*d = 0.
0, 1
Let h(n) be the second derivative of -n + 0 + 1/9*n**3 - 1/36*n**4 + 1/2*n**2. Factor h(q).
-(q - 3)*(q + 1)/3
Let s(r) = 19*r**2 - 16*r + 6. Let l(m) = m**2 + m - 1. Let q(i) = -6*l(i) - s(i). Factor q(o).
-5*o*(5*o - 2)
Factor 0*i + 3/2*i**3 - 3/4*i**4 + 0 - 3/4*i**2.
-3*i**2*(i - 1)**2/4
Factor 7/6*i**5 + 8/3*i**4 - 7/3*i**2 - 11/6*i + 2/3*i**3 - 1/3.
(i - 1)*(i + 1)**3*(7*i + 2)/6
Let p(b) be the third derivative of b**9/3024 - b**8/1680 - b**7/840 + b**6/360 + b**3/2 + 2*b**2. Let n(w) be the first derivative of p(w). Factor n(f).
f**2*(f - 1)**2*(f + 1)
Let u be (-8)/16*(1 - 2). Solve -g + u + 1/2*g**2 = 0 for g.
1
Let i = -241/20 + 64/5. Let 1/4*f**3 + 3/4*f**4 + 1/4*f**5 + 0 - i*f**2 - 1/2*f = 0. What is f?
-2, -1, 0, 1
Let t(r) be the third derivative of r**9/37800 - r**8/6720 + r**7/6300 - r**4/12 - r**2. Let m(b) be the second derivative of t(b). Factor m(p).
p**2*(p - 2)*(2*p - 1)/5
Let l = -43/6 + 221/30. Find s, given that 0 + 2/5*s - l*s**2 = 0.
0, 2
Suppose 0 = -5*d - 3*k + 19, -2*d = -5*k + 2 + 9. Factor 2/3*q**d - 4/3*q + 0.
2*q*(q - 2)/3
Let x(r) be the first derivative of -4 + 2/35*r**5 + 0*r**2 - 4/21*r**3 + 2/7*r + 0*r**4. Factor x(j).
2*(j - 1)**2*(j + 1)**2/7
Suppose -3*b + 5 + 1 = 0. Let y = 246 - 728/3. Determine a, given that -16/3*a - y*a**b + 8/3 = 0.
-2, 2/5
Let w(h) be the first derivative of -10*h**3/3 + 11*h**2 - 4*h - 6. Determine t so that w(t) = 0.
1/5, 2
Let g be (0/(25/(-5)))/1. Solve 0 + 2/5*u**3 + g*u + 0*u**2 = 0 for u.
0
Let m be 28/(-8) - 2/(-4). Let g(f) = -2*f**3 - 3*f**2 + 3*f + 1. Let t(n) = 4*n**3 + 5*n**2 - 7*n - 3. Let l(i) = m*t(i) - 5*g(i). Factor l(v).
-2*(v - 2)*(v + 1)**2
Let v(c) = c**3 - c - 2. Let a(j) = -8*j**3 + 4*j**2 + 4*j + 18. Let f(y) = 2*a(y) + 18*v(y). Solve f(q) = 0 for q.
-5, 0, 1
Suppose -32/13*b**2 + 0 + 8/13*b - 14/13*b**5 + 6/13*b**3 + 32/13*b**4 = 0. Calculate b.
-1, 0, 2/7, 1, 2
Let t = 817/3 - 270. Let l(s) be the first derivative of -t*s**2 + 1/9*s**6 - 4/15*s**5 - 1/3*s**4 + 3 + 4/3*s + 16/9*s**3. Solve l(x) = 0.
-2, 1
Suppose 2 = 2*o + 4. Let j be ((-8)/96)/(o/3). Factor -j*m + 0 - 1/4*m**2.
-m*(m + 1)/4
Let h(a) = 7*a**2 - 32*a + 13. Let f(t) = -8*t**2 + 33*t - 13. Let q(l) = 5*f(l) + 6*h(l). Factor q(p).
(p - 13)*(2*p - 1)
Let v be (-90)/120*-2*(-3)/(-18). Find n such that 0 - 1/2*n - v*n**4 + 1/2*n**3 + 1/4*n**2 = 0.
-1, 0, 1, 2
Suppose -11 = -4*i + b, 7*i + 4*b = 4*i + 32. Factor 0 + 3/2*p**2 + 0*p - 21/2*p**i - 3*p**3 - 6*p**5.
-3*p**2*(p + 1)**2*(4*p - 1)/2
Let u(w) = -5*w**5 - w**4 + 2*w**3 + w**2 + 3. Let j(x) = 26*x**5 + 4*x**4 - 10*x**3 - 4*x**2 - 16. Let m(k) = -3*j(k) - 16*u(k). What is i in m(i) = 0?
-2, -1, 0, 1
Let n be (-1)/(-7) - 40/(-14). Let y(m) be the first derivative of -2/15*m**3 + 2/25*m**5 - n - 1/15*m**6 - 8/5*m + 1/2*m**4 - 8/5*m**2. Factor y(l).
-2*(l - 2)**2*(l + 1)**3/5
What is d in -2 - 13*d**3 - 5*d**2 + 2*d + 2*d**5 - 4*d**4 + 2*d**4 + 9*d**2 + 9*d**3 = 0?
-1, 1
Let f(d) = -12*d**2 + 128*d - 37. Let y(x) = -145*x**2 + 1535*x - 445. Let q(c) = -35*f(c) + 3*y(c). Factor q(a).
-5*(a - 8)*(3*a - 1)
Let d(m) = m - 1. Let o be d(3). Factor 3*h + 0*h**3 - 6*h**o - 4*h + 4*h + 3*h**3.
3*h*(h - 1)**2
Let i = 15 + -15. Let h(s) be the second derivative of 1/30*s**6 + 0*s**5 + s + i*s**3 - 1/12*s**4 + 0 + 0*s**2. Let h(q) = 0. Calculate q.
-1, 0, 1
Let h(u) = -8*u**2 + 4*u + 12. Let m(t) = -t**2 - t. Let f(a) = h(a) - 5*m(a). Solve f(w) = 0.
-1, 4
Let s = 145/258 + 9/86. Factor -1/3*r**4 - 4/3 - 4/3*r + s*r**3 + r**2.
-(r - 2)**2*(r + 1)**2/3
Solve 0*m**5 + 3*m**3 - 6*m**4 + 2*m**5 + m**5 + 0*m**4 = 0 for m.
0, 1
Suppose 3*j + 4 = 46. Let f be 0 - 8/j*-1. Find b such that 2/7*b + 0*b**2 + 2/7*b**5 - f*b**3 + 0*b**4 + 0 = 0.
-1, 0, 1
Let p = -327 - -655/2. What is o in 0 - 1/2*o - p*o**2 = 0?
-1, 0
Let z(u) be the first derivative of -u + 3/5*u**5 + 2 - 2/3*u**3 + 1/6*u**6 - 3/2*u**2 + 1/2*u**4. Factor z(m).
(m - 1)*(m + 1)**4
Let u(t) = t**3 - t**2 - t + 3. Let m be (-2)/(-4) - 2/4. Let a be u(m). Suppose x - a*x**2 + x + 7*x**2 + 2*x**3 = 0. What is x?
-1, 0
Let t be (-22)/(-55) + -3*3/60. Factor 0 - t*s + 0*s**2 + 1/4*s**3.
s*(s - 1)*(s + 1)/4
Let y be 4/3 - 87/(-9). Let t(g) = -g**3 + 11*g**2 + 2*g - 22. Let z be t(y). Find o such that 2/5*o**3 - 2/5*o**2 + 0*o + z = 0.
0, 1
Let v be ((-2)/(-4))/(3/12). Let h be (-2)/(-3)*21/7. Solve 3*y**2 + y**3 + h*y**3 - 4*y**4 - 2*y**v = 0.
-1/4, 0, 1
Let x = -172 + 864/5. What is y in x + 1/5*y**2 + 4/5*y = 0?
-2
Let a(l) be the second derivative of l**6/90 - l**5/60 + l. Let a(i) = 0. What is i?
0, 1
Find b, given that 4 + 0*b**2 + 3*b**2 + 0 + 2 - 9*b = 0.
1, 2
Let l(k) be the first derivative of -k**3/3 + k**2 + 15. What is w in l(w) = 0?
0, 2
Let t be 1 - (-1)/2*2. Let m be 8/t*6/6. Determine j, given that 19*j**m + 20*j**2 + 49*j**2 - 70*j**3 - 14*j + 4 + 6*j**4 - 14*j = 0.
2/5, 1
Suppose -2*w + 8 = 5*n - 4*n, -4*n + 14 = -w. What is t in -t + 1/2*t**w + 1/2 = 0?
1
Let d(f) be the third derivative of -f**7/210 + 7*f**6/120 - f**5/4 + 3*f**4/8 - 9*f**2. Determine z, given that d(z) = 0.
0, 1, 3
Let k(q) be the third derivative of 6*q**2 - 5/8*q**4 + 0 - q**3 + 0*q + 11/20*q**5 - 1/10*q**6. Factor k(x).
-3*(x - 2)*(x - 1)*(4*x + 1)
Let i(m) be the third derivative of -m**6/480 + m**5/240 + 4*m**2. Factor i(l).
-l**2*(l - 1)/4
Let t be 2/(-6) - 374/(-51). Let a = t + -5. Let -2/7 + 4/7*l - 2/7*l**a = 0. What is l?
1
Suppose -2*z + 6 = -4*z. Let y be ((-14)/z)/(-2) + 3. Factor -2/3*q**2 + 0 + 2/3*q**4 - y*q**3 + 2/3*q.
2*q*(q - 1)**2*(q + 1)/3
Let i = -3 - -5. Let s(r) = 3 + i*r**2 + 2*r**2 - 3*r - 6. Let u(l) = -l**2 + l + 1. Let v(j) = -s(j) - 3*u(j). Determine n so that v(n) = 0.
0
Find b, given that -1/4*b**3 + 0 + 0*b - 1/2*b**2 = 0.
-2, 0
Factor -12/7*l**2 + 0 + 3/7*l.
-3*l*(4*l - 1)/7
Let n(v) = -3*v**2 + v + 11. Let i(h) = 6*h**2 - 7*h - 8. Let y(w) = -4*w**2 + 5*w + 5. Let z(f) = -5*i(f) - 7*y(f). Let c(x) = -3*n(x) + 7*z(x). Factor c(r).
-(r + 1)*(5*r - 2)
Let b = 183/86 + -70/43. Let 0 + b*a - 1/2*a**2 = 0. What is a?
0, 1
Let b(s) be the third derivative of 3*s**7/70 - 11*s**6/40 - s**5/30 + 13*s**4/6 + 4*s**3 + 4*s**2 - 2*s. Find h, given that b(h) = 0.
-2/3, 2, 3
Let k(p) = 5*p**4 + 3*p**3 + p**2 - 9*p + 9. Let m = -7 - -16. Let t(i) = -i**4 - i**3 + 2*i - 2. Let s(j) = m*t(j) + 2*k(j). Determine l so that s(l) = 0.
0, 1, 2
Let k(u) = -2*u**4 + 5*u**2 - 3*u. Let r(f) = -3*f. Let t be r(2). Let z(q) = q**4 + q**3 - q**2 + q. Let n(o) = t*z(o) - 2*k(o). Factor n(w).
-2*w**2*(w + 1)*(w + 2)
Suppose -4*x = 3*d - 17, -4 = 4*x - 5*x - d. Suppose -4*w + 2*v = -8, -9 - 1 = -x*w + 3*v. Factor -2*u + w*u + 3*u**2 - u**3 - 4.
-(u - 2)**2*(u + 1)
Let x(a) = 4*a**5 + 12*a**4 - 4*a**3 - 4*a**2 - 8*a - 4. Let d(y) = 12*y**5 + 35*y**4 - 11*y**3 - 13*y**2 - 23*y - 11. Let v(w) = 4*d(w) - 11*x(w). Factor v(l).
4*l*(l - 1)*(l + 1)**3
Let p be ((-6)/4)/(8/48*-3). What is l in -5*l**p - 13/3*l**4 - 1/3*l - 4/3*l**5 + 0 - 7/3*l**2 = 0?
-1, -1/4, 0
Suppose -5*d + 10 = 4*b, -5*b + d + 27 + 0 = 0. What is r in 4 + 4*r + 0*r - 7*r + 5*r**2 - r**3 - b*r = 0?
1, 2
Determine a so that 5*a**5 - 12*a**3 - 6*a**2 - 9*a**5 + 2*a**2 - 12*a**4 = 0.
-1, 0
Let u = 456 - 252. Factor -81*d - 51*d**3 + 69*d**2 - 6*d**4 - u*d**2 + 46 - 16 + 51.
-3*(d + 3)**3*(2*d - 1)
Let z(f) be the first derivative of 1 + 0*f**4 + 0*f + 0*f**2 + 9/20*f**5 - 1/12*f**3. Find d, given that z(d) = 0.
-1/3, 0, 1/3
Let s(m) = -2*m**3 + 2*m**2 - 3*m - 3. Let b(t) = -14*t**3 + 14*t**2 - 22*t - 22. Let o(j) = 6*b(j) - 44*s(j). Let o(p) = 0. Calculate p.
0, 1
Let p(w) be the first derivative of 3*w**4/4 - 7*w**3/3 + 3*w**2 + 6*w + 2. Let q(a) = 9*a**3 - 20*a**2 + 17*a + 17. Let t(n) = -17*p(n) + 6*q(n). Factor t(r).
r**2*(3*r - 1)
Let i = 319 + -947/3. Factor -i*w + 8/3*w**2 - 2/3*w**3 + 4/3.
-2*(w - 2)*(w - 1)**2/3
Let m(l) = -l**4 - 3*l**3 + 10*l**2 - 4*l - 2. Let c = 5 - 10. Let g(r) = -3*r**4 - 5*r**3 + 21*r**2 - 8*r - 5. Let q(h) = c*m(h) + 2*g(h). Factor q(k).
-k*(k - 2)**2*(k - 1)
Factor o**4 -