 w**3/3 + 4. Let m(l) be the third derivative of s(l). What is d in m(d) = 0?
1
Suppose -10*r**3 - 15*r**2 + 5*r**3 + 6*r + 5 - r + 10*r**4 = 0. What is r?
-1, -1/2, 1
Let j(o) = 8*o**4 + 40*o**3 + 67*o**2 + 61*o + 21. Let v(k) = -44*k**4 - 220*k**3 - 368*k**2 - 336*k - 116. Let g(p) = 28*j(p) + 5*v(p). Factor g(r).
4*(r + 1)**3*(r + 2)
Solve 1/2*o**3 + 1/4 - 1/4*o**4 + 0*o**2 - 1/2*o = 0.
-1, 1
Determine s, given that -3 + 2*s**3 - 2*s**3 + 4*s**3 + s**4 + 2*s**2 - 4*s = 0.
-3, -1, 1
Let w = 5 + -11. Let v be (w/4 - -2)*24. Let -4 + 30*a**3 + 67*a**3 - v*a - 25*a**3 + 19*a**2 + 45*a**4 = 0. Calculate a.
-1, -2/3, -1/3, 2/5
Suppose -4*g + 14 = 2*o, -g + 9 = -2*g + 2*o. Let r(c) be the first derivative of 2/3*c**3 + g - 8/7*c + 12/7*c**2. Factor r(k).
2*(k + 2)*(7*k - 2)/7
Let i = 4 + -19. Let l be (-40)/i - 6/9. Factor -2/5*w**l + 0 - 4/5*w.
-2*w*(w + 2)/5
Let s(t) be the third derivative of -t**6/660 + t**5/165 - t**4/132 - 3*t**2. Factor s(f).
-2*f*(f - 1)**2/11
Let l(m) be the second derivative of -m**2 - 67/8*m**4 + 4*m**3 - 93/20*m**6 + 7*m + 0 + 27/28*m**7 + 71/8*m**5. Factor l(s).
(s - 1)**3*(9*s - 2)**2/2
Let u = -107 + 538/5. Let h = 806 + -806. Factor 0*n + 3/5*n**2 + h - u*n**3.
-3*n**2*(n - 1)/5
Let -3/5*q**2 + 0 + 3/5*q = 0. Calculate q.
0, 1
Let g(d) be the first derivative of 12*d**5/55 + 25*d**4/22 + 14*d**3/11 - d**2/11 - 6*d/11 - 19. Solve g(x) = 0 for x.
-3, -1, -1/2, 1/3
Factor 2/3*a - 2/9*a**5 - 2/3*a**4 + 2/9 - 4/9*a**3 + 4/9*a**2.
-2*(a - 1)*(a + 1)**4/9
Let m(f) be the first derivative of -3*f**5/20 + f**4/4 - 3*f - 3. Let n(z) be the first derivative of m(z). Solve n(t) = 0.
0, 1
Let p(d) be the second derivative of -d**6/120 - d**5/40 + d**4/48 + d**3/12 - 7*d. Suppose p(m) = 0. What is m?
-2, -1, 0, 1
Let z(t) be the first derivative of -t**4/14 + 2*t**3/7 - 3*t**2/7 + 2*t/7 - 14. Find u, given that z(u) = 0.
1
Let c(j) = -3*j**3 + j**2 + 2*j. Let p(v) be the first derivative of v**4/2 - v**2 + 5. Let i(m) = 4*c(m) + 5*p(m). Determine f so that i(f) = 0.
0, 1
Suppose 5*z = 6 + 14. Factor -9*q**3 + 4*q**z + q**3 - 4*q**5 + 5*q**4 + 3*q**4.
-4*q**3*(q - 2)*(q - 1)
Let g(k) = -k**4 + 6*k**2 - k**3 - k**3 - 6*k**5 + 0*k**4 + 3*k**4 + 8 + 8*k. Let j(n) = -n**5 + n**2 + n + 1. Let w(u) = g(u) - 8*j(u). Factor w(d).
2*d**2*(d - 1)*(d + 1)**2
Let x be 6*(-2)/(4/3). Let g = x - -31/3. Determine a, given that -2/3 - g*a**2 - 1/3*a**3 - 5/3*a = 0.
-2, -1
Let f(i) be the first derivative of i**4/14 - 2*i**3/21 - 14. Factor f(r).
2*r**2*(r - 1)/7
Let r(q) be the third derivative of -1/144*q**4 + 0*q**3 + 0*q + 0 + 1/360*q**5 + 3*q**2. Find a, given that r(a) = 0.
0, 1
Factor 4*u**3 + 0*u**2 - 18*u**3 + 4*u + 0*u - 10*u**2.
-2*u*(u + 1)*(7*u - 2)
Let u = 25 - 23. Solve 6*y**3 + 2*y - 19*y**2 + 13*y**u - 2*y**4 + 0*y**3 = 0.
0, 1
Let g(b) be the second derivative of b**6/35 + 2*b**5/35 - 11*b**4/42 - 16*b**3/21 - 4*b**2/7 - 26*b. Solve g(x) = 0.
-2, -1, -1/3, 2
Let i(g) be the first derivative of -2*g**3/3 - 10*g**2 - 50*g + 18. Solve i(y) = 0 for y.
-5
Let g = 25 + -22. Factor 0 - 1/4*x**4 + 0*x + 1/2*x**g - 1/4*x**2.
-x**2*(x - 1)**2/4
Let p(g) be the third derivative of g**7/7560 - g**6/1080 + g**5/360 + g**4/24 + 3*g**2. Let v(t) be the second derivative of p(t). Factor v(k).
(k - 1)**2/3
Let l(g) be the second derivative of -g**7/252 + g**6/90 - g**5/120 + 27*g. Factor l(a).
-a**3*(a - 1)**2/6
Let m(n) = -5*n**2 + 50*n - 45. Let z(k) = -10*k**2 + 100*k - 90. Let y(o) = -5*m(o) + 3*z(o). Factor y(j).
-5*(j - 9)*(j - 1)
Let i(f) be the first derivative of f**7/1260 + f**6/108 + 2*f**5/45 + f**4/9 - 4*f**3/3 + 5. Let y(h) be the third derivative of i(h). Factor y(p).
2*(p + 1)*(p + 2)**2/3
Let l(q) = -q**4 - q**3 + q + 1. Let s(r) = 5*r**3 - r - 1. Let k(t) = -l(t) - s(t). Solve k(p) = 0.
0, 4
Suppose 11 = d - 12. Suppose 3*q - d = -7*z + 3*z, 3*q - 15 = 0. Factor z + y + 3*y**2 - 2*y**2 - 2*y**2.
-(y - 2)*(y + 1)
Let b = -4649/6 - -775. Find w, given that -1/6*w**3 - 1/2*w - 1/2*w**2 - b = 0.
-1
Suppose 3*f = 3*m + 18, -4*f + 0 - 4 = 3*m. Let u = f - -1. Factor 5*h**u - 2*h + h**3 - 2*h**4 - 4*h**3 + 2*h**2.
-2*h*(h - 1)**2*(h + 1)
Let h(v) be the second derivative of -v**7/35 + v**6/75 + v**5/25 - v. What is w in h(w) = 0?
-2/3, 0, 1
Let t(r) = -r**3 - 3*r**2 - 5. Let g be t(-4). Factor -10*q**2 - 12 + 3*q**2 + 3*q**2 + 36*q - g*q**2.
-3*(q - 2)*(5*q - 2)
Factor -2/9*h**2 + 2/9*h**4 + 0 + 2/9*h**3 - 2/9*h**5 + 0*h.
-2*h**2*(h - 1)**2*(h + 1)/9
Let y = 11 - 17. Let p(j) = j**4 + 0*j - j**3 + 2*j - 3*j + j**5. Let f(n) = 14*n**5 - 12*n**4 + 6*n**3 - 2*n**2 - 6*n. Let a(c) = y*p(c) + f(c). Factor a(q).
2*q**2*(q - 1)**2*(4*q - 1)
Factor 2/3*b**4 - 8/3 + 8/3*b - 8/3*b**3 + 2*b**2.
2*(b - 2)**2*(b - 1)*(b + 1)/3
Suppose -36*r = -20 - 52. Find a, given that -1/4*a**r + 1/4 + 0*a = 0.
-1, 1
Let z(k) be the second derivative of 0 + 1/25*k**6 - 1/100*k**5 - 2*k + 0*k**2 - 3/70*k**7 + 0*k**3 + 0*k**4. Solve z(r) = 0 for r.
0, 1/3
Let n(h) be the first derivative of 4*h**6/5 - 8*h**5/5 - 3*h**4/4 + 9*h**3/2 - 2*h**2 + 4. Let a(s) be the second derivative of n(s). Factor a(q).
3*(2*q + 1)*(4*q - 3)**2
Let m = -28/15 - -34/15. Factor 1/5 + m*o + 1/5*o**2.
(o + 1)**2/5
Suppose -a + 3 + 0 = 0. Determine m so that 0*m**a - 1/2*m**4 + 1/2*m**2 + 0 + 0*m = 0.
-1, 0, 1
Let d(b) be the first derivative of -b**8/840 + b**6/180 - b**3/3 - 4. Let j(f) be the third derivative of d(f). Factor j(s).
-2*s**2*(s - 1)*(s + 1)
Suppose -2*g = 0, 4*o = -3*g + 2*g + 40. Let k be o/(-6) - (-26)/13. Factor -k*b**2 + 0 + 1/3*b.
-b*(b - 1)/3
Let a = -22 + 24. Solve 3*m**3 + 3*m**2 - a - 4*m**3 + 4 + 5*m - m**4 = 0.
-1, 2
Let z(r) be the first derivative of r**7/84 - r**6/15 + r**5/8 - r**4/12 - 3*r + 7. Let p(b) be the first derivative of z(b). Suppose p(v) = 0. What is v?
0, 1, 2
Factor -2/3*x + 8/9 - 2/9*x**2.
-2*(x - 1)*(x + 4)/9
Let l(j) be the second derivative of -j**5/5 + 2*j**3/3 - 9*j. Factor l(y).
-4*y*(y - 1)*(y + 1)
Let -7*a**5 + 5*a + 88*a**2 - 38*a**5 + 40*a**3 - 30*a**4 - 58*a**2 = 0. What is a?
-1, -1/3, 0, 1
Suppose 16 = 4*l + 48. Let i = l - -10. Factor -4/3 + 14/3*f + 4/3*f**i - 14/3*f**3.
-2*(f - 1)*(f + 1)*(7*f - 2)/3
Let g be 119/35 + -7 - (-1 - 3). Solve -g*z**3 - 4/5*z + 6/5*z**2 + 0 = 0.
0, 1, 2
Factor 20*n**2 + 4*n**2 - 140*n**3 + 20*n**2 + 100*n**4 - 4*n.
4*n*(n - 1)*(5*n - 1)**2
Let g = -4 - -6. Let m be 1 + ((-1)/2 + 4 - 3). Find p, given that -1/2 - p**3 - 1/2*p**5 - p**g + m*p**4 + 3/2*p = 0.
-1, 1
Suppose 3*x = x + 10. Let s(g) be the first derivative of -1/2*g**2 - 1/5*g**x + 1/4*g**4 - 1 + 0*g + 1/3*g**3. Factor s(t).
-t*(t - 1)**2*(t + 1)
Let m be 0 + 3*(-2)/(-2). Let x be 2/m + 4/3. Let -1 - q + x*q**2 - q**2 + 1 = 0. Calculate q.
0, 1
Let k(a) be the third derivative of a**5/270 - a**3/27 - 21*a**2. Factor k(w).
2*(w - 1)*(w + 1)/9
Let w(f) = f**3 + 4*f**2 - 6*f - 1. Let o be w(-5). Let -2*t**4 - t**4 + t**o + 2*t**2 = 0. Calculate t.
-1, 0, 1
Let g(d) be the third derivative of -d**5/60 + d**4/4 - d**3/2 + 7*d**2. Let a(l) = l - 1. Let z(p) = -5*a(p) + g(p). Suppose z(f) = 0. What is f?
-1, 2
Let g be ((-32)/10 + 3)/((-6)/10). Determine h, given that -5/3*h**3 - 4/3*h**4 + g + h**2 + 5/3*h = 0.
-1, -1/4, 1
Let c(k) = -k**3 - k**2 - k + 1. Let l(x) = 7*x**3 + 16*x**2 + 19*x + 2. Let n(d) = 4*c(d) + l(d). Factor n(u).
3*(u + 1)**2*(u + 2)
Let v(p) be the first derivative of -2*p**3/21 + p**2/7 - 4. Solve v(i) = 0.
0, 1
Let v = 2607/1022 - -3/146. Suppose 18/7*u + 4/7 - v*u**3 - 2*u**4 + 10/7*u**2 = 0. What is u?
-1, -2/7, 1
Suppose 26*u - 34*u = -32. Factor 0 + 0*r**2 + 1/3*r**3 + 0*r**u + 0*r - 1/3*r**5.
-r**3*(r - 1)*(r + 1)/3
Factor -39*a**2 + 3*a**2 + 7*a + 10*a**3 + 30*a + 16 - 13*a.
2*(a - 2)**2*(5*a + 2)
Let x(d) be the third derivative of d**7/840 - d**6/480 - d**5/80 + 5*d**4/96 - d**3/12 - 7*d**2. Factor x(p).
(p - 1)**3*(p + 2)/4
Let f(t) be the second derivative of -7*t**5/10 - 2*t**4/3 - 4*t**3/21 + 3*t. Suppose f(b) = 0. Calculate b.
-2/7, 0
Let l(o) be the first derivative of -4*o**5/25 - o**4/5 + 4*o**3/15 + 2*o**2/5 + 6. What is s in l(s) = 0?
-1, 0, 1
Let k(o) be the third derivative of 1/6*o**3 - 1/60*o**5 + 0 + 0*o + o**2 + 0*o**4. Factor k(i).
-(i - 1)*(i + 1)
Let m be 108/45 - (-2)/(-5). Let t(d) be th