et k(n) be the first derivative of -n**6/90 - n**5/30 + 6*n**3 - 11. Let s(c) be the third derivative of k(c). Factor s(h).
-4*h*(h + 1)
Let k(w) be the third derivative of -w**5/90 - w**4/9 + 4*w**3/3 + 21*w**2. What is j in k(j) = 0?
-6, 2
Let z(q) = -q**2 - 2*q. Let f(p) = 112*p**2 + 13*p - 2. Let m(i) = -f(i) + 4*z(i). Factor m(v).
-(4*v + 1)*(29*v - 2)
Let k(o) be the first derivative of -o**2 - 2*o + 7 + 1/10*o**5 + 1/2*o**3 + 1/2*o**4. Factor k(u).
(u - 1)*(u + 1)*(u + 2)**2/2
Let a(r) be the third derivative of -r**5/150 + 5*r**4/12 - 613*r**2. Factor a(q).
-2*q*(q - 25)/5
Let n = -21 - -34. Suppose -i - 3*f + 6*f = n, -f - 1 = -3*i. Solve -4*u**4 - 12*u**i - u + 5*u**4 - 3*u - 12*u**3 - 5*u**4 = 0.
-1, 0
Let v(r) be the first derivative of -4*r**5/35 - 26*r**4/7 + 220*r**3/21 - 8*r**2 - 433. Let v(f) = 0. What is f?
-28, 0, 1
Let v(c) be the second derivative of -c**4/4 - c**3 - 95*c. Determine m so that v(m) = 0.
-2, 0
Let d(j) be the first derivative of -j**6/30 + j**5/4 - j**4/2 - 2*j**3/3 - 6*j**2 - 12. Let b(a) be the second derivative of d(a). Solve b(g) = 0.
-1/4, 2
Factor 834*l**2 - 67 - 264*l - 838*l**2 - 4289.
-4*(l + 33)**2
Let s(n) be the third derivative of -n**5/300 - n**4/30 + 5*n**2. Factor s(z).
-z*(z + 4)/5
Determine a so that 1/5*a**5 - 4/5*a**3 - 4/5*a**2 + 0*a + 1/5*a**4 + 0 = 0.
-2, -1, 0, 2
Let m(g) be the second derivative of -g**6/90 - g**5/30 + g**3/9 + g**2/6 + 65*g. Factor m(b).
-(b - 1)*(b + 1)**3/3
Suppose 6*d = -4 + 28. Let 0*t**d - 8*t**3 + 11*t**2 - 56*t + 4*t**4 - 59*t**2 - 20 = 0. What is t?
-1, 5
Suppose -o + i + 2 = 0, 0 = 5*o - 4*i - 11. Factor z**2 - 10*z**2 - 2*z + z**o + 10*z**2.
z*(z - 1)*(z + 2)
Let d(v) be the second derivative of 0*v**2 - 1/15*v**3 + 1/60*v**4 + 0 + 8*v. Factor d(w).
w*(w - 2)/5
Let w be 1/(2/10) + 53*36/13356. Factor -1/7*s**2 - w + 12/7*s.
-(s - 6)**2/7
Let y(p) be the second derivative of 0 - 1/8*p**4 + 5/12*p**3 - 1/8*p**5 + 3/4*p**2 - 9*p. Let y(g) = 0. What is g?
-1, -3/5, 1
Let v = 29 + -26. Suppose -v*o = o - 8. Factor 4/5*l + 2/5 + 2/5*l**o.
2*(l + 1)**2/5
Suppose -3*i - 3*y = -3, 2*i = -3*i + 4*y + 14. Factor 20*h**i + 15*h - 486 + 5*h**3 + 486.
5*h*(h + 1)*(h + 3)
Let v(c) be the second derivative of -4/3*c**3 - 8*c + 0 - c**4 - c**2 - 1/15*c**6 - 2/5*c**5. Solve v(y) = 0.
-1
Let k(n) be the first derivative of 5/2*n**2 + 0*n + 7/6*n**4 - 3/5*n**5 - 8 + 4/3*n**3. Let z(i) be the second derivative of k(i). Suppose z(d) = 0. What is d?
-2/9, 1
Let h be ((15/(-18))/1)/((-3)/18). Let u(g) be the second derivative of g**3 - 1/4*g**4 + 0*g**2 - 9/20*g**h + 3*g + 0. Factor u(z).
-3*z*(z + 1)*(3*z - 2)
Let o(b) be the third derivative of 0 + 0*b - 3/40*b**4 - 3*b**2 + 1/100*b**5 + 1/5*b**3. What is y in o(y) = 0?
1, 2
Let d(l) be the third derivative of l**5/120 + 3*l**4/8 + 15*l**3/4 + 687*l**2. Solve d(n) = 0.
-15, -3
Suppose -10*h + 450 = -19*h. Let d be 1/(-1 + -2) - h/60. Suppose d + 1/3*w - 1/6*w**2 = 0. Calculate w.
-1, 3
Let v(m) = -m**3 - 36*m**2 + m + 39. Let h be v(-36). Let n(c) be the first derivative of -2*c**2 + 2/3*c**3 - h + 2*c. Suppose n(k) = 0. Calculate k.
1
Let f(a) be the second derivative of -a**4/22 + 46*a**3/33 + 32*a**2/11 - 7*a. Find q, given that f(q) = 0.
-2/3, 16
Suppose 2*h - 34 = -30. Suppose -3*v - f + 67 + 16 = 0, -103 = -3*v - 5*f. Factor -26 - 2*m**4 - m**4 + 3*m**h + v.
-3*m**2*(m - 1)*(m + 1)
Let v = 1580 + -1580. Let w(z) be the first derivative of v*z - z**4 - 14 + 4/5*z**5 - 4/3*z**3 + 2*z**2. Solve w(m) = 0.
-1, 0, 1
Let t(x) be the second derivative of 3*x**5/20 + 7*x**4/4 - 17*x**3/2 + 27*x**2/2 - 415*x. Factor t(n).
3*(n - 1)**2*(n + 9)
Let t(z) be the first derivative of -z**4/6 - 10*z**3/9 - 4*z**2/3 + 344. Factor t(d).
-2*d*(d + 1)*(d + 4)/3
Let s(b) be the third derivative of -5*b**8/336 - 4*b**7/21 + 28*b**5/3 + 170*b**4/3 + 160*b**3 - 445*b**2. Suppose s(x) = 0. Calculate x.
-6, -2, 4
Factor 6/11*k + 0 - 4/11*k**2 - 2/11*k**3.
-2*k*(k - 1)*(k + 3)/11
Suppose 14*a = 23*a. Factor -2/5*f**5 + a + 4/5*f**2 + 0*f**3 - 4/5*f**4 + 2/5*f.
-2*f*(f - 1)*(f + 1)**3/5
Let w be (69/15 + -5)/((-74)/10). Let v = w + 68/111. Solve v*q**2 + 0*q + 1/3*q**3 + 0 - 12*q**4 = 0.
-2/9, 0, 1/4
Let h(p) be the second derivative of 0*p**2 - 45/14*p**7 + 10/3*p**4 + 9*p**6 + 0 - 9*p**5 + 0*p**3 - 36*p. Solve h(s) = 0 for s.
0, 2/3
Let z be 3 + 62 + 0/(-5). Factor -24 - 115*t**4 - z*t**2 + 135*t**3 + 10*t + 24 + 35*t**5.
5*t*(t - 1)**3*(7*t - 2)
Let a(y) be the third derivative of 0*y - 8*y**2 - 14/3*y**3 + 0 + 1/15*y**5 - y**4. Factor a(k).
4*(k - 7)*(k + 1)
Find x, given that 38 + 2/3*x**2 - 44/3*x = 0.
3, 19
Let a(v) = v**4 - v**2 + v - 1. Let t(p) = 2*p**4 - 6*p**3 + 3*p**2 + 7*p - 6. Let d(i) = 2*a(i) - 2*t(i). Solve d(b) = 0.
-1, 1, 5
Let q(d) be the second derivative of -d**4/6 + 28*d**3 - 1764*d**2 + 3*d + 40. Factor q(g).
-2*(g - 42)**2
Factor 7/3*l**4 + 5/3*l - 5/3*l**3 + 2/3 - 3*l**2.
(l - 1)**2*(l + 1)*(7*l + 2)/3
Let k be (1 - 0)/(11/(-99)). Let s = k - -11. Factor -4 - 9*x - 2 - 2*x**2 - x**s.
-3*(x + 1)*(x + 2)
Let m be (-2 - -11)/(-4 - (-44)/8). Let f = 6 - m. Suppose 0*r - r**3 + f - 1/3*r**4 - 2/3*r**2 = 0. Calculate r.
-2, -1, 0
Let r = 23 + -32. Let i = r + 15. Factor -2*m**3 + m**3 - 5*m**3 + 3*m**2 - 3*m**3 + i*m**4.
3*m**2*(m - 1)*(2*m - 1)
Let f(k) = -k**2 - 6*k + 6. Let h be f(0). Solve 313*a**4 - 4*a**2 - h*a**5 - 4*a**5 - 2*a**3 - 297*a**4 = 0.
-2/5, 0, 1
Let a(l) = -l**2 - 3*l - 3. Let j be a(-3). Let f = 1 - j. Factor 2 + 3*h**4 - 5*h**3 + 11*h**3 - 6*h**f + 1 - 6*h.
-3*(h - 1)**3*(h + 1)
Factor -34/11*c**2 + 126/11*c + 162/11 + 2/11*c**3.
2*(c - 9)**2*(c + 1)/11
Let v(m) be the second derivative of -m**6/15 + 3*m**5/5 + 13*m**4/16 + 5*m**3/12 - 11*m**2 + m. Let f(s) be the first derivative of v(s). Factor f(k).
-(k - 5)*(4*k + 1)**2/2
Find i such that 2/5*i**3 - 4/5 - 8/5*i + 1/5*i**4 - 3/5*i**2 = 0.
-2, -1, 2
Let i(u) = -3*u**2 - 12*u - 5. Let o(b) = -2*b**2 - 11*b - 6. Let x(g) = 3*i(g) - 4*o(g). Solve x(p) = 0 for p.
-1, 9
Let g(p) be the first derivative of 5*p**6/6 - 4*p**5 + 5*p**4/2 + 20*p**3/3 - 15*p**2/2 + 38. Solve g(x) = 0 for x.
-1, 0, 1, 3
Let l(s) be the first derivative of s**3 - 60*s**2 + 117*s + 65. Suppose l(y) = 0. Calculate y.
1, 39
Let o(w) be the third derivative of 0*w - w**2 - 3/280*w**6 + 3/490*w**7 + 1/140*w**5 + 0 - 1/784*w**8 + 0*w**3 + 0*w**4. Factor o(z).
-3*z**2*(z - 1)**3/7
Let s be ((-21)/(-63))/((-1)/3). Let m(q) = q**2 + q. Let u be m(s). What is g in -4*g**2 - 6*g - 5*g**3 + 4 + 6*g**3 + 5*g**3 + u*g**2 = 0?
-1, 2/3, 1
Factor -68/3*n**3 + 0 + 0*n + 2/3*n**5 + 0*n**2 + 10*n**4.
2*n**3*(n - 2)*(n + 17)/3
Let i(h) be the second derivative of -h**4/6 - 17*h**3 - 2601*h**2/4 - 66*h. Factor i(t).
-(2*t + 51)**2/2
Suppose -2*q = -5 + 1. Let g = 9747 + -9742. Factor -2/7*k**g - 18/7*k**3 - 4/7*k - q*k**2 - 10/7*k**4 + 0.
-2*k*(k + 1)**3*(k + 2)/7
Let o be ((-203)/42 - -5)/1. Let r(f) be the first derivative of -1/24*f**6 - o*f**3 + 3/8*f**2 + 5 - 1/8*f**4 + 3/20*f**5 - 1/4*f. Factor r(a).
-(a - 1)**4*(a + 1)/4
Factor 3/5*l**3 + 156/5*l**2 + 2028/5*l + 0.
3*l*(l + 26)**2/5
Factor -1/4*g**2 + 0*g + 0 + 1/4*g**3.
g**2*(g - 1)/4
Let m be (-2 - (-20)/6)*3. Suppose -i - 6*d + 8*d + m = 0, 4*i - 5 = -3*d. What is r in -3/4 + r - 1/4*r**i = 0?
1, 3
Let m(s) = -s**3 + s**2 + 4*s - 1. Let n(l) = -5*l**3 - 37*l**2 - 46*l + 1. Let j(g) = -5*m(g) - n(g). Factor j(f).
2*(f + 1)*(f + 2)*(5*f + 1)
Let f(p) = 5*p**3. Let v(t) = -t**2 + 3*t - 1. Let s be (2 + 2 - 3) + 3. Let w be v(s). Let a(o) = 6*o**3 + o**2 - o. Let m(i) = w*f(i) + 4*a(i). Factor m(j).
-j*(j - 2)**2
Let y = 5647 + -5626. Solve 147/2 + 3/2*z**2 - y*z = 0.
7
Let b be (0/1)/1 + 13 + -13. Let p(c) be the first derivative of 0*c**5 - 1/2*c**4 + b*c**3 + 1/3*c**6 + 0*c - 4 + 0*c**2. What is f in p(f) = 0?
-1, 0, 1
Let x(q) be the first derivative of -2*q**5/25 - q**4/5 + 2*q**2/5 + 2*q/5 + 103. Solve x(l) = 0.
-1, 1
Let p(r) be the second derivative of -r**5/170 - r**4/34 - r**3/17 - r**2/17 - 170*r. Factor p(j).
-2*(j + 1)**3/17
Let l = -113 - -115. Find i such that -33*i**2 - 7*i**l - 4*i**4 - 8*i**2 - 24*i**3 - 32*i = 0.
-2, 0
Let w(b) be the first derivative of -b**3/8 + 3*b**2/2 + 39. Let w(m) = 0. What is m?
0, 8
Let k = 28 - 27. Sup