be the third derivative of i(k). Factor r(h).
-2*(h - 1)**2*(3*h + 1)
Let l(u) be the third derivative of -u**5/360 - 5*u**4/144 - u**3/9 - 17*u**2. Let l(s) = 0. Calculate s.
-4, -1
Let x(n) be the third derivative of 1/32*n**4 + 0 - 3/80*n**5 + 1/4*n**3 + 2*n**2 + 1/280*n**7 - 1/160*n**6 + 0*n. Find g such that x(g) = 0.
-1, 1, 2
Suppose 5*j + 0*j = 10. Let 6*i**j + 3*i**4 - i**4 - i + 5*i - 8*i**4 - 2*i**5 - 2*i**3 = 0. Calculate i.
-2, -1, 0, 1
Suppose -4*t = -5*t - 3. Let u = -5/2 - t. Factor a - u - 1/2*a**2.
-(a - 1)**2/2
Suppose -11*p + 24 = -5*p. Let j(g) be the second derivative of 3*g + 0 + 0*g**2 - 3/16*g**p - 3/20*g**5 + 1/8*g**3. Suppose j(a) = 0. What is a?
-1, 0, 1/4
Suppose -s = -2*b - 5*s + 24, -5*b - s = -15. Solve -h**2 + 5*h + h**b - 3*h**2 + 4*h = 0.
0, 3
What is o in -15 + 245*o**2 - 5 - 123*o**2 - 117*o**2 = 0?
-2, 2
Let v(m) be the second derivative of 1/210*m**6 + 1/14*m**2 + 2*m - 1/42*m**4 - 1/70*m**5 + 1/42*m**3 + 0 + 1/294*m**7. Factor v(o).
(o - 1)**2*(o + 1)**3/7
Let t(n) = -n**5 - n**4 + n**3 - n**2 - 1. Let v(h) = -2*h**5 + 8*h**4 + 2*h**3 - 2*h**2 + 3. Let x(w) = -3*t(w) - v(w). Determine b, given that x(b) = 0.
-1, 0, 1
Let n(l) = l**2 + 4*l - 3. Let c be n(-4). Let t = c - -6. Find d, given that -5*d**3 - d**2 + 2*d**t + 2*d**3 = 0.
-1, 0
Let w(r) be the second derivative of r**7/294 - r**6/105 - 3*r**5/140 + r**4/21 + 2*r**3/21 + 14*r. What is q in w(q) = 0?
-1, 0, 2
Let l(y) be the second derivative of -y**4/12 + y**3 - y**2 - 5*y. Let r be l(5). Factor -1/2*n + 1/2*n**r - 1/4 + 0*n**2 + 1/4*n**4.
(n - 1)*(n + 1)**3/4
Let j = 25/2 + -11. Factor 1/2*n**2 - 3/2*n**3 + 0*n + 0 - 1/2*n**5 + j*n**4.
-n**2*(n - 1)**3/2
Let x(d) be the first derivative of 2 - d**2 - 2/3*d**3 + 0*d. Suppose x(f) = 0. What is f?
-1, 0
Factor 9/4*c**2 + 3/2*c + 3/4*c**3 + 0.
3*c*(c + 1)*(c + 2)/4
Factor x + 0 + 1 - 4*x + 41*x**3 + 3*x**2 - 42*x**3.
-(x - 1)**3
Let l be ((12/3)/8)/20. Let o = l + 99/40. Factor -3/2*n**3 - n + 0 - o*n**2.
-n*(n + 1)*(3*n + 2)/2
Let g(a) be the first derivative of -3*a**5/10 - a**4 - 2*a**3/3 - 23. Solve g(m) = 0 for m.
-2, -2/3, 0
Let s(i) be the first derivative of -1/14*i**4 + 8/21*i**3 - 1 + 4/7*i - 5/7*i**2. Factor s(v).
-2*(v - 2)*(v - 1)**2/7
Suppose -3*s + 27 = 2*k, -3*k - 2*s + 37 = -s. Suppose -10*l + k*l = 6. What is g in -102/7*g**l + 2/7 - 26/7*g**2 + 6/7*g - 72/7*g**4 = 0?
-1, -1/3, 1/4
Let u(j) = -j**2 + 7*j - 7. Let d be u(5). Let c be (-5)/2*(-24)/15. Determine g, given that 4/3 + 20*g**c + 100/3*g**d + 80/3*g**2 + 14/3*g**5 + 10*g = 0.
-1, -2/7
Let w(d) = -d**3 + 8*d**2 + d - 2. Let l be w(8). Let x be (l/(-4))/((-12)/320). Factor 29*j**3 - 11*j**2 - 11*j**3 - j**2 - 16 - x*j.
2*(j - 2)*(3*j + 2)**2
Let p(n) be the third derivative of -n**6/30 - 11*n**5/15 - 4*n**4 + 24*n**3 - 16*n**2. Factor p(a).
-4*(a - 1)*(a + 6)**2
Factor -4*g - g**3 - 5*g**2 + 0 - 3 - 2*g - g.
-(g + 1)**2*(g + 3)
Suppose -g + 2*o - 1 = 3*o, -g = -4*o - 19. Factor -3/4*i**2 + 1/4*i**4 - 1/4*i**g + 1/4*i + 1/2.
(i - 2)*(i - 1)*(i + 1)**2/4
Let r(h) = 0*h - h**4 - 2*h**3 + 1 + 4*h**3 + h - 3*h**3. Let q(y) = 3*y**4 - 3*y**3 - 8*y**2 + 2*y + 6. Let v(l) = -q(l) + 6*r(l). Factor v(g).
-g*(g - 1)*(3*g + 2)**2
Let q(l) be the third derivative of -l**10/30240 + l**8/3360 - l**6/720 + l**4/24 + 2*l**2. Let t(g) be the second derivative of q(g). What is n in t(n) = 0?
-1, 0, 1
Let y(a) be the first derivative of 1/12*a**6 - 1/2*a - 3/4*a**2 + 3/10*a**5 - 1/3*a**3 + 1/4*a**4 + 3. Factor y(d).
(d - 1)*(d + 1)**4/2
What is t in 0 + 6/7*t - 8/7*t**2 + 2/7*t**3 = 0?
0, 1, 3
Solve 2/3*x**4 - 8/3*x - 10/3*x**3 + 0 + 16/3*x**2 = 0.
0, 1, 2
Let l be (0 - -4)/(-1)*(-1)/7. Factor -2/7*p**2 - 2/7 + l*p.
-2*(p - 1)**2/7
Factor 9/4*k**2 - 1 + 3*k - 7/4*k**3.
-(k - 2)*(k + 1)*(7*k - 2)/4
Let x(y) be the first derivative of -5/6*y**4 + 0*y + 0*y**2 + 8/15*y**5 - 1 + 2/9*y**3. Factor x(n).
2*n**2*(n - 1)*(4*n - 1)/3
Let p(f) be the second derivative of -f**7/18 - f**6/3 - 43*f**5/60 - 2*f**4/3 - 2*f**3/9 + 2*f. Determine l, given that p(l) = 0.
-2, -1, -2/7, 0
Let g(u) be the first derivative of u**6/4 - 21*u**5/10 + 27*u**4/4 - 10*u**3 + 6*u**2 - 2. Factor g(n).
3*n*(n - 2)**3*(n - 1)/2
Suppose -6*w**2 + 22*w**3 + 17*w**3 + 9*w - 42*w**3 = 0. Calculate w.
-3, 0, 1
Let g(b) = -3*b**2 + 9*b + 9. Let j(n) = n + 7. Let u be j(-6). Let a(f) = f + 1. Let l(z) = u*g(z) - 5*a(z). Factor l(h).
-(h - 2)*(3*h + 2)
Suppose -4 = -2*h - 2. What is z in 2*z - z - 2*z**3 + z**4 - h + z = 0?
-1, 1
Let f be 126/49 - 2 - (-8)/14. Solve f + 8/7*n + 2/7*n**2 = 0 for n.
-2
Let l(j) be the second derivative of -1/10*j**5 + 1/6*j**4 + 0 + 1/42*j**7 - 1/30*j**6 - 1/2*j**2 - j + 1/6*j**3. Suppose l(d) = 0. Calculate d.
-1, 1
Let w(s) be the second derivative of -1/27*s**3 - s + 1/9*s**2 + 1/90*s**5 + 0 - 1/54*s**4. Factor w(h).
2*(h - 1)**2*(h + 1)/9
Factor 1/3*r**4 + 0*r**3 + 0*r + 1/3 - 2/3*r**2.
(r - 1)**2*(r + 1)**2/3
Let a(r) be the first derivative of -9/14*r**2 + 8 + 0*r - 1/7*r**3. Solve a(w) = 0 for w.
-3, 0
Let v(l) be the third derivative of 0*l + 0 + 1/540*l**6 - 1/108*l**4 + 0*l**3 + 4*l**2 + 0*l**5. Solve v(t) = 0 for t.
-1, 0, 1
Let q be 1/3 + 2/6. Let r = 2482/933 - -2/311. Factor q*x**2 + r - 8/3*x.
2*(x - 2)**2/3
Suppose -5*q = -h - 2, -7*q - 8 = -4*h - 3*q. Determine g so that 0 - 5/3*g**4 - 17/3*g**h - 4/3*g - 16/3*g**2 = 0.
-2, -1, -2/5, 0
Let v = 217/3 + -71. Factor -1/3 - 1/3*n**4 - 2*n**2 - 4/3*n**3 - v*n.
-(n + 1)**4/3
Let o(x) be the third derivative of x**8/33600 - x**7/8400 - x**5/60 + x**2. Let w(g) be the third derivative of o(g). Factor w(d).
3*d*(d - 1)/5
Let n = -5 + 12. Factor -4*x**3 - 2*x + 2 - 3 + 2 - n*x**2.
-(x + 1)**2*(4*x - 1)
Let u(y) be the second derivative of 2/19*y**2 + 0 + 1/190*y**5 + 5/57*y**3 + 6*y + 2/57*y**4. Solve u(x) = 0.
-2, -1
Let u(l) be the first derivative of -2/3*l + 1 + 1/6*l**2 + 1/9*l**3. Solve u(r) = 0 for r.
-2, 1
Find n such that -1/4*n - 1/4*n**2 + 0 = 0.
-1, 0
Let f be 6/9 - 14/(-6). Factor -2 + 0 + 0*h**3 - 4*h + 2*h**2 + 2*h**f + 2*h.
2*(h - 1)*(h + 1)**2
Let a(h) be the first derivative of 6*h**5/85 - h**4/34 - 10*h**3/51 + h**2/17 + 4*h/17 + 30. Determine c, given that a(c) = 0.
-1, -2/3, 1
Let b(x) be the second derivative of -x**7/4200 - x**6/1800 + x**3 + 6*x. Let v(p) be the second derivative of b(p). Determine q, given that v(q) = 0.
-1, 0
Suppose -3*b - 2*j - j + 24 = 0, 3*b + j - 14 = 0. Let -f + 2 - f**2 - 3*f + b*f**2 = 0. What is f?
1
Let a(w) = 15*w**4 - 36*w**3 + 24*w**2 - 6. Let s be 2*(9/2)/3. Let d(u) = 16*u**4 - 37*u**3 + 23*u**2 + u - 7. Let g(y) = s*d(y) - 4*a(y). Factor g(x).
-3*(x - 1)**3*(4*x + 1)
Let w be -2*(-3)/6*-1. Let i(c) = -c**3 + c. Let o be i(w). Factor o - 1/4*q**3 + 0*q + 0*q**2.
-q**3/4
Let i(k) = -k - 4*k - k - 1 + 5*k. Let s(u) = 4*u**2 - u - 3. Let m(x) = 3*i(x) - s(x). Suppose m(v) = 0. Calculate v.
-1/2, 0
Let c(u) = -5*u**4 - 2*u**3 - 3*u**2 + 2*u - 4. Let v(o) = -o**4 - o**3 - o**2 + o - 1. Let w(i) = 5*c(i) - 20*v(i). Suppose w(m) = 0. What is m?
-1, 0, 1, 2
Let y(p) = 4*p**2 - p - 1. Let a be y(-1). Factor -l**a + 2*l**3 + 2*l**2 + l**3 + l**4 + l**4.
l**2*(l + 1)*(l + 2)
Let w(p) = -3*p**2 - 2*p - 3. Let y(a) = -3*a**2 - 1 - 2*a + 3 - 4. Let x(v) = -4*w(v) + 6*y(v). Factor x(j).
-2*j*(3*j + 2)
Factor -2/17*h**3 - 6/17*h**2 - 2/17 - 6/17*h.
-2*(h + 1)**3/17
Let l be ((-254)/(-889))/(8/21). Factor -9/2*p - l*p**2 - 27/4.
-3*(p + 3)**2/4
Let j(u) be the third derivative of -1/300*u**6 + 0*u**3 + 1/150*u**5 + 0*u**4 + u**2 + 0*u + 0. Let j(v) = 0. What is v?
0, 1
Let n(m) be the first derivative of 2*m**3/9 + 4*m**2/3 - 10*m/3 + 31. Let n(l) = 0. Calculate l.
-5, 1
Find m, given that 1/6*m**2 + 1/3 - 1/2*m = 0.
1, 2
Let b(t) = 5*t**2 - t + 6. Let r(h) be the first derivative of -4*h**3/3 - 5*h - 1. Let n(s) = -3*b(s) - 4*r(s). Determine o so that n(o) = 0.
-2, -1
Let c(b) = -b**5 - 2*b**4 - 9*b**3 + 24*b**2 - 8*b + 4. Let f(m) = 6*m**5 + 9*m**4 + 45*m**3 - 120*m**2 + 39*m - 21. Let o(d) = 21*c(d) + 4*f(d). Factor o(g).
3*g*(g - 2)*(g - 1)**2*(g + 2)
Suppose 0 - 2/15*o - 2/15*o**2 = 0. What is o?
-1, 0
Solve -2/5*y**3 + 8/5*y**2 + 4/5 - 2*y = 0.
1, 2
Let f(j) be the second derivative of 2*j**7/105 + j**6/10 + j**5/5 + j**4/6 - 3*j**2/2 + j. Let s(