d derivative of q**7/840 + q**6/180 + q**5/120 - q**3/2 + q. Let s(r) be the second derivative of n(r). Factor s(v).
v*(v + 1)**2
Let b(m) = -m**2 + 24*m + 25. Let y be b(25). Solve y - 3/2*i**2 - 1/2*i**3 + i - 1/2*i**5 + 3/2*i**4 = 0.
-1, 0, 1, 2
Let v(b) be the second derivative of -5/12*b**4 + 0*b**2 + 0 + b**3 + 2*b. Let p(r) = -r**2 + r. Let d(a) = -22*p(a) + 4*v(a). Determine k so that d(k) = 0.
-1, 0
Let y be 22*3/(-4)*48/(-84). Suppose -108/7*u + 9*u**3 - 24/7 - y*u**2 = 0. Calculate u.
-2/3, -2/7, 2
Let o(r) = 8*r + 2. Let c(i) = i**2 - 9*i - 3. Suppose 25*z - 6 = 26*z. Let j(s) = z*o(s) - 4*c(s). Factor j(k).
-4*k*(k + 3)
Let u(l) be the second derivative of 0 + 1/6*l**4 - l**2 + 0*l**3 - 5*l. Factor u(v).
2*(v - 1)*(v + 1)
Suppose -2*g - 6 = 4*v, 0 = v + 3*v - 2*g + 18. Let p = v + 3. Let 0*l**2 + 0*l + p + 2/5*l**4 + 0*l**3 = 0. Calculate l.
0
Let s = -39 - -43. Suppose 4*d - 6*d = -s. Suppose 2/3*f**4 - 2/3*f**d - 2/3*f**3 + 2/3*f**5 + 0*f + 0 = 0. What is f?
-1, 0, 1
Let c be (-18)/99 - (-371)/1980. Let k(t) be the third derivative of 1/72*t**4 + 0*t**3 + 0 - 2*t**2 - c*t**5 + 0*t. Factor k(u).
-u*(u - 1)/3
Factor -6/13*t**3 - 2/13*t**2 + 6/13*t + 2/13*t**4 + 0.
2*t*(t - 3)*(t - 1)*(t + 1)/13
Suppose 15 = -5*w + 2*d + 3*d, 0 = -3*w + d - 3. Factor w - 2/9*i**4 - 2/9*i**2 + 4/9*i**3 + 0*i.
-2*i**2*(i - 1)**2/9
Let m(k) be the first derivative of 3 - 1/12*k**3 - 1/4*k**2 + 0*k. Let m(b) = 0. Calculate b.
-2, 0
Solve 1/6*x**3 - 1/6*x - 1/6*x**2 + 1/6*x**4 + 0 = 0.
-1, 0, 1
Let y be ((-5)/(-45))/((-2)/(-6)). Let j be -3 - (1 - (-1 + 7)). Factor -1/3*w**4 - y + 0*w + 0*w**3 + 2/3*w**j.
-(w - 1)**2*(w + 1)**2/3
Let j(c) be the second derivative of -1/30*c**5 - c**2 - 1/120*c**6 + 0 - 1/24*c**4 + 0*c**3 + c. Let d(y) be the first derivative of j(y). Factor d(t).
-t*(t + 1)**2
Let i(v) = -v**3 - v**2 - v. Let c(d) = 24*d**3 + 20*d**2 + 20*d + 2. Let f(r) = -2*c(r) - 44*i(r). Suppose f(h) = 0. What is h?
-1, 1
Let j(t) be the first derivative of -t**6/2 + 27*t**5/5 - 81*t**4/4 + 27*t**3 + 26. Factor j(k).
-3*k**2*(k - 3)**3
Let u(k) be the second derivative of k**4/4 - k**3 + 3*k**2/2 + 2*k. Solve u(s) = 0 for s.
1
Let w(q) be the second derivative of -4*q**7/231 + 7*q**6/165 + q**5/55 + 3*q. Suppose w(n) = 0. Calculate n.
-1/4, 0, 2
Suppose 9*b - 34 = -8*b. Let i be 122/9 - (-6)/(-27). Determine g, given that -i*g**3 - 10*g + 22*g**b + 4/3 = 0.
1/4, 2/5, 1
Let p(z) be the second derivative of 1/3*z**4 + 0 + 0*z**2 + 9*z - 2/3*z**3. Factor p(o).
4*o*(o - 1)
Let v(b) be the first derivative of 7*b**6/24 + 3*b**5/2 + 25*b**4/8 + 10*b**3/3 + 15*b**2/8 + b/2 - 16. What is k in v(k) = 0?
-1, -2/7
Let u(k) be the first derivative of -k**6/15 - 2*k**5/25 + 3*k**4/10 + 2*k**3/3 + 2*k**2/5 - 15. Solve u(t) = 0.
-1, 0, 2
Factor -o - 1/2*o**2 - 1/2.
-(o + 1)**2/2
Let d(x) be the third derivative of x**7/70 - 7*x**6/120 + x**4/6 + 3*x**2. Suppose d(g) = 0. What is g?
-2/3, 0, 1, 2
Let g(v) be the second derivative of 0 + 1/6*v**3 - 2*v - 1/24*v**4 + 0*v**2 + 1/60*v**6 - 1/20*v**5. Factor g(j).
j*(j - 2)*(j - 1)*(j + 1)/2
Let l(o) = 10*o**3 - 3*o**2 - 10*o + 10. Let c(j) = 3*j**3 - j**2 - 3*j + 3. Let u(b) = -14*c(b) + 4*l(b). Determine f so that u(f) = 0.
-1, 1
Let y be 144/(-140) - 3/(-5). Let u = y - -13/14. Factor -u*d**4 - 2*d - 1/2 - 2*d**3 - 3*d**2.
-(d + 1)**4/2
Suppose -4 = 4*x - 24, 3*x = 5*b + 5. Let -4/3*t**4 + 4/3*t**b - 2/3*t + 0*t**3 + 2/3*t**5 + 0 = 0. What is t?
-1, 0, 1
Factor -3*p**5 + 3*p - 12*p**3 - 3/2 + 3*p**2 + 21/2*p**4.
-3*(p - 1)**4*(2*p + 1)/2
Let y(c) = -6*c**3 + 20*c**2 - 10*c + 2. Let t(g) = g**3 + g. Let x(a) = -15*t(a) + 5*y(a). Determine b, given that x(b) = 0.
2/9, 1
Let s be 3*-1 + 899/279. Factor 2/9*q**2 + s - 4/9*q.
2*(q - 1)**2/9
Let o = -3 + 6. Let d(c) be the first derivative of 2/3*c**o - 2 - 3/16*c**4 + 1/2*c - 7/8*c**2. Solve d(v) = 0 for v.
2/3, 1
Let m = 8 - 12. Let f = m - -7. Factor 4*l**2 + 2*l**f + 0*l**3 - 6*l**2.
2*l**2*(l - 1)
Factor 1/2*o - 1 + 1/2*o**2.
(o - 1)*(o + 2)/2
Let u(j) be the second derivative of 0*j**2 - 1/180*j**6 - 1/60*j**5 - 1/2*j**3 + 0 - j + 0*j**4. Let q(h) be the second derivative of u(h). Factor q(a).
-2*a*(a + 1)
Let s(t) = -t**2 - t - 1. Let x(v) = -4*v**4 + 8*v**3 + 2*v**2 + 6*v + 6. Let o(h) = -6*s(h) - x(h). Find k such that o(k) = 0.
0, 1
Let c(r) be the first derivative of -2*r**6/21 + 36*r**5/35 - 32*r**4/7 + 32*r**3/3 - 96*r**2/7 + 64*r/7 + 6. Suppose c(z) = 0. Calculate z.
1, 2
Solve 4/5*p**4 + 2/5*p**2 - 1/5*p + 7/5*p**3 + 0 = 0.
-1, 0, 1/4
Let m(u) = -9*u**2 + 12*u + 9. Let z(y) = -5*y**2 + 6*y + 4. Let x(c) = 4*m(c) - 9*z(c). Determine w so that x(w) = 0.
0, 2/3
Factor 96*z**3 + 4*z**4 - 4*z**2 - 96*z**3.
4*z**2*(z - 1)*(z + 1)
Let t(c) = 12*c**2 + 6*c - 8. Suppose f = 4 + 1. Let m be 20/6*15/f. Let x(b) = -b**2 - b + 1. Let j(l) = m*x(l) + t(l). Factor j(y).
2*(y - 1)**2
Let w(m) be the first derivative of 1/20*m**5 + 1/4*m + 2 - 1/8*m**4 + 1/24*m**6 - 1/6*m**3 + 1/8*m**2. What is t in w(t) = 0?
-1, 1
Let a(k) be the first derivative of 2/3*k**3 - 1/4*k**2 + 2 - 1/2*k**4 + 0*k. Solve a(z) = 0 for z.
0, 1/2
Find r, given that -1/2 - r**2 + 5/4*r + 1/4*r**3 = 0.
1, 2
Let n(h) = 2*h**2 - 2*h - 2. Let s be n(2). Factor -2*f**2 + 2*f**s + f**3 - f**5.
-f**3*(f - 1)*(f + 1)
Let o = -3 - -5. Solve 2*t**2 + 0*t**4 + 6*t**3 + o*t**4 + t**2 + t**4 = 0.
-1, 0
Suppose 10*b**2 - 7 + 3 - 4 - 5*b**3 + 5*b - 2 = 0. Calculate b.
-1, 1, 2
Let h be 21/(-3)*2*16/(-56). Suppose 0*m + 0 - 2/5*m**3 - 2/5*m**h + 4/5*m**2 = 0. What is m?
-2, 0, 1
Factor 9/4*n**3 + 3/4*n**2 + 0*n + 0 + 3/4*n**5 + 9/4*n**4.
3*n**2*(n + 1)**3/4
Let k(l) be the first derivative of -l**7/4200 - l**6/900 - l**5/600 - 5*l**3/3 + 2. Let r(n) be the third derivative of k(n). Factor r(y).
-y*(y + 1)**2/5
Suppose 4*x = 1 + 3. Suppose w - 5 = -x. Find d such that 3*d**2 + 12*d**w + 6*d**4 - 24*d**3 + 5*d**2 = 0.
0, 2/3
Suppose u = -4*k, 0 = 4*u - k - 4 - 13. Let c(b) be the first derivative of 0*b - 12/35*b**5 + 2 + 4/21*b**3 + 0*b**2 + 1/14*b**u. Solve c(f) = 0 for f.
-1/2, 0, 2/3
Let a be (6 - (-52)/(-9)) + 17/45. Factor 0*u + 0 - a*u**2 - 3/5*u**3.
-3*u**2*(u + 1)/5
Find t, given that 15*t - 5*t**2 + 4*t + 31*t - 125 = 0.
5
Let t be 9/(6 + -24)*0. Factor 0*v**4 - 2/3*v**5 - 2/3*v + t + 4/3*v**3 + 0*v**2.
-2*v*(v - 1)**2*(v + 1)**2/3
Let q(s) be the first derivative of s**6/8 + 3*s**5/20 - 3*s**4/16 - s**3/4 + 2. Determine i so that q(i) = 0.
-1, 0, 1
Let h(n) be the second derivative of n**4/6 + n**3/2 - 3*n**2/2 + 2*n. Let x(j) = -7*j**2 - 11*j + 11. Let w(d) = 22*h(d) + 6*x(d). Solve w(l) = 0 for l.
0
Let o(y) = -y**2 + 3*y + 1. Let j be o(2). Suppose -t**j + t**2 - 3*t + 2*t + t**4 - 2*t**4 + 2*t = 0. What is t?
-1, 0, 1
Let x(p) be the third derivative of -p**7/105 - 11*p**6/540 - p**5/135 + 4*p**2. Factor x(i).
-2*i**2*(i + 1)*(9*i + 2)/9
Suppose 5*a = 20, -m + 3*a = -2*m + 16. Let w(x) be the first derivative of -1 + 0*x**m + 0*x + 1/3*x**3 + 0*x**2 - 1/5*x**5. Suppose w(n) = 0. Calculate n.
-1, 0, 1
Let u(z) be the first derivative of -2/3*z**4 + 10/3*z**3 - 4 - 4*z**2 - 8/3*z. Suppose u(b) = 0. What is b?
-1/4, 2
Factor -26/5*y**2 + 22/5*y + 8/5*y**3 - 4/5.
2*(y - 2)*(y - 1)*(4*y - 1)/5
What is j in -2/5*j**3 + 0 - 6/5*j**4 + 4/5*j**2 + 0*j = 0?
-1, 0, 2/3
Let m(f) be the third derivative of 1/6*f**3 + 0 + 1/120*f**5 + 1/16*f**4 - 5*f**2 + 0*f. Solve m(y) = 0.
-2, -1
Let o(g) be the third derivative of g**8/112 + g**7/35 - g**5/10 - g**4/8 - 77*g**2. Factor o(a).
3*a*(a - 1)*(a + 1)**3
Let n = -1/437 - -885/4807. Factor 0 + 4/11*t + n*t**2.
2*t*(t + 2)/11
Let b(n) be the second derivative of -n**7/5040 - n**6/1440 - n**4/6 + n. Let c(y) be the third derivative of b(y). Factor c(m).
-m*(m + 1)/2
Let m(q) be the first derivative of q**3/24 - q**2/16 + 13. Let m(z) = 0. Calculate z.
0, 1
Let i(d) be the first derivative of -1/2*d**2 - 3 - 1/3*d**3 + 0*d. Determine j, given that i(j) = 0.
-1, 0
Factor 33*j**5 - 56*j**5 + 27*j**5 - 4*j**4.
4*j**4*(j - 1)
Let d = 35 - 40. Let t(m) = -3*m**3 + m**2 + 0*m**2 - 2*m**4 + 5 + 4*m**4. Let j(f) = -f**3 + f**2 + 1. Let o(s) = d*j(s) + t(s). Solve o(q) = 0.
-2, 0, 1
Let g = -1 - -4. Suppose -15 = -3*k - 4*v, 2*k - g*k + 5 = -4*v. Factor k*n**2 + 4 - n**2 + 4*n - 