derivative of 1/540*p**6 + 0*p**2 + 1/90*p**5 - 1/3*p**3 + 0*p**4 + 0*p - 2. Let f(a) be the third derivative of z(a). Factor f(y).
2*y*(y + 2)/3
Let x = -41/3 + 14. Let u(k) be the third derivative of 0*k + 0 + x*k**3 + k**2 + 1/6*k**4 + 1/30*k**5. What is n in u(n) = 0?
-1
Let k(c) be the first derivative of c**2 - 4/3*c - 2/9*c**3 - 4. Solve k(t) = 0 for t.
1, 2
Suppose -4*f = -36 + 24. Let 3/2*y + 1/2*y**f - 3/2*y**2 - 1/2 = 0. What is y?
1
Let v be (40/12*-1)/(-2). Let x = 2 + 3. Find q such that 8/3*q**4 - 1/3 + v*q - 4/3*q**x - 1/3*q**3 - 7/3*q**2 = 0.
-1, 1/2, 1
Suppose 0 = -x - 5 - 31. Let b be 3*-2*3/x. Factor -1/2*m + m**3 - 1/2*m**4 - b - 1/2*m**5 + m**2.
-(m - 1)**2*(m + 1)**3/2
Suppose -4*q + 17 = 5. Determine s so that -s**3 + 6*s - 5*s + 2*s**2 + 2*s**q = 0.
-1, 0
Let c(v) be the first derivative of -3*v**5/5 - 3*v**4/2 + v**3 + 3*v**2 + 38. Let c(r) = 0. Calculate r.
-2, -1, 0, 1
Suppose 5*p - 13 - 2 = 0. Factor -n + 0 + 1 - 1 + n**p.
n*(n - 1)*(n + 1)
Suppose 0 = -5*n - 2*y - 0*y, 2*n + 5*y = -21. Let m(z) be the first derivative of -1/15*z**3 - 1/5*z - 2 - 1/5*z**n. Factor m(g).
-(g + 1)**2/5
Let v = 129 + -257/2. Let 1/2*r**3 + 0 + 0*r + 0*r**2 - v*r**4 = 0. Calculate r.
0, 1
Suppose s - 7 = -3*s - 3*h, -5*s + 17 = h. Factor -1/4*y**2 + 0 + 1/4*y**s - 1/4*y + 1/4*y**3.
y*(y - 1)*(y + 1)**2/4
Let i(v) be the second derivative of v**6/36 + 3*v**5/20 + 17*v**4/72 - v**2/3 + 30*v. Factor i(y).
(y + 1)**2*(y + 2)*(5*y - 2)/6
What is f in 0 - f**3 - 3/2*f - 13/2*f**2 + 4*f**4 = 0?
-1, -1/4, 0, 3/2
Let y(n) = -4*n**4 - 12*n**3 - 16*n**2 - 8*n + 2. Let i(b) = 5*b**4 + 13*b**3 + 16*b**2 + 8*b - 3. Let w(v) = -2*i(v) - 3*y(v). Solve w(h) = 0.
-2, -1, 0
Let a be -6*6/(-9)*1. Suppose 3*n = 2 + a. Determine u so that 0*u**2 + u**3 - 2*u**3 - u**n = 0.
-1, 0
Factor 2*i**4 - i**4 + 0*i**3 - 3*i**3 + i**5 - i**2 + 2*i**3.
i**2*(i - 1)*(i + 1)**2
Let p(m) be the second derivative of 6*m + 0*m**2 + 0 + 1/26*m**4 + 1/130*m**5 + 0*m**3. Determine q so that p(q) = 0.
-3, 0
Let m = 454 + -452. Factor -2/7*x + 4/7*x**3 + 0 - 2/7*x**5 + 0*x**4 + 0*x**m.
-2*x*(x - 1)**2*(x + 1)**2/7
Let t be 56/90 - (-4)/(-10). Let c(s) be the first derivative of 2/3*s**2 - 1 - t*s**3 - 2/3*s. Factor c(n).
-2*(n - 1)**2/3
Let v(p) be the second derivative of 25*p**4/12 + 5*p**3/6 + 37*p. Determine x so that v(x) = 0.
-1/5, 0
Let p(h) be the first derivative of 1/9*h**3 + 1/6*h**2 - 2/3*h + 2. Factor p(c).
(c - 1)*(c + 2)/3
Let m(u) be the first derivative of -u**5/30 - u**4/12 - u**2/2 + 2. Let q(c) be the second derivative of m(c). Solve q(a) = 0 for a.
-1, 0
Let u(n) be the third derivative of -n**6/24 + n**5/2 - 5*n**4/2 + 20*n**3/3 + 14*n**2. Let u(w) = 0. Calculate w.
2
Let m be (-1)/(-11) + (-26)/(-198). Factor 0*w + 2/9 - m*w**2.
-2*(w - 1)*(w + 1)/9
Suppose 2*l + 2*h + 2 = 0, -6*h = 3*l - 2*h + 8. Let -3*k**3 - k**l + 2*k + 0*k**3 + k**5 + 0*k**4 - k**2 + 2*k**4 = 0. Calculate k.
-2, -1, 0, 1
Factor -147*d**2 + 127*d - 3 - 24 + 12*d - 13*d.
-3*(7*d - 3)**2
Let y = -2 + 7. Let j be (-1 - -4) + (-8)/(-4). Factor -2*n**y + n**3 + n**j - n**4 + n**2 + 0*n**4.
-n**2*(n - 1)*(n + 1)**2
Let m(a) = a + 1. Let n(t) = -t**2 - 2*t - 7. Let w(d) = 35*m(d) + 5*n(d). Let w(i) = 0. What is i?
0, 5
Let g(l) = -1 - l + 2 + 7. Let s be g(6). Factor -4*c**s + 3*c - 2*c - 2 + 6*c - 2*c + c**3.
(c - 2)*(c - 1)**2
Let b(f) = f**2. Let g be b(-2). Suppose w = 3*w - 10. Factor 13/4*s**g + 9/4*s**3 - 1/4*s**2 + 0 + 5/4*s**w - 1/2*s.
s*(s + 1)**3*(5*s - 2)/4
Factor 2*r**2 + 4*r**3 + 2*r**2 - 4*r + 0*r - 67*r**4 + 63*r**4.
-4*r*(r - 1)**2*(r + 1)
Let w(c) be the first derivative of c**4 - 12*c**3 + 48*c**2 - 64*c + 54. Solve w(l) = 0 for l.
1, 4
Let g be (16/(-12))/(10*(-2)/6). Factor 1/5*s + g - 1/5*s**2.
-(s - 2)*(s + 1)/5
Let 10/7*a**2 + 5/7*a**4 + 5/7*a + 10/7*a**3 + 1/7*a**5 + 1/7 = 0. Calculate a.
-1
Let w be 16/14 + (-26)/91. Factor w*i**2 + 6/7*i**3 - 9/7*i + 3/7 - 9/7*i**4 + 3/7*i**5.
3*(i - 1)**4*(i + 1)/7
Let r(o) be the third derivative of 2*o**7/105 - 2*o**5/5 + 4*o**4/3 - 2*o**3 + 3*o**2. Factor r(i).
4*(i - 1)**3*(i + 3)
Suppose 5*j = 2*j + 12. Factor 12*u**3 - j*u**2 - 1 + 2 - 2*u + 0*u**2 - 7*u**2.
(u - 1)*(3*u + 1)*(4*u - 1)
Factor 0 - 2/15*x**3 + 0*x + 2/15*x**2.
-2*x**2*(x - 1)/15
Let g(s) be the second derivative of -1/36*s**3 + 6*s + 1/72*s**4 - 1/12*s**2 + 0 + 1/120*s**5. Solve g(f) = 0.
-1, 1
Let c(t) = -t + 9. Let z be c(6). Determine d so that -d + d**2 + 1 + 4*d + d**z + 2*d**2 = 0.
-1
Let o(g) be the third derivative of g**8/2016 - g**7/315 + g**6/180 + g**2 + 14. Factor o(a).
a**3*(a - 2)**2/6
Suppose 4 - 22 = -6*x. Factor 0 - 22/9*p**2 - 4/9*p - 28/9*p**x.
-2*p*(2*p + 1)*(7*p + 2)/9
Let -40*h - 22*h**4 - 2*h**3 - 60*h**2 + 43*h**3 - 3*h**4 + 49*h**3 = 0. Calculate h.
-2/5, 0, 2
Let o(w) = 15*w**2 + 15*w. Let k(y) = -y**2 - y. Let m(f) = -20*k(f) - o(f). Factor m(b).
5*b*(b + 1)
Let w(d) be the second derivative of 3*d + 0 - 2/3*d**2 - 1/9*d**3 + 1/18*d**4. Find n, given that w(n) = 0.
-1, 2
Let n = 6447 + -489965/76. Let f = n - -3/19. Factor -3/4*o + f*o**2 + 1/2.
(o - 2)*(o - 1)/4
Let a(u) be the first derivative of 3 - 6/7*u + 1/7*u**3 - 3/14*u**2. Factor a(m).
3*(m - 2)*(m + 1)/7
Factor 2/11*j**2 - 2/11*j**3 + 2/11*j - 2/11.
-2*(j - 1)**2*(j + 1)/11
Factor 8 + 2*k**2 - k - 4*k**4 + 3*k**3 - 8 - 4*k**5.
-k*(k + 1)**2*(2*k - 1)**2
Let o(p) = p**5 + p**4 + 2*p**3 + 2*p**2 - 3*p. Let u(y) = 2*y**5 + 3*y**4 + 5*y**3 + 4*y**2 - 7*y. Let m(g) = -7*o(g) + 3*u(g). Solve m(w) = 0 for w.
-1, 0, 1, 2
Suppose -3*c + 5*o - 31 = 0, 2*o - 24 + 6 = 4*c. Let a = c - -2. Determine q, given that q**3 + q**2 - 2*q**3 + a*q**3 = 0.
0, 1
Factor 0*n**2 - 2/7*n**4 - 4/7*n**3 + 4/7*n + 2/7.
-2*(n - 1)*(n + 1)**3/7
Let r be 0 + 1 + 1 + -2. Let j = r - -1. Let h(n) = n**2 - n + 2. Let z(f) = f**2 + 1. Let g(i) = j*h(i) - 2*z(i). Factor g(s).
-s*(s + 1)
Let u be ((-90)/(-35))/3*(-14)/(-3). Let o(y) be the second derivative of -1/18*y**3 + 0 + 1/24*y**u + 1/10*y**5 + 0*y**2 - y + 7/180*y**6. Factor o(w).
w*(w + 1)**2*(7*w - 2)/6
Let p(f) be the first derivative of f**6/63 - 4*f**5/105 - f**4/42 + 4*f**3/63 - 38. What is s in p(s) = 0?
-1, 0, 1, 2
Let r(o) = -o**3 - 7*o**2 - 8*o - 8. Let f be r(-6). Suppose -g + 1 = -1, 2*t = f*g. Find z such that t + 4*z**2 + z**2 + 6*z**2 - 10*z**2 + 4*z = 0.
-2
Let a(h) be the second derivative of -2*h + 0 + 0*h**3 + 0*h**4 + 0*h**2 + 1/20*h**5. What is i in a(i) = 0?
0
Let u(k) = -3*k**2 + 6*k - 3. Let z(r) = -1 - 3 + 3 - r. Let a be z(3). Let m(t) = 8*t**2 - 17*t + 8. Let g(i) = a*m(i) - 11*u(i). Factor g(c).
(c + 1)**2
Let r = -7 + 7. Let c(y) be the first derivative of -4/9*y**3 - 1 + r*y**2 - 7/6*y**4 - 2/3*y**5 + 0*y. Solve c(w) = 0.
-1, -2/5, 0
Let z(y) be the third derivative of y**6/360 + y**5/60 + y**4/24 + y**3/18 + 3*y**2. What is w in z(w) = 0?
-1
Let -1/8*g**5 - 80*g**2 - 160*g - 20*g**3 - 128 - 5/2*g**4 = 0. What is g?
-4
Suppose 0 = 2*b - 19 - 5. Let i(a) = 2*a - 19. Let s be i(b). Factor 0*p + 0*p**2 + 1/4*p**4 + 1/2*p**3 - 1/4*p**s + 0.
-p**3*(p - 2)*(p + 1)/4
Let f(o) be the first derivative of o**4/5 - 2*o**2/5 + 10. Suppose f(a) = 0. What is a?
-1, 0, 1
Suppose 8 = -a - 5*r, -4*a = a + 5*r. Let b(g) be the second derivative of 0*g**a + 1/90*g**5 + 0*g**3 + 1/54*g**4 + 2*g + 0. Factor b(p).
2*p**2*(p + 1)/9
Let i be (16/(-50))/(6/(-15)). Factor 2/5 + 2/5*w**2 - i*w.
2*(w - 1)**2/5
Let v(r) be the second derivative of -r**9/11760 - r**8/1960 - r**7/1470 + r**4/2 + 4*r. Let q(m) be the third derivative of v(m). Let q(d) = 0. What is d?
-2, -2/3, 0
Suppose -2*b = y + 3, 21 = y - 0*b - 4*b. Let u(v) be the second derivative of 0*v**2 - 1/20*v**y + 3*v + 0 + 0*v**3 - 1/12*v**4. Determine w so that u(w) = 0.
-1, 0
Let x(r) be the third derivative of -r**6/30 - r**5/15 + 5*r**4/6 - 2*r**3 + 3*r**2. Find a, given that x(a) = 0.
-3, 1
Factor -8/11*c - 1/11*c**2 - 16/11.
-(c + 4)**2/11
Determine d, given that -2*d - 2/3*d**3 + 2*d**2 + 2/3 = 0.
1
Determine o, given that 1/4*o**3 + 0*o + 0 - 1/2*o**2 = 0.
0, 2
Factor -1/4*u + 1/2 - 1/4*u**2.
-(u - 1)*(u + 2)/4
Suppose 2*c + 3*g = -3, -4*c - 4 = 5*g + 1. Suppose 4/3*x**4 + 0*x + c*x**2 + 2/3*x**5 + 2/3*x**3 + 0 = 0. Calculate x.
-1, 0
Factor -86*a**4 + 39*a**4 + 45*a**4 - 4*a**3 - 