) be the third derivative of p(f). Factor n(z).
-4*z**3*(z + 1)/3
Let x be 2/(-8)*(0 + 4 - 4). Factor x - 2/3*d**2 + 2/3*d.
-2*d*(d - 1)/3
Let g(d) be the third derivative of d**7/42 - d**6/12 - 7*d**5/12 - 5*d**4/6 + 3*d**2. Factor g(j).
5*j*(j - 4)*(j + 1)**2
Let u(b) be the second derivative of -b**4/8 + 3*b**3/4 - 3*b**2/2 - 18*b. Let u(x) = 0. What is x?
1, 2
Let k(y) be the second derivative of 0 + 0*y**2 - 1/720*y**6 + 1/2*y**3 + 0*y**5 - 3*y + 1/48*y**4. Let z(h) be the second derivative of k(h). Factor z(n).
-(n - 1)*(n + 1)/2
Let m(w) = -3*w - 12. Let n be m(-5). Factor 1/3*o**2 + 2/3*o - 8/3*o**n + 5/3*o**4 + 0.
o*(o - 1)**2*(5*o + 2)/3
Let p(h) be the second derivative of -1/12*h**3 - 1/24*h**4 + 0 - 2*h + 0*h**2. Suppose p(t) = 0. What is t?
-1, 0
Suppose 6*n = 14*n. Factor -2/3*d**3 - 2/9*d + 2/3*d**2 + n + 2/9*d**4.
2*d*(d - 1)**3/9
Let s be (4 - 1*9/2)*0. Let i(c) be the third derivative of s*c**3 + 1/120*c**6 + 4*c**2 + 0*c**4 + 0*c + 0 + 1/30*c**5. Factor i(y).
y**2*(y + 2)
Let x(p) be the second derivative of -p**6/15 - p**5/10 + p**4/2 + p**3/3 - 2*p**2 + 8*p. Let x(g) = 0. Calculate g.
-2, -1, 1
Let h(x) be the first derivative of 0*x**2 - 1/20*x**4 + 0*x - 1/15*x**3 - 3. Let h(m) = 0. Calculate m.
-1, 0
Factor -4/5*x**4 + 4/5*x**2 + 0 + 2/5*x + 0*x**3 - 2/5*x**5.
-2*x*(x - 1)*(x + 1)**3/5
Let g(x) = -5*x**3 + 35*x**2 - 35*x + 25. Let w(q) = 5*q**3 - 33*q**2 + 36*q - 24. Let b(o) = -4*g(o) - 5*w(o). Factor b(h).
-5*(h - 2)**2*(h - 1)
Suppose -4/7 + 4/7*w - 1/7*w**2 = 0. What is w?
2
Suppose 1 = 3*t + r, -4*t + 2 = -3*r - 8. Factor -9 + g**2 + t + 7.
(g - 1)*(g + 1)
Let t(i) be the third derivative of i**7/105 + i**6/180 + i**3/3 + 3*i**2. Let s(m) be the first derivative of t(m). Factor s(k).
2*k**2*(4*k + 1)
Suppose -2*d - 4 = -4*i, -3*d - 18 = -4*i - 8*d. Let s(f) be the second derivative of 0*f**2 - i*f - 1/90*f**5 + 1/27*f**3 + 0 + 0*f**4. Factor s(x).
-2*x*(x - 1)*(x + 1)/9
Let o(r) = r**3 + 10*r**2 + r + 12. Let a be o(-10). Solve 8*u**4 + a*u**2 + 0*u**5 + 3*u**3 + 4*u**3 + 3*u**5 = 0.
-1, -2/3, 0
Let x be (3/(-42))/(48/(-14)). Let v(f) be the second derivative of 0*f**2 + 0 + 1/24*f**3 + x*f**4 + 3*f. Factor v(j).
j*(j + 1)/4
Let i(f) be the third derivative of f**8/1344 - 17*f**7/840 + 47*f**6/240 - 19*f**5/24 + 161*f**4/96 - 49*f**3/24 + 6*f**2. Factor i(d).
(d - 7)**2*(d - 1)**3/4
Let y(v) be the first derivative of v**5 - 15*v**4/4 + 5*v**3 - 5*v**2/2 - 19. Factor y(o).
5*o*(o - 1)**3
Let f(c) be the third derivative of -c**6/30 - 2*c**5/15 - 4*c**2. Factor f(t).
-4*t**2*(t + 2)
Suppose 0 = 5*z - 4*t - 2, -3*t = 5*z - 4*z - 8. Let 0*m + 0*m**3 + 2/13*m**4 + 0 - 2/13*m**z = 0. What is m?
-1, 0, 1
Let d(z) be the second derivative of z**8/10080 + z**7/1680 + z**6/720 + z**5/720 + z**3/6 - 2*z. Let m(b) be the second derivative of d(b). Factor m(v).
v*(v + 1)**3/6
Let s be 28/10 + -3 + (-78)/(-15). Let f(q) be the second derivative of 0*q**2 + 0*q**s + 0 + 1/75*q**6 - q + 0*q**3 - 1/30*q**4. Factor f(r).
2*r**2*(r - 1)*(r + 1)/5
Let u be ((-1 - (-3)/3)/(-2))/(-1). Factor u + 3/2*r**2 - 1/2*r.
r*(3*r - 1)/2
Suppose -w = -2 + 10. Let h be w/3*72/(-224). Suppose h*c + 2/7*c**2 + 4/7 = 0. Calculate c.
-2, -1
Let g be (-6 + 2 - -2)*(-6 - -4). Let k(o) be the first derivative of -5/6*o**3 + 2 - 2*o**2 - 1/8*o**g - 2*o. Determine f, given that k(f) = 0.
-2, -1
Let i(u) be the third derivative of u**6/300 + u**5/150 - u**4/12 + u**3/5 + 2*u**2 + 6*u. Factor i(r).
2*(r - 1)**2*(r + 3)/5
Let d = 325 - 325. Find n such that 0*n - 3/4*n**4 - 3*n**2 + d - 3*n**3 = 0.
-2, 0
Find n such that -n**2 + 0 + 0*n**2 + 1 - 4*n - 4 = 0.
-3, -1
Factor -2/13*n**5 + 6/13*n**2 + 0*n + 10/13*n**4 - 14/13*n**3 + 0.
-2*n**2*(n - 3)*(n - 1)**2/13
Suppose -3*d + 6*d = 12. Let m(y) be the third derivative of -2/15*y**3 + 5*y**2 - 1/150*y**5 + 0 + 1/20*y**d + 0*y. Factor m(c).
-2*(c - 2)*(c - 1)/5
Let s(q) be the second derivative of q**4/84 - q**2/14 + 7*q. Factor s(f).
(f - 1)*(f + 1)/7
Factor 243/5*y**3 - 12/5 - 351/5*y**2 + 24*y.
3*(y - 1)*(9*y - 2)**2/5
Let p be -3 + 7 - (-1 + 2). Let c(l) be the first derivative of -1/12*l**p + 1/4*l + 0*l**2 - 1. Factor c(f).
-(f - 1)*(f + 1)/4
Let w be 11/3 - 18/6. Solve 4/3 - w*a**2 - 2/3*a = 0 for a.
-2, 1
Suppose 39 = 3*a - 2*d, 8 = -2*d + 2. Let t = -6 + a. Suppose -r**t - 5*r - 3*r**3 + 6*r**3 - r**3 + 4*r = 0. What is r?
-1, 0, 1
Let w(a) be the second derivative of -a**6/50 - 3*a**5/25 - a**4/4 - a**3/5 + 16*a. Factor w(p).
-3*p*(p + 1)**2*(p + 2)/5
Let a(d) be the third derivative of -d**7/105 - d**6/20 - d**5/15 - 6*d**2. Solve a(i) = 0.
-2, -1, 0
Factor 0 - 2/3*y**3 - 2/3*y**2 + 4*y.
-2*y*(y - 2)*(y + 3)/3
Let i = -38 - -115/3. Let -1/3*r + i*r**2 + 1/3*r**3 - 1/3 = 0. What is r?
-1, 1
Let g = 8 + -15/2. Let x(n) be the first derivative of 2/3*n**3 + 0*n + n**2 + 2 - g*n**4 - 2/5*n**5. What is t in x(t) = 0?
-1, 0, 1
Let t(m) be the first derivative of -2/27*m**3 + 2/9*m - 1/18*m**4 - 4 + 1/9*m**2. Let t(a) = 0. What is a?
-1, 1
Let j(y) be the third derivative of y**7/420 + y**6/80 - y**4/12 - 6*y**2. What is g in j(g) = 0?
-2, 0, 1
Factor 3/2*w**2 + 0*w + 0.
3*w**2/2
Let h(j) = j**3 - 5*j**2 - 8*j + 14. Let b be h(6). Let v(g) be the first derivative of g**b - 1/3*g**3 + 2 - g. Determine z so that v(z) = 0.
1
Let w(a) be the third derivative of a**5/540 + a**4/72 + a**3/27 + 8*a**2. Determine o, given that w(o) = 0.
-2, -1
Let m(n) = n**3 + 5*n**2 - 6*n + 5. Let k be m(-6). Suppose k*d - 5 = 5. Factor z**5 + 0 + 0 - 5*z**2 + 4*z**d + 3*z**3 - 3*z**4.
z**2*(z - 1)**3
Factor 11*r**2 + 59*r**2 + 44*r**3 + 10*r**4 + 10 - 4*r**2 + 40*r - 2.
2*(r + 1)**2*(r + 2)*(5*r + 2)
Determine w, given that -2/11*w**2 - 4/11*w - 2/11 = 0.
-1
Find a, given that 0 + 4/11*a**2 + 2/11*a**3 - 6/11*a = 0.
-3, 0, 1
Suppose -5*m + 9 + 71 = 0. Suppose 4*p = 4 + m. Suppose -3*g**5 + 5*g**5 + 2*g**3 + 5*g**4 + g**2 - 1 - 4*g - p*g**2 = 0. Calculate g.
-1, -1/2, 1
Let f(p) be the second derivative of 0 + 5*p + 2/15*p**3 + 0*p**2 + 2/15*p**4 + 1/20*p**5 + 1/150*p**6. What is w in f(w) = 0?
-2, -1, 0
Let z = -69 + 69. Let p(s) be the first derivative of 0*s + 4 - 1/21*s**6 - 4/21*s**3 + 4/35*s**5 + z*s**2 + 1/14*s**4. Let p(u) = 0. What is u?
-1, 0, 1, 2
Find u such that -18 + 46*u**3 + 14 + 26*u + 8 + 14*u**4 + 35*u**2 + 19*u**2 = 0.
-1, -2/7
Factor 0*j**5 + 9*j + 2*j**3 - 10*j**3 + 2*j**2 - 6*j**4 + j**5 - 2*j**5 + 4.
-(j - 1)*(j + 1)**3*(j + 4)
Suppose -m + 2 = 2*l + 1, 5*l + 5*m - 5 = 0. Find v, given that l*v + 1/2*v**3 + 1/4 - 3/4*v**2 = 0.
-1/2, 1
Factor -22*k + 3*k**3 - 16*k + 35*k.
3*k*(k - 1)*(k + 1)
Let q(k) be the third derivative of 27*k**7/560 - k**6/20 + k**5/60 + k**3/3 + 3*k**2. Let b(j) be the first derivative of q(j). Factor b(w).
w*(9*w - 2)**2/2
Let y(o) be the third derivative of o**5/30 + o**4/3 - 5*o**3/3 - 3*o**2. Determine v, given that y(v) = 0.
-5, 1
Factor 4*g + 3*g**2 + 4*g - 3*g + 3 + g.
3*(g + 1)**2
Let f(z) = -2*z**5 - 6*z**4 + 10*z**3 + 6*z**2 + 4*z + 6. Let l(p) = -p**4 + p**3 + p**2 + p + 1. Let r(j) = -2*f(j) + 12*l(j). Let r(n) = 0. Calculate n.
-1, 0, 1
Let d(j) be the second derivative of -1/240*j**5 - 1/2*j**2 + 1/24*j**4 - 1/8*j**3 + 3*j + 0. Let l(x) be the first derivative of d(x). Factor l(p).
-(p - 3)*(p - 1)/4
Let u(a) be the first derivative of a**4 + 4*a**3 + 6*a**2 + 4*a - 4. Solve u(f) = 0 for f.
-1
Suppose -5*l + 2*t + 8 = 0, 5*l - 2*t - t = 12. Let x(v) be the second derivative of -1/30*v**4 + 2*v + 0*v**3 + 0 + 1/75*v**6 + l*v**5 + 0*v**2. Factor x(n).
2*n**2*(n - 1)*(n + 1)/5
Suppose -4*p + 8*p = -8. Let x be (2 + -4)*(p - -1). Find n such that 4*n**3 - 3*n**2 - x*n**3 + 2*n**2 = 0.
0, 1/2
Let l(s) be the second derivative of s**7/8820 + s**6/2520 + s**4/4 - 2*s. Let y(p) be the third derivative of l(p). Factor y(g).
2*g*(g + 1)/7
Let j(c) = -2*c**2 - 9*c + 5. Let t(w) = w**2 + 8*w - 4. Let o(x) = 2*j(x) + 3*t(x). Let f be o(5). Factor f - l**2 + l - l**3 - 4 + 2.
-(l - 1)*(l + 1)**2
Let x(k) be the first derivative of k**8/168 - 4*k**7/315 - k**6/45 - k**2/2 - 1. Let h(w) be the second derivative of x(w). Find m such that h(m) = 0.
-2/3, 0, 2
Let l(j) = j**2 + j. Let f(g) = 10*g**2 + 5*g + 3. Let o(c) = -2*f(c) + 18*l(c). Solve o(a) = 0 for a.
1, 3
Let y = -427/6 - 