 u**4/42 - u**3/42 - 2*u. Factor n(k).
-k*(k + 1)**2/7
Let k(l) be the second derivative of 0 + 4/27*l**3 - 1/54*l**4 - 4/9*l**2 - 3*l. Factor k(m).
-2*(m - 2)**2/9
Let p(q) = q**5 - q**4 - q**3 - q**2 + q. Let u(w) = 4*w**5 - 16*w**4 - 22*w**3 - 14*w**2 + 6*w. Let k(t) = 6*p(t) - u(t). Suppose k(d) = 0. What is d?
-2, -1, 0
Let g(h) = 6*h**2 + 17*h. Let d(n) = 2*n**2 + 6*n. Suppose 4*l = 5*l + 6. Let b(p) = l*g(p) + 17*d(p). Factor b(w).
-2*w**2
Factor 12/11*u**2 + 0 + 0*u + 18/11*u**3 - 6/11*u**5 + 0*u**4.
-6*u**2*(u - 2)*(u + 1)**2/11
Let u be (-7)/((5 - 2)/(-9)). Solve 40 - 6*o**2 - 40 + 12*o**4 - u*o**3 = 0.
-1/4, 0, 2
Let u(z) be the second derivative of 2*z**6/15 + z**5/40 - z**4/3 - z**3/12 + 2*z + 4. Factor u(c).
c*(c - 1)*(c + 1)*(8*c + 1)/2
Suppose 13 - 29 = -8*z. Solve -2/5*y**z + 0 - 4/5*y = 0.
-2, 0
Let t(p) be the first derivative of -p**6/180 + p**4/36 + p**2 + 3. Let m(g) be the second derivative of t(g). Factor m(u).
-2*u*(u - 1)*(u + 1)/3
Suppose -6 = -12*m + 14*m - 3*k, m + 2*k = 11. Let p be (-1)/(-2)*(-8)/(-5). Factor 2/5*f**m + p*f**2 + 0 + 2/5*f.
2*f*(f + 1)**2/5
Let o(b) be the second derivative of b**6/20 - 3*b**5/40 - 9*b**4/8 - 11*b**3/4 - 3*b**2 - 11*b. Factor o(g).
3*(g - 4)*(g + 1)**3/2
Let s(r) = 6*r**3 + 6*r**2. Let z(i) = i**3 + i**2 + i + 1. Let j(w) = -s(w) + 3*z(w). Let j(a) = 0. Calculate a.
-1, 1
Let u be 6 + 1*((-6)/3 - 1). Let d(n) be the first derivative of 0*n**2 + 1/3*n**3 + 0*n - u. Factor d(p).
p**2
Factor 0*g**2 + 3/5*g**5 + 0 - 6/5*g**4 + 0*g + 0*g**3.
3*g**4*(g - 2)/5
Factor -22/7*i**3 - 2/7 - 2/7*i + 18/7*i**2 + 8/7*i**4.
2*(i - 1)**3*(4*i + 1)/7
Find t, given that 4/9*t**3 + 0 - 4/9*t**4 - 16/9*t + 16/9*t**2 = 0.
-2, 0, 1, 2
Let z(v) = 1. Let y = 3 - 1. Suppose -t - 6 = y*t. Let a(w) = -w**4 - 2*w**3 - w**2 - 1. Let u(d) = t*z(d) - 2*a(d). What is r in u(r) = 0?
-1, 0
Let w be 6/(-4)*(6/9 + -1). Let c = -1 + 1. Factor c + w*j**2 - 1/2*j.
j*(j - 1)/2
Factor 3*x**2 + 1/2 + 7/2*x.
(x + 1)*(6*x + 1)/2
Let f(o) be the first derivative of o**6/27 - 4*o**5/45 - o**4/6 + 8*o**3/27 + 4*o**2/9 + 45. Factor f(a).
2*a*(a - 2)**2*(a + 1)**2/9
Suppose 10 = -2*r, 5*n - n + 138 = -2*r. Let v be (n/120)/((-12)/10). Factor 0*x**2 + 0 - 2/9*x**3 + v*x.
-2*x*(x - 1)*(x + 1)/9
Let u(o) be the first derivative of o**3/8 - 3*o**2/8 + 3*o/8 + 5. Factor u(a).
3*(a - 1)**2/8
Suppose 13*x - 31 - 8 = 0. Factor 5/2*r - 3/2*r**2 - 1/2*r**x - 1 + 1/2*r**4.
(r - 1)**3*(r + 2)/2
Solve -1/6*b**5 + 0*b**2 + 0 + 0*b + 1/3*b**4 + 0*b**3 = 0.
0, 2
Let k(r) be the third derivative of r**5/330 + 5*r**4/66 + 25*r**3/33 + r**2 - 4*r. Suppose k(x) = 0. What is x?
-5
Let d(y) be the third derivative of -y**8/504 - y**7/315 + y**6/180 + y**5/90 + 2*y**2. Let d(l) = 0. Calculate l.
-1, 0, 1
Let h(o) be the third derivative of -3*o**2 + 0*o**3 - 1/420*o**6 - 1/210*o**5 + 0*o**4 + 0 + 1/1176*o**8 + 0*o + 1/735*o**7. Find s such that h(s) = 0.
-1, 0, 1
Suppose 10*r = 7*r. Let n(c) be the second derivative of 0 - 1/10*c**3 + r*c**2 + 1/20*c**4 + c. Factor n(o).
3*o*(o - 1)/5
Let c(j) be the first derivative of j**5/5 + j**4/2 - 4*j**3/3 - 4*j**2 - 3. Factor c(b).
b*(b - 2)*(b + 2)**2
Let x(c) be the second derivative of -8*c**6/45 - 2*c**5/3 - 11*c**4/12 - 5*c**3/9 - c**2/6 - 16*c. Suppose x(d) = 0. Calculate d.
-1, -1/4
Factor 1/4*f**2 - 1/4 - 1/4*f**3 + 1/4*f.
-(f - 1)**2*(f + 1)/4
Let g = -170 - -172. Factor 1/2*j**g - 1 - 1/2*j.
(j - 2)*(j + 1)/2
Let q(k) = -k**2 - k + 1. Let r(a) be the third derivative of a**5/15 + a**4/4 + 2*a**2. Let b(u) = 2*q(u) + r(u). Factor b(o).
2*(o + 1)**2
Suppose -2*r - 3 - 15 = 0. Let h(f) = 3*f**2 + 2. Let u(j) = -13*j**2 + j - 9. Let m(x) = r*h(x) - 2*u(x). Solve m(p) = 0 for p.
-2, 0
Let k(b) be the second derivative of -b**6/90 + b**4/18 - b**2/6 + 3*b. Determine y, given that k(y) = 0.
-1, 1
Let o(m) = 8*m**2 - 2*m + 1. Suppose -5*k + 40 = -0*k + 5*i, k + 3*i = 18. Let x(w) = -w**2. Let q(p) = k*o(p) + 21*x(p). Factor q(f).
3*(f - 1)**2
Let q(x) be the third derivative of -x**7/840 - x**6/120 - x**4/24 + 4*x**2. Let u(b) be the second derivative of q(b). Find z such that u(z) = 0.
-2, 0
Let q(b) = -14*b**2 - 24*b + 3. Let d(o) = 8*o**2 + 12*o - 2. Let n(g) = -13*d(g) - 6*q(g). Suppose n(a) = 0. What is a?
-1, 2/5
Let d(t) = t**3 - 26*t**2 + 2*t - 52. Let a be d(26). Factor 0*n - 1/6*n**2 + 0 + 1/6*n**4 + a*n**3.
n**2*(n - 1)*(n + 1)/6
Suppose 5*d - 19 = -0*b + 3*b, -b - 5*d + 27 = 0. Solve 1/4*l + 0*l**b + 0 - 1/4*l**3 = 0.
-1, 0, 1
Factor -4*c**2 + 88*c - 86*c + 4*c**3 - 5*c**2.
c*(c - 2)*(4*c - 1)
What is o in 9 - 3*o**2 + 3 - 2*o**2 + 8 = 0?
-2, 2
Let p(c) = 11*c**2 + 41*c - 7. Let w(a) be the first derivative of -4*a**3/3 - 7*a**2 + 2*a + 2. Let t = 9 - 26. Let f(k) = t*w(k) - 6*p(k). Factor f(l).
2*(l - 2)**2
Let p(g) be the third derivative of -g**5/240 + g**3/6 + 8*g**2. Let p(l) = 0. Calculate l.
-2, 2
Let z = -5 - -1. Let t(p) = -p**2 - 4*p - 4. Let n(v) be the second derivative of -v**4/12 - v**3/2 - 3*v**2/2 + 4*v. Let y(g) = z*n(g) + 3*t(g). Factor y(r).
r**2
Let j(b) be the second derivative of 2*b + 1/12*b**4 + 1/2*b**2 + 1/3*b**3 + 0. Factor j(o).
(o + 1)**2
Let l = -13 + 15. Let a(j) be the second derivative of 0*j**3 + 2*j + 1/20*j**5 + 0*j**l + 0 + 1/15*j**6 + 1/42*j**7 + 0*j**4. Factor a(v).
v**3*(v + 1)**2
Let l be (10/(-6))/(3/(-27)). Suppose 0 = 4*f - f - l. Factor -5*y - 3*y**3 + f - 2 + 7*y**2 - 2.
-(y - 1)**2*(3*y - 1)
Suppose -14*j + 12*j = l - 7, 3*j - 13 = -4*l. Suppose 0*w**2 + 2/3*w**4 - 4/3*w**5 + 2/3*w**j + 0*w + 0 = 0. Calculate w.
-1/2, 0, 1
Let a be (-1)/2 - 14/(-4). Let v(i) be the second derivative of 7/15*i**a + 0 + 1/3*i**4 - 9/25*i**6 + 9/35*i**7 - 9/25*i**5 + 1/5*i**2 - i. Factor v(j).
2*(j - 1)**2*(3*j + 1)**3/5
Let h(q) be the second derivative of 7*q**6/75 + 8*q**5/25 + 11*q**4/30 + 2*q**3/15 - 29*q. Solve h(z) = 0.
-1, -2/7, 0
Let a(h) = -3*h**3 + 3*h**2 - h + 5. Let b(v) = 5*v**3 - 5*v**2 + 2*v - 9. Let m = -6 + -1. Let c(y) = m*a(y) - 4*b(y). Let c(f) = 0. What is f?
-1, 1
Let o(g) be the third derivative of 0 - 2/35*g**7 - 1/40*g**5 + 1/64*g**8 + 11/160*g**6 + 0*g**4 + 0*g**3 + 0*g - 3*g**2. Factor o(t).
3*t**2*(t - 1)**2*(7*t - 2)/4
Let t(z) be the second derivative of -1/5*z**2 + 1/60*z**4 - 1/30*z**3 + 0 + 2*z. Determine x so that t(x) = 0.
-1, 2
Let b(q) be the second derivative of -q**9/12096 - q**8/6720 - q**3/2 - 6*q. Let w(y) be the second derivative of b(y). Solve w(h) = 0.
-1, 0
Let t(y) be the second derivative of -y**7/2100 + y**5/100 - y**4/30 - y**3/2 + 4*y. Let z(x) be the second derivative of t(x). Factor z(d).
-2*(d - 1)**2*(d + 2)/5
Let p be ((-17)/10 - (-3)/15) + 3. Suppose -3*h + p*h**2 + 3/2 = 0. Calculate h.
1
Let k(p) be the first derivative of -p**6/720 - p**5/120 - p**4/48 - p**3 + 9. Let m(r) be the third derivative of k(r). Factor m(b).
-(b + 1)**2/2
Let s(c) be the first derivative of 2*c**3/63 + 4*c**2/21 + 2*c/7 + 30. Factor s(l).
2*(l + 1)*(l + 3)/21
Suppose b - 5*b - 28 = 4*l, 0 = 5*b - 4*l - 10. Let z be (1*b/(-4))/2. Factor 0*u - z + 1/4*u**2.
(u - 1)*(u + 1)/4
Suppose 2*s = -3*k + 21, -3*s + 12 = s. Let w = 5 - k. Determine z, given that 0*z + 2/11*z**2 + w = 0.
0
Let p be -2*((-44)/20 - -2). Let b(s) = s**3 + 6*s**2 - 6*s + 9. Let o be b(-7). Determine h so that 0*h**3 + 0*h**o + 0 - 2/5*h**5 + 0*h - p*h**4 = 0.
-1, 0
Let y be 72/60 - 12/(-15). Solve 1/3 - 40/3*j**3 - 10/3*j + 11*j**y + 16/3*j**4 = 0.
1/4, 1
Let f = 2/171 - -9224/855. Determine z so that f - 108/5*z + 72/5*z**2 - 16/5*z**3 = 0.
3/2
Let i be -5*(-1 + 6 + 0). Let c be (3/(-6))/(i/10). Factor 0*u + c*u**3 - 1/5*u**4 + 0 + 0*u**2.
-u**3*(u - 1)/5
Let l be -12*((-5)/3)/5. Solve 4*a + 3*a - 2*a**l + 6*a**2 - 3*a = 0 for a.
-1, 0, 2
Suppose 3*k**2 - 7/3*k**3 + 2/3*k**4 - 5/3*k + 1/3 = 0. What is k?
1/2, 1
Factor -25/3 - 20/3*y**2 - 35*y.
-5*(y + 5)*(4*y + 1)/3
Factor 6*u + 2*u**4 - 5*u**4 + 22*u**2 - 13*u**2.
-3*u*(u - 2)*(u + 1)**2
Let z(k) be the third derivative of -11*k**7/42 - 35*k**6/24 - 7*k**5/3 - 5*k**4/6 + 4*k**2. Solve z(w) = 0.
-2, -1, -2/11, 0
Let t = -4 + 7. Factor -9*a**4 + 7*a**4 - a**t + a**4.
-a**3*(a + 1)
Let h(z) = z**2 - 13*z + 16. Let u be h(12). Factor -1 + 1 + u*s - s**2 + 3*s**2.
2*s*(s + 2)
Let g be ((-4)/(-3))/((-4)/(-6)). Let p(