**2 + 2/9*v**4 - 2/9*v**3.
2*v*(v - 1)**2*(v + 1)/9
Let t(y) be the third derivative of -y**7/945 + y**6/270 - y**4/54 + y**3/27 - 6*y**2. Factor t(r).
-2*(r - 1)**3*(r + 1)/9
Let z(x) be the first derivative of -3 + 2*x + 8/3*x**3 + 5*x**2. Let z(c) = 0. What is c?
-1, -1/4
Let h(t) = t**2 + 2*t - 1. Let j be h(-3). Suppose -6*u**2 + 10*u - 2 - 2*u**4 + 4*u**4 - 4 + j - 2*u**3 = 0. What is u?
-2, 1
Let h(d) = 7*d + 1. Let n be h(-1). Let l = 10 + n. Factor -l*t**4 - 2*t**2 - 3*t**3 - t - t**2 + 3*t**4.
-t*(t + 1)**3
Let s(i) be the third derivative of i**6/1620 - i**5/270 - i**3/3 - i**2. Let q(j) be the first derivative of s(j). Factor q(m).
2*m*(m - 2)/9
Let w(r) be the third derivative of r**9/20160 + r**8/3360 - r**7/1680 - r**6/120 + r**5/20 + 3*r**2. Let j(x) be the third derivative of w(x). Factor j(s).
3*(s - 1)*(s + 1)*(s + 2)
Let o(m) be the third derivative of -m**5/420 + m**4/168 + m**3/21 + 13*m**2. Let o(d) = 0. Calculate d.
-1, 2
Let o(b) be the second derivative of -b**5/40 + 3*b**4/16 - b**3/2 + b**2/2 - b. Let w(z) be the first derivative of o(z). Find d such that w(d) = 0.
1, 2
Let o = -15/16 - -77/48. Let t(w) be the first derivative of o*w**3 + 4 + w**2 + 1/6*w**4 + 2/3*w. Factor t(r).
2*(r + 1)**3/3
Let v be ((-2)/(-3))/((-6)/(-63)). Let i be 4/35 + 2/v. Factor -2/5*q**3 + 2/5*q**2 + 0 + i*q - 2/5*q**4.
-2*q*(q - 1)*(q + 1)**2/5
Let r = 11 - 7. Factor -o**2 + r*o**2 + 10*o + 4 + 2*o**3 + 5*o**2.
2*(o + 1)**2*(o + 2)
Let g(b) be the third derivative of b**8/13440 + b**7/2016 + b**6/720 + b**5/30 - 3*b**2. Let q(y) be the third derivative of g(y). Factor q(n).
(n + 1)*(3*n + 2)/2
Suppose -4*q + 2*v + 274 = 0, 2*q - 3*v = 6*q - 279. Let g = q - 413/6. Factor 19/3*c**2 + 4/3 + 14/3*c + 4/3*c**4 + g*c**5 + 25/6*c**3.
(c + 1)**2*(c + 2)**3/6
Let f be (-6 + 4)*(-3 - -1). Suppose -f*o = -15 + 7. Determine y so that -y**o + 2 - 1 + 0 = 0.
-1, 1
Let n(j) = 3*j**2 + 7*j - 7. Let y be n(1). Solve 48/5 + 975*i**4 + 456*i**2 + 960*i**y + 375*i**5 + 528/5*i = 0.
-1, -2/5
Let t be ((-7)/(-14))/((-2)/(-12)). Determine y, given that y + 0*y**t - y - y**3 = 0.
0
Let s(m) = -11*m**3 + 6*m**2 + 12*m. Let o(v) = -5*v**3 + 3*v**2 + 6*v. Let r(z) = 5*o(z) - 2*s(z). Find u, given that r(u) = 0.
-1, 0, 2
Let h(a) = a**3 + 22*a**2 - 43*a + 120. Let g be h(-24). Let f(k) = k**2 + 6*k + 5. Let u be f(-5). Factor 1/5*y**5 + 0*y**2 - 1/5*y**4 + u + g*y**3 + 0*y.
y**4*(y - 1)/5
Let l(s) be the second derivative of -s**7/1260 + s**6/45 - 4*s**5/15 + 7*s**4/12 + 9*s. Let z(w) be the third derivative of l(w). What is u in z(u) = 0?
4
Suppose -4*z - 60 = -5*y, -4*y + 45 = -3*z - 3*y. Let q be 9/(-36) + z/(-28). Solve 6/7*i + 6/7*i**4 - 2/7*i**5 - 4/7*i**3 - q - 4/7*i**2 = 0.
-1, 1
Let c(m) be the first derivative of m**4/14 - 2*m**3/7 + 3*m**2/7 - 2*m/7 - 2. Factor c(l).
2*(l - 1)**3/7
Let x(d) be the first derivative of 25*d**4/7 + 60*d**3/7 + 48*d**2/7 + 16*d/7 - 6. Suppose x(c) = 0. What is c?
-1, -2/5
Let t = 298/165 - 20/33. Let z(q) = q**3 + 8*q**2 + q + 10. Let i be z(-8). Let 0*u**3 - 2*u**i + 11/5*u**4 - 6/5*u + t*u**5 - 1/5 = 0. Calculate u.
-1, -1/2, -1/3, 1
Let n be (4/6)/(6/27). Suppose w + 14 = n*w. Factor 11*o + 2*o**5 - w*o**4 - o + 2*o**2 - 22*o**2 - 2 - 3*o**4 + 20*o**3.
2*(o - 1)**5
Let k(l) be the first derivative of -l**3 + 0*l + 3/5*l**5 - 3/2*l**2 + 8 + 3/4*l**4. Factor k(u).
3*u*(u - 1)*(u + 1)**2
Let q(d) be the second derivative of -d**5/100 - d**4/15 + d**3/10 + 9*d**2/5 - 17*d. Suppose q(g) = 0. What is g?
-3, 2
Let u be (5/(-3))/(104/12). Let q = u - -9/13. Determine r so that 2 + q*r**3 + 0*r - 3/2*r**2 = 0.
-1, 2
Suppose -2*l - 3*f - 6 = 0, -4*l + 23 + 5 = -4*f. Let c(b) = b**4 + b**3 - b**2 + b + 1. Let k(x) = -4*x**4 - 2*x - 3. Let n(p) = l*c(p) + k(p). Factor n(w).
-w*(w - 1)**3
Let z(b) be the third derivative of -b**6/840 + b**5/210 + b**4/24 + 2*b**3/21 + 6*b**2. Factor z(c).
-(c - 4)*(c + 1)**2/7
Let q(n) be the first derivative of -3*n**4/4 - n**3 + 3*n**2/2 + 3*n + 3. Determine r, given that q(r) = 0.
-1, 1
Let s be (-48)/72 - 16/(-18). Factor 0 + 0*d + 2/9*d**2 - 2/9*d**4 + 2/9*d**5 - s*d**3.
2*d**2*(d - 1)**2*(d + 1)/9
Let z(h) be the second derivative of h**7/2100 - h**6/180 + 2*h**5/75 - h**4/15 + 2*h**3/3 - 3*h. Let x(d) be the second derivative of z(d). Factor x(k).
2*(k - 2)**2*(k - 1)/5
Let t(d) be the third derivative of d**6/300 - d**5/75 - d**4/20 - 5*d**2. Let t(w) = 0. Calculate w.
-1, 0, 3
Let d(h) = 18*h**4 + 18*h**3 - 26*h**2 - 6*h. Let z(q) = -37*q**4 - 35*q**3 + 51*q**2 + 11*q. Let s(r) = -5*d(r) - 2*z(r). Find j, given that s(j) = 0.
-2, -1/4, 0, 1
Let q(l) be the first derivative of 1/21*l**3 + 0*l + 1/2*l**2 - 1/42*l**4 - 1 + 1/210*l**5. Let p(m) be the second derivative of q(m). Factor p(v).
2*(v - 1)**2/7
Let q(g) = -g**3 + 10*g**2 - 10*g + 14. Let i be q(9). Factor 0*s - 2/3*s**4 - 2/3*s**i + 0 + 0*s**2 + 4/3*s**3.
-2*s**3*(s - 1)*(s + 2)/3
Find h such that 62 - h**2 + h**2 - 224 - 2*h**2 - 36*h = 0.
-9
Let n = -39 - -39. Factor n*i**3 - 4/5 + 8/5*i**2 - 4/5*i**4 + 0*i.
-4*(i - 1)**2*(i + 1)**2/5
Let z = -1 - -4. Let -3 - 6*w**3 + 6*w + z*w**4 + 1 - 1 = 0. What is w?
-1, 1
Let u(a) = 3*a**3 - 11*a**2 - 35*a - 32. Let c(t) = -2*t**3 + 5*t**2 + 17*t + 16. Let f(n) = 10*c(n) + 6*u(n). Determine s so that f(s) = 0.
-4, -2
Let c(f) = -4*f**3 + 25*f**2 - f - 15. Let u(p) = 6*p**3 - 38*p**2 + 2*p + 22. Let r(d) = -8*c(d) - 5*u(d). Determine j, given that r(j) = 0.
-1, 1, 5
Let b(t) = -71*t**3 - 225*t**2 - 266*t - 101. Let n(z) = 24*z**3 + 75*z**2 + 89*z + 34. Let q(g) = -4*b(g) - 11*n(g). What is k in q(k) = 0?
-2, -1, -3/4
Let v(o) be the third derivative of o**6/120 + 2*o**5/15 - 5*o**4/12 - 3*o**3/2 + 2*o**2. Let a be v(-9). Determine r, given that 2/5*r**2 - 2/5 + a*r = 0.
-1, 1
Let f(h) = -h**2 + 3*h. Let k(s) = -s. Let i(u) = -f(u) - 4*k(u). Let g(m) = -5*m**2 - 10*m + 3. Let d(x) = g(x) + 6*i(x). Solve d(r) = 0.
1, 3
Let z(o) be the second derivative of -o**6/225 + o**5/75 + 7*o**4/90 + 4*o**3/45 + 28*o. Suppose z(v) = 0. Calculate v.
-1, 0, 4
Let l(m) be the second derivative of m**7/7560 + m**6/360 + m**5/40 + m**4/12 + 4*m. Let h(b) be the third derivative of l(b). Solve h(j) = 0 for j.
-3
Suppose 2*f + 5*k = -2*f + 18, -3*f - 2 = -4*k. Factor -2/3 + 0*a + 2/3*a**f.
2*(a - 1)*(a + 1)/3
Let q(s) be the third derivative of -s**7/280 + s**6/40 - s**5/20 - s**3/2 - 8*s**2. Let f(v) be the first derivative of q(v). Factor f(c).
-3*c*(c - 2)*(c - 1)
Let r(n) = -10*n - 145. Let y be r(-15). Find h such that 3/4*h**y - h**4 + 2 + 3/2*h**2 + 5*h - 13/4*h**3 = 0.
-1, -2/3, 2
Let f(x) be the third derivative of x**5/180 - x**4/24 + x**3/9 + 5*x**2. Solve f(d) = 0.
1, 2
Let m(h) = 8*h**3 + 2*h**2 + 5. Suppose 3*i + 6 = 21. Let d(p) = p**3 + p**2 + 1. Let u(f) = i*d(f) - m(f). Factor u(x).
-3*x**2*(x - 1)
Factor 4/5*z + 4/5 + 1/5*z**2.
(z + 2)**2/5
Let g = -4 + 7. Suppose -o + 0 + 0 - o**5 - 4*o**2 - 4*o**4 - 6*o**g = 0. What is o?
-1, 0
Factor -3/4*n**2 + 0 - 1/4*n**3 - 1/2*n.
-n*(n + 1)*(n + 2)/4
Factor 2/9*a**5 - 4/9*a**3 + 2/9 + 2/9*a**4 - 4/9*a**2 + 2/9*a.
2*(a - 1)**2*(a + 1)**3/9
Let h(l) = l + 15. Let p be h(-11). Determine f, given that 3*f + 9*f**5 - 5*f**p - f**4 - 17*f**2 + 23*f**2 - 12*f**3 = 0.
-1, -1/3, 0, 1
Factor -2*c - 12*c**2 - 12 - 29*c - 9*c.
-4*(c + 3)*(3*c + 1)
Let r be 0/1 - (7 + -8). Suppose n - 4*y + 5 = -r, 2*n - 14 = -5*y. Find o, given that -4/7 + 18/7*o - n*o**2 = 0.
2/7, 1
Suppose 2*x = -x + 2*v + 37, 5*x + 5*v = 20. Let b be 1 - 3*(-6)/x. Suppose 0*f**4 + 2 - b + 2*f**2 - f**4 = 0. What is f?
-1, 1
Let a(x) be the third derivative of -x**7/1155 - x**6/165 - x**5/66 - x**4/66 + 5*x**2. Factor a(r).
-2*r*(r + 1)**2*(r + 2)/11
Let d be ((-4)/(-3))/(-4)*54/(-9). Factor 0*s**d - 4/5*s**3 - 2/5 + 2/5*s**4 + 4/5*s.
2*(s - 1)**3*(s + 1)/5
Let h = 1 - 1. Suppose h*x - 2*x = -6. Factor -2*f - x*f + 6*f - f**2.
-f*(f - 1)
Suppose -4*q = -7*q + 9. Let -1/3*b**4 + 0 - 1/3*b**5 + 1/3*b**q + 1/3*b**2 + 0*b = 0. What is b?
-1, 0, 1
Let s be ((-18)/5 + 4)/((-7)/(-10)). Suppose s*t**3 + 0*t**4 + 0*t**2 - 2/7*t**5 - 2/7*t + 0 = 0. What is t?
-1, 0, 1
Let o(s) be the second derivative of 0*s**3 + 3/40*s**5 + 0*s**2 + 0 + 6*s - 1/4*s**4. Factor o(i).
3*i**2*(i - 2)/2
Let q be -2 + 2 - (2