- 2/3*k**3. Factor v(l).
2*l*(l - 1)**2*(l + 1)
Factor 3/2*k**2 + 5/2*k - 25/6 + 1/6*k**3.
(k - 1)*(k + 5)**2/6
Let m(l) be the third derivative of -l**8/3150 + l**6/1800 - l**5/30 - 2*l**2. Let a(q) be the third derivative of m(q). Solve a(c) = 0 for c.
-1/4, 1/4
Let x = -60/11 + 202/33. Determine z, given that -x*z**3 - 2/9*z**5 - 2/3*z**4 + 0*z - 2/9*z**2 + 0 = 0.
-1, 0
Let f(j) = -9*j**3 + 27*j**2 - 4*j. Let x(v) = -9*v**3 + 26*v**2 - 4*v. Let w(g) = -6*f(g) + 7*x(g). Suppose w(n) = 0. Calculate n.
0, 2/9, 2
Let y = 38 + -35. Suppose 2*o - y = o. Factor 4*n**3 - o*n**2 + 0 + 2/3*n - 5/3*n**4.
-n*(n - 1)**2*(5*n - 2)/3
Let x be (-30)/(-8) + (-10)/(-40). Suppose 0 = -x*b + 4*q + 28, 0*b - 3*q = 4*b + 7. Let -70/3*i**4 - 8*i**5 - 4/3*i + 0 - 10*i**b - 24*i**3 = 0. What is i?
-1, -2/3, -1/4, 0
Find u such that -27/5*u - 21/5*u**3 + 0 - 3/5*u**4 - 9*u**2 = 0.
-3, -1, 0
Let x(f) be the first derivative of -1/3*f**3 + 2/5*f - 1/2*f**2 + 3/25*f**5 + 1/4*f**4 - 3. Let x(y) = 0. Calculate y.
-2, -1, 1/3, 1
Let y be 20/(-30) + 20/3. Let o(z) be the second derivative of 1/45*z**y - 1/15*z**5 + 0*z**2 + 0*z**3 + 0 + 1/63*z**7 + 0*z**4 - 3*z. Factor o(q).
2*q**3*(q - 1)*(q + 2)/3
Let r(u) = 3*u**2 + 13*u - 5. Let o(k) = 4*k**2 + 20*k - 8. Let s(v) = -5*o(v) + 8*r(v). Factor s(a).
4*a*(a + 1)
Let h be 2*(-3)/(-24)*8. Let t(c) be the first derivative of -4*c - 3*c**h - 2/3*c**3 + 2. Factor t(n).
-2*(n + 1)*(n + 2)
Let n(q) be the second derivative of q**6/10 - 9*q**5/10 + 2*q**4 + 3*q**3 - 27*q**2/2 - q. Find j such that n(j) = 0.
-1, 1, 3
Determine d so that 0 - 4/11*d - 2/11*d**2 + 4/11*d**3 + 2/11*d**4 = 0.
-2, -1, 0, 1
Suppose -4 + 16 = 4*l. Determine y, given that 15*y + l*y**2 - y**2 - 15*y = 0.
0
Let j(a) = 12*a**4 - 9*a**3 - 46*a**2 - 34*a - 26. Let r(b) = -4*b**4 + 3*b**3 + 15*b**2 + 11*b + 9. Let n(s) = -6*j(s) - 17*r(s). Let n(t) = 0. Calculate t.
-1, -1/4, 3
Let p(d) be the second derivative of d**5/20 - d**4/2 + 5*d. Let g(i) = i**2. Let j(m) = -14*g(m) - 2*p(m). Factor j(z).
-2*z**2*(z + 1)
Let j = 30 - 27. Let m(l) be the third derivative of 0 - 1/24*l**4 + 1/120*l**6 + 1/60*l**5 + 3*l**2 - 1/6*l**j + 0*l. Let m(i) = 0. Calculate i.
-1, 1
Let a(f) be the second derivative of -f**5/100 - f**4/30 - 8*f. Factor a(g).
-g**2*(g + 2)/5
Let o(u) be the first derivative of -u**4/72 - 4*u + 4. Let l(b) be the first derivative of o(b). Suppose l(t) = 0. What is t?
0
Let u(j) be the first derivative of 7*j**3 + 33*j**2/2 - 13*j - 8. Let v(w) = -10*w**2 - 16*w + 6. Let p(h) = -2*u(h) - 5*v(h). Factor p(a).
2*(a + 2)*(4*a - 1)
Suppose -3 = -2*r + 1. Factor 0*y**3 + 13*y**3 + r*y**5 - 5*y**3 + 8*y**4.
2*y**3*(y + 2)**2
Factor -24*x**4 - 28*x**3 + 0 - 25/6*x**2 - 1/6*x.
-x*(x + 1)*(12*x + 1)**2/6
Let c(b) be the first derivative of 0*b**2 + 0*b**4 + 3 - 2/35*b**5 - 2/7*b + 4/21*b**3. Suppose c(m) = 0. Calculate m.
-1, 1
Let k(v) = 3*v**3 + 13*v**2 + v + 3. Let s(d) = -10*d**3 - 38*d**2 - 4*d - 8. Let q be (-3)/(-12) - 13/4. Let h(n) = q*s(n) - 8*k(n). Find f such that h(f) = 0.
-1, -2/3, 0
Let c = 443/117 - 32/9. Let s = 31/91 + c. Find k, given that -2/7*k**2 - s*k - 2/7 = 0.
-1
Factor 32*j**3 - 14*j**2 + 16*j**3 - 20*j**3 - 8*j - 6*j**4.
-2*j*(j - 4)*(j - 1)*(3*j + 1)
Let f(u) be the second derivative of -u**5/10 + u**3 - 2*u**2 - 13*u. Suppose f(l) = 0. What is l?
-2, 1
Let u = -8 - -15. Let f = u + -11/2. Factor -f*l + 1 + 1/2*l**2.
(l - 2)*(l - 1)/2
Let u = 317/610 + -6/305. Factor -u - 2/3*q - 1/6*q**2.
-(q + 1)*(q + 3)/6
Suppose -12 = 2*z + 2*z. Let m = z - -7. Factor -2*w**5 + 0*w**m - w**2 + 2*w**2 - 3*w**4.
-w**2*(w + 1)**2*(2*w - 1)
Let d be (-2)/(-6) - (-14)/(-6). Let c be (2/d)/((-4)/8). Factor -c*h + 17*h**3 - 2*h - 3*h**3 - 10*h**2.
2*h*(h - 1)*(7*h + 2)
Let f(l) = l**2 + l - 1. Let a(h) = -2*h**2 - 18*h - 2. Let k(y) = a(y) - 2*f(y). Let k(i) = 0. What is i?
-5, 0
Let k(j) be the second derivative of -j**6/60 - j**5/8 - j**4/3 - j**3/3 + 3*j. Let k(i) = 0. Calculate i.
-2, -1, 0
Let w = -1 + 1. Suppose h + 14 = -4*t, -12 + w = 4*h + 5*t. Determine q, given that -q**h + 0*q**5 - 2*q**3 - q**3 + 3*q**5 + q**4 = 0.
-1, -1/3, 0, 1
Let v(i) be the first derivative of -i**7/21 - 7*i**6/60 + i**5/20 - 3*i - 3. Let c(t) be the first derivative of v(t). Suppose c(q) = 0. Calculate q.
-2, 0, 1/4
Suppose 4 = 2*h - 2. Let j = 3 - 1. Find z, given that -2*z**h + 2*z - z**4 + 3*z**4 - 3*z**j + z**2 = 0.
-1, 0, 1
Let g(q) be the first derivative of -q**4/14 - 2*q**3/7 + 12. Factor g(z).
-2*z**2*(z + 3)/7
Suppose o = 7 - 3. Let j be (-4)/14*(0 - o). Let 2/7*d**2 - j*d + 8/7 = 0. Calculate d.
2
Let l(i) be the first derivative of -1/4*i**4 + 4 + 2*i**3 + 8*i - 6*i**2. Factor l(s).
-(s - 2)**3
Let b(h) = -4*h**4 + 6*h**3 + 22*h**2 + 28*h + 12. Let x(q) = 9*q**4 - 13*q**3 - 43*q**2 - 56*q - 25. Let g(u) = -5*b(u) - 2*x(u). Factor g(v).
2*(v - 5)*(v + 1)**3
Factor -t**2 - 1 + 0 + 6*t**2 - 4*t**2.
(t - 1)*(t + 1)
Let l(m) = m**2 + 6*m - 2. Let b be l(-7). Find n, given that -5*n**2 - 6*n**3 + 12*n**4 + 43*n - 7*n**2 + 9*n**b - 46*n = 0.
-1, -1/3, 0, 1
Let s be (1 + -1)/2 + 3. Let d(z) be the first derivative of 0*z - 1 - z**2 + 1/2*z**4 + 0*z**s. Determine u, given that d(u) = 0.
-1, 0, 1
Let v(n) be the third derivative of n**7/70 + n**6/20 + n**5/20 - 17*n**2. Solve v(p) = 0.
-1, 0
Let v(i) = i**3 + 9*i**2 + 22*i + 24. Let t be v(-6). Factor t + d - 5/2*d**3 + 3/2*d**2.
-d*(d - 1)*(5*d + 2)/2
Let f = -7 - -13. Let n(o) be the first derivative of -3/2*o**4 - 5/9*o**f + 1 - 8/5*o**5 + 0*o**2 - 4/9*o**3 + 0*o. Solve n(b) = 0.
-1, -2/5, 0
Let z(c) = c**2 - 12*c - 10. Let g be z(13). Let p(m) be the second derivative of m + 1/25*m**6 + 0*m**g + 0 + 4/25*m**5 + 1/5*m**4 - 1/5*m**2. Factor p(k).
2*(k + 1)**3*(3*k - 1)/5
Let g(a) = 3*a**2 + 2. Let w(p) = 9*p**2 + 7. Let d be 5 - -6*(-2)/4. Let q(m) = d*w(m) - 7*g(m). Factor q(f).
-3*f**2
Suppose 0 = 7*g - 2*g. Suppose g = h - 2*h + 4. Factor -a**5 - a**3 + a**4 - a**4 - 2*a**h.
-a**3*(a + 1)**2
Let w(q) be the first derivative of -2*q**3 + 6/5*q**5 - 5/2*q**4 + q**2 + 4/3*q**6 + 0*q + 3. Solve w(u) = 0 for u.
-1, 0, 1/4, 1
Suppose 0 = -4*x + 14 - 6. Let k be (x - 0)*-1*-1. Factor 2*q**4 - 6*q**3 - q**3 + 5*q**3 - 2*q**k + 2*q**5.
2*q**2*(q - 1)*(q + 1)**2
Factor -8/3 - 2/3*l**2 - 8/3*l.
-2*(l + 2)**2/3
Let s(i) = -10*i**5 + i**4 + 13*i**3 + 2*i**2 + 4*i - 4. Let g(h) = 11*h**5 - 12*h**3 - h**2 - 3*h + 3. Let o(b) = 4*g(b) + 3*s(b). Let o(x) = 0. What is x?
-1, 0, 2/7, 1/2
Let m = 4981/13 + -383. Factor 0 + m*a**2 - 2/13*a.
2*a*(a - 1)/13
Let k(f) be the third derivative of 0 - 1/150*f**5 + 2*f**2 - 1/30*f**4 - 1/15*f**3 + 0*f. Factor k(s).
-2*(s + 1)**2/5
Let m(u) = u**2 - u. Let k(o) = -6*o**2 - 6*o - 10. Let v(w) = -w**2 - 1. Let q(g) = k(g) - 10*v(g). Let x(f) = -6*m(f) + q(f). Factor x(c).
-2*c**2
Let u(o) = 4*o**2 + 9*o + 4. Let r(s) = s**2 + s - 1. Let i(v) = 4*r(v) + u(v). Let w(g) = 20*g**2 + 32*g. Let x(a) = -12*i(a) + 5*w(a). Factor x(t).
4*t*(t + 1)
Let i(s) be the first derivative of s**4/7 + 16*s**3/21 - 11. Factor i(o).
4*o**2*(o + 4)/7
Let t be 2/42*(-6)/(-60). Let h(v) be the third derivative of 1/60*v**5 + 0*v + 0*v**4 + 0 + 1/60*v**6 + t*v**7 - v**2 + 0*v**3. Find p, given that h(p) = 0.
-1, 0
Let s(v) = -v**2 + 10*v - 5. Let p = -5 - -14. Let x be s(p). Solve 0 + 0*w - 1/3*w**3 + 1/3*w**2 + 1/3*w**5 - 1/3*w**x = 0 for w.
-1, 0, 1
Let y(i) be the second derivative of -i**5/120 + i**4/48 + 5*i**2/2 - 3*i. Let z(t) be the first derivative of y(t). Determine m so that z(m) = 0.
0, 1
Let n be (-10 - -8)*(-2)/(-4). Let f be (1 - n) + -2 - -3. Suppose 3*q**f + 5*q**4 + 4*q**5 - q**5 + q**4 = 0. Calculate q.
-1, 0
Factor 8*n + 184*n**2 - 375*n**2 + 187*n**2.
-4*n*(n - 2)
Let p(n) be the first derivative of -n**4/12 + n**2/2 - 2*n/3 - 10. Factor p(z).
-(z - 1)**2*(z + 2)/3
Solve 6*q**2 + 3/2*q**3 + 0 + 9/2*q = 0.
-3, -1, 0
Let x be (-10)/(1 - (4 + -1)). Let w(m) be the third derivative of 0 + 0*m**3 + 1/480*m**6 + 4*m**2 + 0*m**x + 0*m**4 + 0*m. Factor w(a).
a**3/4
Suppose 0 = 2*x + 5*f + 9, 0 = -x + f + 5 + 1. Find z, given that 4*z + 0*z - x*z**3 - z = 0.
-1, 0, 1
Let f(p) be the third derivative of 0*p + 43/60*p**5 + 1/6*p**3 + 11/24*p**4 + 4*p**2 + 73/120*p**6 + 0 + 4/15*p**7 + 1/21*p**8. Factor f