rd derivative of n**5/180 + n**4/72 + 3*n**2. What is q in u(q) = 0?
-1, 0
Solve -10*d**4 + 4*d**5 + 8*d**4 - 5*d**5 = 0.
-2, 0
Let i(s) be the first derivative of -1/6*s**2 - 5/18*s**3 - 7 - 1/6*s**4 - 1/30*s**5 + 0*s. Factor i(u).
-u*(u + 1)**2*(u + 2)/6
Suppose w = -6*v + v + 50, 3*v - 30 = -5*w. Suppose u + 4*f = -u + 20, -2*u + 2*f - v = 0. Factor 0 + 2/3*b**3 + u*b**2 - 2/3*b**5 + 0*b + 0*b**4.
-2*b**3*(b - 1)*(b + 1)/3
Let n = -23 + 25. Let q(v) be the third derivative of -v**n + 0 + 1/12*v**4 - 1/6*v**3 - 1/60*v**5 + 0*v. Determine l so that q(l) = 0.
1
Factor 0*a**3 - 2/5*a**4 + 0 + 6/5*a**2 + 4/5*a.
-2*a*(a - 2)*(a + 1)**2/5
Suppose -4*s - 532 = -544. Factor -2/3*p**s - 2/3*p**2 + 0*p + 0.
-2*p**2*(p + 1)/3
Let j(t) be the first derivative of -t**3/3 + 9*t**2 - 81*t - 31. Suppose j(i) = 0. What is i?
9
Suppose 5*x**3 - 18*x + 4*x + 4*x - 5*x**2 = 0. What is x?
-1, 0, 2
Let h(c) be the second derivative of 6*c**6/5 - 3*c**5/5 - 23*c**4/3 - 26*c**3/3 - 4*c**2 + 42*c. Determine x, given that h(x) = 0.
-1, -1/3, 2
Let j be -3 - 2*(12/8 - 4). Let q = 194/423 + -2/141. Factor -2/9 - j*d**4 - 28/9*d**2 - 4/3*d - q*d**5 - 32/9*d**3.
-2*(d + 1)**4*(2*d + 1)/9
Let x(f) be the second derivative of -f**4/4 + f**3/2 + 3*f**2 + 8*f. Suppose x(n) = 0. Calculate n.
-1, 2
Let j(z) be the first derivative of -8*z + 2/3*z**3 + 0*z**2 + 10. Suppose j(d) = 0. Calculate d.
-2, 2
Let t be (-8)/(-12) - 20/(-6). Let z be t/(-3*2/(-3)). Factor 8*j + 2*j**3 - 10*j**2 + 16*j - 16 - 6*j**z + 4*j**2.
2*(j - 2)**3
Let a(y) be the second derivative of -y**4/3 + 12*y**3 - 162*y**2 - 7*y + 1. Factor a(z).
-4*(z - 9)**2
Let s(o) = -o**2 + 4*o + 1. Let j be s(4). Let t = j - -5. Suppose -w**3 - 4*w + t*w + w**2 + 0*w**2 = 0. What is w?
-1, 0, 2
Let w(i) = i**2 - i - 1. Let r(x) = -2*x**2 - 3*x + 12. Let c(u) = 5*r(u) + 15*w(u). Solve c(o) = 0 for o.
3
Let w(h) = -5*h**4 + h**3 + h**2 - 3*h - 3. Let k(q) = -q**2 - q**4 + q + 3*q**4 - q**4 + q**3 + 1. Let d(c) = 3*k(c) + w(c). Factor d(p).
-2*p**2*(p - 1)**2
Suppose 0 = -2*j + 8. Solve -h**4 + 1 - 2*h**2 + h**4 + h**j = 0 for h.
-1, 1
Factor 3*c**3 + 2 - 1 - 3*c**2 - 1.
3*c**2*(c - 1)
Let n(f) be the second derivative of -f**6/45 - f**5/15 - f**4/18 - 3*f. Determine t so that n(t) = 0.
-1, 0
Solve 1/3*v**2 - v**4 - 2/3*v**3 + 0*v + 0 = 0.
-1, 0, 1/3
Let z = -1/26 - 97/13. Let g = 8 + z. Determine x, given that g*x**4 + 0*x + 0*x**2 + 1/2*x**3 + 0 = 0.
-1, 0
Let a be -2*6/16*-4. Factor 7*j**3 - 2*j - 1 + 10*j**4 + 3*j**5 - 1 - 3*j + a*j**3.
(j + 1)**4*(3*j - 2)
Let b(j) = -j**3 - j**2. Let w(k) = 5*k - 2*k**3 - 1 + 1 - 2 - 2*k**3 - 9*k**2. Let f(v) = 5*b(v) - w(v). Determine g, given that f(g) = 0.
1, 2
Let g be ((-18)/(-6) + (-10)/3)*-2. Factor c**2 + g - 7/3*c.
(c - 2)*(3*c - 1)/3
Let p(q) be the third derivative of -4*q**2 - 2/105*q**7 + 1/3*q**4 - 1/84*q**8 + 1/10*q**6 + 0*q**3 + 0*q + 0 + 1/3*q**5. Factor p(y).
-4*y*(y - 2)*(y + 1)**3
Let k(m) = -m**4 - m**3 + m**2 - m + 1. Let p(l) = 7*l**4 + 7*l**3 - 11*l**2 + 9*l - 6. Let w(i) = -6*k(i) - p(i). Solve w(z) = 0.
-3, 0, 1
Let l(v) be the second derivative of -3/2*v**2 + 1/4*v**4 + 7*v + 0 + 0*v**3. What is f in l(f) = 0?
-1, 1
Let t = -1/4 + 5/12. Let a(h) be the second derivative of -t*h**4 + h + 0 + 4/9*h**3 + 4/3*h**2. Determine r, given that a(r) = 0.
-2/3, 2
Let c(z) be the third derivative of z**9/30240 - z**8/10080 - z**5/15 - 7*z**2. Let g(b) be the third derivative of c(b). Let g(j) = 0. What is j?
0, 1
Suppose 2*v = -6, -p + v = -4*p + 45. Suppose 4*r + 146 = 2*y, 0 = -3*r + 1 - p. Factor 3*f**2 - y*f**3 + 2*f + f**2 + 0*f**3 + 2*f.
-f*(7*f - 2)*(9*f + 2)
Let h = -32 - -37. Let j(f) be the first derivative of 1/12*f**6 - 1/6*f**3 + 1 + 0*f - 1/8*f**4 + 0*f**2 + 1/10*f**h. Determine u, given that j(u) = 0.
-1, 0, 1
Factor 3*q**4 + 5 + 10*q**2 - 8*q**4 - 5 - 5.
-5*(q - 1)**2*(q + 1)**2
Let o(j) = -3*j - 9. Let x be o(-3). Factor 0*r + x - 24/5*r**5 + 0*r**2 - 4/5*r**3 - 22/5*r**4.
-2*r**3*(3*r + 2)*(4*r + 1)/5
Let p(u) be the first derivative of -u**6/180 - u**5/90 + u**4/36 + u**3/9 - 4*u**2 + 2. Let n(s) be the second derivative of p(s). Factor n(b).
-2*(b - 1)*(b + 1)**2/3
What is a in -1/5*a**3 + 1/5*a - 1/5*a**2 + 1/5 = 0?
-1, 1
Let d be (1 + 0)/((-3)/(-6)). Factor 2/7 - 4/7*a + 2/7*a**d.
2*(a - 1)**2/7
Determine j, given that -12*j**2 + 8*j + 4*j**4 + j**4 - j**4 = 0.
-2, 0, 1
Let t be (3 - 8/(-3)) + -3. Let y be (-2)/36*-3*4. Determine p so that y*p**2 - t*p + 8/3 = 0.
2
Factor -8/7*j**2 + 32/7 - 16/7*j + 4/7*j**3.
4*(j - 2)**2*(j + 2)/7
Let z(o) be the second derivative of -o**4/60 - o**3/30 + o. Factor z(y).
-y*(y + 1)/5
Let q(j) = j**3 + 3*j**2 - 5*j - 1. Suppose 2*x + 13 = 5. Let k be q(x). Factor h**k + 0*h + 3*h**2 - h + 3*h.
h*(h + 1)*(h + 2)
Let n(m) be the second derivative of m + 1/10*m**6 - 1/7*m**7 - 1/2*m**3 - 1/4*m**4 + 9/20*m**5 + 0*m**2 + 0. Determine x, given that n(x) = 0.
-1, -1/2, 0, 1
Let k = 1435072/247 + -5810. Let f = 500/741 - k. Solve 0*m**3 - f*m**2 + 1/3*m**5 - 1/3*m + 2/3*m**4 + 0 = 0 for m.
-1, 0, 1
Suppose 4*a = -321 - 99. Let z be (-51)/a + 2/(-10). Factor -2/7*r**2 + 0 - z*r.
-2*r*(r + 1)/7
Let j(z) be the first derivative of -10*z**3/9 + 8*z**2/3 - 2*z - 6. Solve j(g) = 0 for g.
3/5, 1
Let l(p) = -p - 6. Let x be l(-9). Suppose -5*g + 23 = 8, 3*u + x*g = 15. Factor -2*f + 7 - 3 + 3*f**2 - u*f**2 - 3*f**2.
-2*(f - 1)*(f + 2)
Let w = 208 - 1038/5. Factor 2/5 - w*n**2 + 0*n.
-2*(n - 1)*(n + 1)/5
Let b = 5498/45 - 934/9. Let s = b + -18. Factor 0 + 0*u**2 + s*u**3 + 0*u.
2*u**3/5
Suppose -4*s = -2*k - 24, 0 = -k + 2*s - s - 8. Let b = 4 + k. Factor b - 14/3*i**2 - 4/3*i.
-2*i*(7*i + 2)/3
Let a be 2/(-3)*(-6)/40. Let v(x) be the first derivative of 2 - 2/5*x + 2/15*x**3 + a*x**4 - 1/5*x**2. Find k, given that v(k) = 0.
-1, 1
Let f(a) be the second derivative of 1/6*a**4 + 0 - 3*a + 2/3*a**3 + a**2. Determine h so that f(h) = 0.
-1
Suppose -4*g - 18 + 6 = -4*z, -3*g - 1 = z. Let i be ((-4)/(-8)*0)/1. Factor -4 + 0*l + 6*l - 2*l**z + i*l.
-2*(l - 2)*(l - 1)
Let a be 8 - 35/4 - (-2 - -1). Factor -a*f**3 + 5/4*f**2 - 9/4 - 3/4*f.
-(f - 3)**2*(f + 1)/4
Let o(u) be the first derivative of -2/3*u**3 - 2*u - 2*u**2 + 4. Factor o(s).
-2*(s + 1)**2
Let u be 6 + -3 + (-4)/(-12)*-3. Factor 6/5*y + 2/5*y**3 + 2/5 + 6/5*y**u.
2*(y + 1)**3/5
Factor 12/5*l + 18/5 + 2/5*l**2.
2*(l + 3)**2/5
Determine r so that 0*r**3 - 1/5*r**4 + 0*r**2 + 0 + 0*r = 0.
0
Let n(k) = -5*k**2 + 21*k. Let y be (11/2)/(3/(-6)). Let v(o) = o**2 - 4*o. Let i(g) = y*v(g) - 2*n(g). Factor i(s).
-s*(s - 2)
Factor 8/7*x**3 + 0*x**2 - 12/7*x**4 + 4/7*x**5 + 0 + 0*x.
4*x**3*(x - 2)*(x - 1)/7
Let q(t) = -t + 1. Let u(y) = 70*y**4 + 195*y**3 + 190*y**2 + 72*y + 13. Let j(l) = -3*q(l) + u(l). Suppose j(r) = 0. Calculate r.
-1, -1/2, -2/7
Let d(x) = x**4 + 2*x**3 - x**2 + 2*x. Let z(u) = -5*u**4 - 9*u**3 + 5*u**2 - 9*u. Let s(k) = -9*d(k) - 2*z(k). Factor s(j).
j**2*(j - 1)*(j + 1)
Let -2 + 9*z + 15*z**2 - 2 - 2 = 0. Calculate z.
-1, 2/5
Let a(y) be the second derivative of y**5/30 - y**4/3 + 4*y**3/3 - y**2/2 - 3*y. Let j(g) be the first derivative of a(g). Find q such that j(q) = 0.
2
Let g(x) be the second derivative of 3*x**8/224 + x**7/35 - x**6/120 - x**5/30 + x**4/48 + x**2/2 + 2*x. Let p(j) be the first derivative of g(j). Factor p(y).
y*(y + 1)**2*(3*y - 1)**2/2
Let w(q) = 6*q**2 - 2*q - 3. Let z be w(3). Let r be z/27*(-2)/(-5). Suppose 0 + 2/3*f**2 - 2/3*f**4 + 0*f - 2/3*f**3 + r*f**5 = 0. What is f?
-1, 0, 1
Let t be ((-1)/(-2))/((-51)/4). Let p = 422/357 + t. Factor 2/7 + p*o + 6/7*o**2.
2*(o + 1)*(3*o + 1)/7
Let x(v) be the third derivative of v**8/84 - 2*v**7/35 + v**6/10 - v**5/15 + 4*v**2 + 9. Find h such that x(h) = 0.
0, 1
Let k(z) = 2*z - 9. Let r be k(7). Let d = 3/7 + 1/14. Factor x**4 + d*x + 0 - x**2 - 1/2*x**r + 0*x**3.
-x*(x - 1)**3*(x + 1)/2
Let k(r) = 3*r**4 - 5*r**3 + 5*r**2 - 3*r. Let g(q) = -q**3 + q**2. Let h(o) = -4*g(o) - k(o). Find i such that h(i) = 0.
0, 1
Suppose -1/3*q**3 + 5/3*q**2 + 4/3 - 8/3*q = 0. Calculate q.
1, 2
Let o(h) be the first derivative of -1/12*h**4 - 1/6*h**2 + 1/60*h**5 + 2*h + 1/6*h**3 - 3. Let v(m) be the first derivative of o(m). What is j in v(j) = 0?
1
Let w(r) be the third derivative of r**5/60 - r**4/8 - 5*