 0. Find q such that j(q) = 0.
1
Let l(h) be the third derivative of 1/90*h**5 + 0*h**3 + h**2 + 0*h + 0 - 1/36*h**4. Factor l(y).
2*y*(y - 1)/3
Let q(n) = -3*n**4 + 8*n**3 + 17*n**2 - 11*n - 11. Let h(y) = y**4 - 3*y**3 - 6*y**2 + 4*y + 4. Let l(c) = -11*h(c) - 4*q(c). Let l(v) = 0. What is v?
-2, 0, 1
Suppose 12 = x - 3*n + 13, 5*n = -4*x + 30. Determine l, given that -5/4*l + 1/4*l**x + 1/2 - l**4 + l**3 + 1/2*l**2 = 0.
-1, 1, 2
Let y(v) be the third derivative of -v**5/20 - 5*v**4/8 - 15*v**2. Find n, given that y(n) = 0.
-5, 0
Let k(n) = -5*n**5 - 5*n**4 - 4*n**3 - 4*n**2 - 5*n - 5. Let f(w) = 4*w**5 + 4*w**4 + 4*w**3 + 4*w**2 + 4*w + 4. Let s(m) = 7*f(m) + 6*k(m). Factor s(a).
-2*(a - 1)**2*(a + 1)**3
Let v be (4/(-2))/((-1)/3). Let z = 8 - v. Factor 2/9*o + 2/9*o**4 + 0 - 2/9*o**3 - 2/9*o**z.
2*o*(o - 1)**2*(o + 1)/9
Suppose 1 - 4 = -g. Suppose 10*l - 2*k = 5*l + 35, l - g*k - 20 = 0. Find d such that -2 - 3*d**2 - 1 + 1 + l*d**2 = 0.
-1, 1
Let q(c) be the first derivative of -1/4*c**4 + 0*c**5 + 1/6*c**6 + 0*c**2 + 3 + 0*c + 0*c**3. Find f, given that q(f) = 0.
-1, 0, 1
Suppose 0 = 15*y - 14*y - 3. Factor 0 - 1/2*p**y - 1/2*p**5 + 0*p**2 + 0*p + p**4.
-p**3*(p - 1)**2/2
Factor -2*q**2 - 25 + 35 + 27*q**2 + 35*q.
5*(q + 1)*(5*q + 2)
Let j(t) = t**3 + 3*t**2 - 15*t + 11. Let l(d) = 2*d**3 + 10*d**2 - 46*d + 34. Let q(f) = -10*j(f) + 3*l(f). Solve q(m) = 0 for m.
-2, 1
Let o(t) = t - 9. Let f be o(5). Let s be ((-4)/(-3))/(f/(-6)). Solve 0*x**s - 2*x + 6*x**2 + 0*x**2 = 0 for x.
0, 1/3
Let o(d) be the first derivative of -d**7/126 - d**6/45 + d**4/18 + d**3/18 - 4*d + 5. Let n(z) be the first derivative of o(z). Factor n(b).
-b*(b - 1)*(b + 1)**3/3
Let x(w) be the second derivative of -11*w**7/105 + 3*w**6/25 + w**5/25 - 10*w. Factor x(g).
-2*g**3*(g - 1)*(11*g + 2)/5
What is u in 0*u**2 + u**3 - 2*u**2 - 5*u + 6*u = 0?
0, 1
Let g = -4 - -8. Let i = -3 - -5. Factor 6*y**3 + 5*y - y - 2*y**g - 2*y - 6*y**i.
-2*y*(y - 1)**3
Let o = -4 - -25. Let y be (6/o)/(4/7). Suppose -2*f - y*f**2 - 2 = 0. What is f?
-2
Let w = 1/7 - -3/28. Let o = 15/124 - -4/31. Factor 0 - o*y**2 + w*y.
-y*(y - 1)/4
Suppose 3 = g - 5*d, 3*g + 2*d - 12 = -g. Suppose -g*p = -p. Factor 0 + 1/3*z**4 - 1/3*z**5 + 0*z + 0*z**2 + p*z**3.
-z**4*(z - 1)/3
Let y(u) = -7*u - 37. Let z be y(-6). Determine b, given that 6/7*b**3 + 0*b**4 + 0*b + 0 - 4/7*b**2 - 2/7*b**z = 0.
-2, 0, 1
Factor -1/6*m**5 - 10/3*m**3 + 0*m + 4/3*m**4 + 0 + 8/3*m**2.
-m**2*(m - 4)*(m - 2)**2/6
Let l(g) = -3*g + 6. Let b be l(4). Let k(y) = y**3 + 7*y**2 + 7*y + 8. Let o be k(b). Let -8/5*w - 2/5*w**o - 8/5 = 0. What is w?
-2
Factor -18*r**2 + 10*r + 21*r**2 + 9*r - 7*r.
3*r*(r + 4)
Suppose 4*x = 23 + 25. Suppose o - x = -3*o. Let -o*j - 31 + 31 + 3*j**2 = 0. Calculate j.
0, 1
Let b(u) be the third derivative of u**6/8 - 5*u**5/12 + 5*u**4/24 + 5*u**3/6 + 12*u**2. Factor b(k).
5*(k - 1)**2*(3*k + 1)
Let x = 45/46 - -12/23. Let o = -13/2 + 8. Factor -x*v + o*v**2 - 1/2*v**3 + 1/2.
-(v - 1)**3/2
Let n(r) be the first derivative of -r**6/24 - 3*r**5/20 + r**4/16 + 11*r**3/12 + 3*r**2/2 + r + 10. Determine m so that n(m) = 0.
-2, -1, 2
Let c(h) be the first derivative of 17*h**5 + 45*h**4 + 35*h**3 + 5*h**2 + 11. Factor c(a).
5*a*(a + 1)**2*(17*a + 2)
Let o(s) be the second derivative of 0 + s**2 + 0*s**4 - 1/2*s**3 + 2*s + 1/20*s**5. Find g, given that o(g) = 0.
-2, 1
Suppose 3*x - 16 = 4*v - x, -24 = 5*v - 3*x. Let q be (-4)/v - 32/48. Factor -4/3*n**4 + 1/3*n**5 - 4/3*n**2 + 2*n**3 + 1/3*n + q.
n*(n - 1)**4/3
Suppose 0 = -4*d + c + 11, -d - 5*c - 3 = 10. Let j**4 - j - 5*j**3 - 3*j + 3*j**d + 2*j**2 + 3*j**2 = 0. What is j?
0, 1, 2
Let p(i) be the third derivative of 0 + 0*i - 1/4*i**4 + 0*i**5 - 6*i**2 + 0*i**3 + 9/80*i**6. Determine q, given that p(q) = 0.
-2/3, 0, 2/3
Let g(j) = -j + 1. Let t(f) = 17*f**2 + 12*f - 4. Let x(b) = -4*g(b) - t(b). Let i(q) = -6*q**2 - 3*q. Let y(m) = -11*i(m) + 4*x(m). Factor y(c).
-c*(2*c - 1)
Let c = 2/575 + 2294/1725. Suppose c*l + 0 + 2*l**2 = 0. Calculate l.
-2/3, 0
Let o = -5 - -8. Factor j - j**o + j**5 - j.
j**3*(j - 1)*(j + 1)
Let z(h) be the third derivative of -1/300*h**6 - 1/525*h**7 + 0 - 3*h**2 + 0*h + 1/150*h**5 + 1/60*h**4 + 0*h**3. Let z(n) = 0. What is n?
-1, 0, 1
Let w = -1 + 5. Let p be (10 + (-5 - -4))/2. What is h in 15/2*h**2 + 1 + 3/2*h**w - 11/2*h**3 - p*h = 0?
2/3, 1
Let r(u) be the third derivative of -4*u**2 - 1/240*u**6 + 1/120*u**7 + 0*u + 0*u**3 + 0*u**4 + 0*u**5 + 0. Let r(s) = 0. Calculate s.
0, 2/7
Let n be (60/495)/((-268)/(-270)). Let b = n + 4/67. Factor 4/11*m**3 - 6/11*m + 2/11*m**5 + 6/11*m**4 - b - 4/11*m**2.
2*(m - 1)*(m + 1)**4/11
Let y = -931 + 6523/7. Let 6/7*f**3 + y*f**2 + 2/7*f**4 + 2/7*f + 0 = 0. What is f?
-1, 0
Factor -1/3*o**3 + 0*o**2 + 0 + 1/3*o.
-o*(o - 1)*(o + 1)/3
Let n(g) be the first derivative of -g**7/140 + g**6/30 - 11*g**5/180 + g**4/18 + g**3 - 2. Let o(s) be the third derivative of n(s). Let o(t) = 0. What is t?
1/3, 2/3, 1
Let n(k) = -7*k**2 - 7*k - 1. Let b(q) = 3*q**2 + 3*q. Let c(s) = -10*b(s) - 4*n(s). Suppose c(l) = 0. Calculate l.
-2, 1
Determine c, given that 8/11*c**3 + 0*c + 0 + 2/11*c**4 + 6/11*c**2 = 0.
-3, -1, 0
Let x(v) be the first derivative of -3*v**4/4 + 6*v**3 + 3*v**2/2 - 18*v - 45. Factor x(k).
-3*(k - 6)*(k - 1)*(k + 1)
Suppose -3*d - 4*s = -0*d - 19, -d = 4*s - 17. Let k(i) = i. Let o(r) = -7*r**2 + 4*r + 2. Let n(g) = d*k(g) + o(g). Factor n(u).
-(u - 1)*(7*u + 2)
Let j(w) be the second derivative of w**7/1260 + w**6/120 + w**5/30 - w**4/12 - 3*w. Let p(m) be the third derivative of j(m). Factor p(x).
2*(x + 1)*(x + 2)
Determine t, given that -18*t**3 - 10*t - 24*t**2 + 15*t**4 - 11*t**2 + 8*t**3 = 0.
-1, -1/3, 0, 2
Let a(z) be the third derivative of 0*z + 1/120*z**6 + 0*z**3 + 0 - 1/12*z**5 + 1/8*z**4 + 1/210*z**7 + 6*z**2. Factor a(l).
l*(l - 1)**2*(l + 3)
Suppose -6 - 6 = -3*n. Suppose k - p + 0 + 3 = 0, -n*p = -12. Let k + 0*q - 2/11*q**2 = 0. What is q?
0
Let h(i) be the third derivative of 0*i + 4*i**2 - 1/300*i**6 + 0*i**5 + 0*i**3 + 0*i**4 + 0 + 0*i**7 + 1/840*i**8. Factor h(l).
2*l**3*(l - 1)*(l + 1)/5
Let l = -39 - -42. Let p(y) = -y. Let w be p(-2). Factor 3/2*m**w - 3/2*m - 1/2*m**l + 1/2.
-(m - 1)**3/2
Factor 3/8*m**2 - m + 1/4*m**3 - 1/8*m**4 + 1/2.
-(m - 2)*(m - 1)**2*(m + 2)/8
Let o(w) be the third derivative of -w**8/2688 + w**6/480 - w**4/192 - 13*w**2. Factor o(s).
-s*(s - 1)**2*(s + 1)**2/8
Suppose 6*s = -0*s. Suppose -4*d + 6*d - 4 = s. Factor -2/5*f**4 + 2/5*f - 2/5*f**3 + 2/5*f**d + 0.
-2*f*(f - 1)*(f + 1)**2/5
Let y be (-64)/(-12) + (-1)/3. Find s such that -1/2*s**y - 1/2*s**2 + 1/2*s**4 + 0 + 0*s + 1/2*s**3 = 0.
-1, 0, 1
Let n(r) be the first derivative of -r**4/6 - 2*r**3 - 9*r**2 - 3*r - 3. Let g(i) be the first derivative of n(i). Solve g(w) = 0.
-3
Let h(u) be the second derivative of -u**5/5 + u**4/6 - 2*u**3/3 + 2*u. Let a(f) = -7*f**3 + 4*f**2 - 7*f. Let q(p) = -3*a(p) + 5*h(p). Solve q(i) = 0.
0, 1
Let i(o) be the second derivative of -o**4/6 + 4*o**3/3 - 4*o**2 - 16*o. Factor i(x).
-2*(x - 2)**2
Suppose -5*k + 4*k + 24 = 5*b, 2*b - 12 = -k. Let f(q) = q**2 - 3*q - 2. Let g be f(b). Factor -4/7*p**3 + 4/7*p + 0*p**g - 2/7 + 2/7*p**4.
2*(p - 1)**3*(p + 1)/7
Let q(f) = 3*f**2 + 2*f - 2. Let p(m) = 3*m**2 - 5. Let o(y) = 4*y**2 + y - 5. Let i(d) = 4*o(d) - 3*p(d). Let r(b) = 4*i(b) - 10*q(b). Factor r(g).
-2*g*(g + 2)
Let b be (-12)/(-8) + 6/(-4). Let n(k) be the second derivative of 0 - 1/70*k**5 + b*k**3 + 0*k**2 - 1/42*k**4 + 2*k. Let n(p) = 0. Calculate p.
-1, 0
Let q(m) = -5*m**5 - 5*m**4 + 4*m**3 - 3*m - 3. Let w(g) = 4*g**5 + 4*g**4 - 4*g**3 + 2*g + 2. Let l = -19 - -16. Let f(c) = l*w(c) - 2*q(c). Factor f(r).
-2*r**3*(r - 1)*(r + 2)
Let n(a) be the first derivative of a**7/60 + a**6/20 + a**5/30 + a**3/3 - 3. Let k(b) be the third derivative of n(b). Factor k(z).
2*z*(z + 1)*(7*z + 2)
Let r = 0 + 0. Let o(p) = p + 3. Let h be o(5). Factor -2 + z**5 - 11*z + z**4 - h*z**2 + 4*z + z**4 + r*z**4 - 2*z**3.
(z - 2)*(z + 1)**4
Suppose 5*a + 15 = 5. Let o be 0/2*1/a. Factor 1/2*g**2 - 1/2 + o*g.
(g - 1)*(g + 1)/2
Factor u**2 - 31*u**4 - 22*u**4 - 22*u**4 + 74*u**4.
-u**2*(u - 1)*(u + 1)
Let w(p) = -p**3 + 1. Let o be 1 - -2 - (-15)/(-3). Let y(b) =