 = 3*o. Let c be (-119)/(-231) - s/22. Determine t, given that 0 + c*t**2 - 1/3*t = 0.
0, 1
Factor 21*g - 28*g - 41*g + 3*g**2 - 2*g**3 + 5*g**3 + 60.
3*(g - 2)**2*(g + 5)
Let h be (2 + -5)*8/(-6). What is i in -h*i - i**3 + 2*i + 3*i**3 = 0?
-1, 0, 1
Suppose 0 = u + 4*z - 8, -u = -2*z + 4*z - 4. Let m(b) be the second derivative of 0 + 1/3*b**3 + 1/2*b**2 + u*b**4 - 1/10*b**5 - 1/30*b**6 - b. Factor m(j).
-(j - 1)*(j + 1)**3
Let u be 2 + ((-6)/(-16) - (-4472)/704). Factor 2/11 + u*h**2 - 128/11*h**3 - 24/11*h.
-2*(4*h - 1)**3/11
Let w(a) be the first derivative of 2*a**5/5 - a**4/2 + 2*a**3/3 - a**2 + 4*a + 1. Let h(l) = l**3 - l**2 - 1. Let q(u) = -4*h(u) - w(u). Factor q(c).
-2*c*(c - 1)*(c + 1)**2
Let w(p) = -3*p**3 + 3*p**2 - 2. Let t(a) = 4*a**3 - 4*a**2 + 3. Let x(f) = -4*t(f) - 6*w(f). Suppose x(l) = 0. What is l?
0, 1
Let d be (8/(-90)*-3)/((-6)/(-9)). Find p, given that 0 + 6/5*p**3 + 6/5*p**2 + 2/5*p**4 + d*p = 0.
-1, 0
Let l(v) be the second derivative of 0*v**2 + 0 - 2/15*v**6 + 1/30*v**5 + 3*v - 1/14*v**7 + 1/9*v**4 - 1/18*v**3. Factor l(y).
-y*(y + 1)**2*(3*y - 1)**2/3
Let 0 - 10/9*q**2 + 2/3*q**4 + 4/9*q - 8/9*q**3 = 0. What is q?
-1, 0, 1/3, 2
Let q(y) be the third derivative of 0*y**3 + 0*y + 1/8*y**4 + 0 + 1/120*y**6 + 3*y**2 - 1/15*y**5. Factor q(k).
k*(k - 3)*(k - 1)
Suppose 13/7*g**3 + 2/7*g + 6/7*g**4 + 9/7*g**2 + 0 = 0. What is g?
-1, -2/3, -1/2, 0
Let r(a) be the second derivative of 0*a**4 + 1/100*a**5 + 3*a + 0*a**3 + 0 + 1/210*a**7 + 1/75*a**6 + 0*a**2. Find o such that r(o) = 0.
-1, 0
Let h(o) = -o - 4. Let d be h(-7). Determine g, given that -2*g + 3*g**3 - 2*g**2 - 6*g**5 + 2*g**5 + 4*g**4 + 3*g**d - 2*g**4 = 0.
-1, -1/2, 0, 1
Let a = -11 + 11. Suppose -4*y + 12 + a = 0. Let -8/9*d + 0 - 32/9*d**2 - 10/9*d**y + 50/9*d**4 = 0. Calculate d.
-2/5, 0, 1
Suppose -2*n + 10 = k, 3*n - 11 = -k + 2. Let i(z) be the first derivative of 4 + 23*z**k + 24*z**5 + 25/3*z**6 + 0*z + 8*z**3 + z**2. Factor i(j).
2*j*(j + 1)**2*(5*j + 1)**2
Factor 74*k + 3*k**2 + 15 - 112*k + 56*k.
3*(k + 1)*(k + 5)
Let m = 48 - 139/4. Suppose -1 - 9/2*d**4 + 6*d + 51/4*d**3 - m*d**2 = 0. Calculate d.
1/2, 2/3, 1
Let z(r) be the third derivative of 9*r**2 - 1/360*r**6 + 0*r**5 + 0*r**3 + 0*r + 1/630*r**7 + 0 + 0*r**4. Factor z(b).
b**3*(b - 1)/3
Let k be -2*(-15)/6 - 4 - -2. Let v(p) be the first derivative of -2/15*p**k - 4/5*p**2 - 2 - 8/5*p. Find m such that v(m) = 0.
-2
Let v = 44 + -42. Suppose 13 = -4*m + 29. Let -2*n + 2*n**5 - 6*n**2 + 2*n**v + 2*n**4 + 2 - n**3 - 3*n**3 + m*n = 0. What is n?
-1, 1
Factor 0*r**2 - 3 - 3 - 3*r + 3*r**2.
3*(r - 2)*(r + 1)
Factor 6/7*n + 0*n**2 + 4/7 - 2/7*n**3.
-2*(n - 2)*(n + 1)**2/7
Let i(z) be the first derivative of z**8/420 - z**7/210 - z**6/90 + z**5/30 + 4*z**3/3 + 5. Let n(q) be the third derivative of i(q). What is v in n(v) = 0?
-1, 0, 1
Let q(d) be the third derivative of -d**7/4200 + d**6/1200 + d**5/100 - d**4/24 - 3*d**2. Let x(p) be the second derivative of q(p). Factor x(v).
-3*(v - 2)*(v + 1)/5
Suppose -2/15 - 4/15*y**2 + 8/15*y**3 - 8/15*y + 2/5*y**4 = 0. What is y?
-1, -1/3, 1
Find s, given that 7*s + 6*s + 7*s - 3*s**2 + 18 - 17*s = 0.
-2, 3
Suppose 4*b - 3 = -3*h, -2*h = -b + 2*h + 15. Let l = -77 - -233/3. Factor 0 + 2/3*i**4 - 2/3*i**2 + l*i - 2/3*i**b.
2*i*(i - 1)**2*(i + 1)/3
Suppose 4*h - 2*p = 3*p - 87, -93 = 5*h - p. Let c(u) = -u**2 + u + 1. Let l(b) = 15*b**2 - 24*b - 18. Let s(k) = h*c(k) - l(k). Factor s(f).
3*f*(f + 2)
Let u(j) be the first derivative of 0*j + 1/5*j**5 + 4/3*j**3 + 1/2*j**6 + 0*j**2 + 3 - 2*j**4. What is n in u(n) = 0?
-2, 0, 2/3, 1
Let d(o) = -2*o**5 - 6*o**4 + 4. Let r(s) = s**4 - 1. Let v(l) = 0*l**2 + 2*l**2 + 4 + l**3 - 6*l**2. Let m be v(4). Let c(n) = m*r(n) + d(n). Factor c(j).
-2*j**4*(j + 1)
Let q(h) be the first derivative of -h**4/4 + 3*h**3 - 9*h**2/2 + 11*h - 3. Let l be q(8). Factor -3*b**4 + b**4 + 3*b**2 - b**2 - 2*b + 2*b**l.
-2*b*(b - 1)**2*(b + 1)
Suppose 0 = -0*t + t - 294. Let c be 380/15 + (-3)/9. Factor c*r - t*r**2 + 59*r - 38*r**3 - 5 + 381*r**3 - 3.
(7*r - 2)**3
Let p(t) be the third derivative of t**8/336 + t**7/210 - t**6/60 - t**5/30 + t**4/24 + t**3/6 - 5*t**2. Determine x, given that p(x) = 0.
-1, 1
Let w(f) be the second derivative of f**7/14 - f**6/10 - 3*f**5/10 + 2*f. Let w(q) = 0. Calculate q.
-1, 0, 2
Let z be (-15)/675 - (-2)/15. Let g(d) be the first derivative of -3 + 0*d + 2/27*d**3 + z*d**2. Suppose g(t) = 0. What is t?
-1, 0
Let h(i) be the first derivative of -i**6/300 + i**4/60 + 5*i**2/2 + 2. Let y(m) be the second derivative of h(m). Factor y(g).
-2*g*(g - 1)*(g + 1)/5
Let d be 80/18 + (-14 - -6 - -4). Factor -d*r**3 + 2/9*r**4 - 2/9 + 0*r**2 + 4/9*r.
2*(r - 1)**3*(r + 1)/9
Let q(r) be the third derivative of r**6/60 + r**5/15 + r**4/12 + 3*r**2 + 2*r. Factor q(b).
2*b*(b + 1)**2
Let d(k) = -k**3 - 9*k**2 - 6*k + 18. Let x be d(-8). Let n(q) be the second derivative of -1/54*q**4 - 2/27*q**3 + x*q + 0*q**2 + 0. Factor n(m).
-2*m*(m + 2)/9
Let k = 613224/35 - 17516. Let j = k + -22/5. Factor j*w**3 + 2/7*w**2 + 0 + 0*w.
2*w**2*(w + 1)/7
Let -6*t**2 - 73*t - 9*t**3 - 6*t**4 + 3*t**4 + 73*t = 0. What is t?
-2, -1, 0
Let b(q) = 2*q + 19. Let m be b(-8). Factor 2*n + 6*n**2 - 2*n**2 - 3*n**3 - m - n**2 + n.
-3*(n - 1)**2*(n + 1)
Let h be 8/(-6)*78/(-4). Suppose 2*o = 2*l + h, 4*l - 2*l + 42 = 4*o. Determine q so that -4*q + o*q**2 - 9*q**4 - 4*q**3 + 8*q + q**3 = 0.
-2/3, 0, 1
Suppose v + 0*v - 2 = 0. Factor r - 1/2 - 1/2*r**v.
-(r - 1)**2/2
Let y(a) be the second derivative of a**5/10 + a**4/3 - 4*a**3/3 - 8*a**2 - 30*a. Solve y(q) = 0.
-2, 2
Let a(b) be the third derivative of -b**7/210 + b**6/40 + 5*b**2. Suppose a(h) = 0. What is h?
0, 3
Factor -4/3*i**2 + 1/3*i**5 - i + 2/3*i**3 + 4/3*i**4 + 0.
i*(i - 1)*(i + 1)**2*(i + 3)/3
Let d(s) = -2*s - 4*s + s**2 + 4*s + 2. Let n(w) = 5*w**2 - 8*w + 9. Suppose 0*j - 5*j + 40 = l, -2*l = 10. Let x(i) = j*d(i) - 2*n(i). Solve x(c) = 0 for c.
-2, 0
Let z(n) be the second derivative of -n**5/5 + n**4 - 18*n. Factor z(s).
-4*s**2*(s - 3)
Let d = -37/24 + 5/3. Let x(m) be the second derivative of d*m**4 + 1/60*m**6 - 3/40*m**5 + 2*m + 0*m**2 - 1/12*m**3 + 0. Factor x(k).
k*(k - 1)**3/2
Let g(t) be the second derivative of t**4/54 - t**3/27 - 2*t**2/9 - 8*t. Find o such that g(o) = 0.
-1, 2
Suppose 3*c - 27 = -3*b, b - 2 = -2*c + 13. Suppose c + 2 = 4*f. Factor 2 - 14*y - 8*y**f + 2*y**2 - 6.
-2*(y + 2)*(3*y + 1)
Suppose 12/7*z**2 - 6/7*z**5 - 2/7*z + 8/7*z**3 - 4/7 - 8/7*z**4 = 0. Calculate z.
-1, 2/3, 1
Let k(n) = 2*n**3 + 2*n**2 - 2*n - 8. Let j(c) = 5*c**3 + 3*c**2 - 5*c - 16. Let q(f) = 6*j(f) - 13*k(f). What is a in q(a) = 0?
-1, 1, 2
Let w = 31/2 - 15. Let q(l) be the second derivative of -1/24*l**4 - 2*l + 0 + w*l**2 + 1/12*l**3. Let q(v) = 0. Calculate v.
-1, 2
Let i(x) be the first derivative of -x**6/2 + 9*x**5/5 - 9*x**4/4 + x**3 + 3. Determine n, given that i(n) = 0.
0, 1
Let f(h) be the third derivative of 4*h**2 + 0*h - 1/45*h**6 + 0 - 1/210*h**7 + 0*h**3 - 1/60*h**5 + 1/36*h**4. Factor f(a).
-a*(a + 1)*(a + 2)*(3*a - 1)/3
Let h = 7 + 3. Let x be (-13)/(-15) - 2/h. Solve 1/3*l - l**3 + 0 + 0*l**2 - x*l**4 = 0 for l.
-1, 0, 1/2
Factor 44*l**2 - l**4 - 44*l**2.
-l**4
Suppose 0*o + 9 = 3*o + c, -4*c + 4 = -4*o. Determine n so that -3*n**3 + o*n**3 - 2*n**3 + 3*n**4 + 3*n + 4*n**2 - 7*n**2 = 0.
-1, 0, 1
Let z(y) = -12*y. Let d be z(4). Let k be ((-9)/(-42))/((-9)/d). Suppose -k*i**2 + 0 - 8/7*i - 2/7*i**3 = 0. Calculate i.
-2, 0
Let p(y) be the third derivative of -241/540*y**6 - 8/27*y**3 - 23/27*y**5 + 3*y**2 - 2/189*y**8 - 104/945*y**7 - 19/27*y**4 + 0 + 0*y. Factor p(b).
-2*(b + 2)**3*(4*b + 1)**2/9
Let u(p) be the first derivative of 0*p - 5/6*p**3 - 3/10*p**5 - 1/4*p**2 - 1 - 7/8*p**4. Factor u(a).
-a*(a + 1)**2*(3*a + 1)/2
Let h(f) be the first derivative of -f**3/6 + f**2/2 - f/2 - 7. Suppose h(q) = 0. Calculate q.
1
Let k(j) = -6*j**3 - 99*j**2 - 84*j. Suppose -8 = 6*x - 2*x. Let i(z) = z**3 + 14*z**2 + 12*z. Let o(g) = x*k(g) - 15*i(g). Factor o(y).
-3*y*(y + 2)**2
Let k = 8 - 4. Suppose -6*w**3 - 4*w**2 + w - 4*w**2 - 2*w**5 + 8*w**k + 7*w = 0. Calculate w.
-1, 0, 1, 2
Let b(i) be the first derivative of -3*i**4/4 + 3*i**2/2 - 6. Let b(l) = 0. What is l