0, 1
Suppose 0 = r - 3*r + 4. Let d(o) be the second derivative of 0*o**3 + 1/12*o**4 - 1/2*o**r + 0 - 3*o. Find m, given that d(m) = 0.
-1, 1
Let j(a) = a**5 - a**4 + a**3 + a**2. Let r(b) = -2*b**5 - 2*b**4 + 7*b**3 - 13*b**2 + 5*b - 1. Let t(d) = -3*j(d) - r(d). Find k such that t(k) = 0.
1
Let k(w) be the second derivative of w**4/90 - 2*w**3/45 + w**2/15 + 12*w. Factor k(c).
2*(c - 1)**2/15
Let q(s) be the first derivative of -2*s**3/21 + 2*s**2 - 14*s - 23. Suppose q(o) = 0. What is o?
7
Let l(p) = -4*p**2 + 2*p + 2. Let f(a) = -9*a**2 + 4*a + 3. Let b(t) = -2*f(t) + 5*l(t). Let b(q) = 0. Calculate q.
-1, 2
Suppose 3*z - h + 5 = 0, -4*h - 12 = z - 32. Factor z*v + 3/4*v**3 + 0 + 0*v**2.
3*v**3/4
Let g(p) be the second derivative of 1/12*p**3 - 1/4*p**2 + 10*p + 1/24*p**4 - 1/40*p**5 + 0. Factor g(o).
-(o - 1)**2*(o + 1)/2
Let f(j) be the first derivative of -j**5/25 + j**4/5 + 2*j**3/15 - 6*j**2/5 - 9*j/5 + 2. Factor f(v).
-(v - 3)**2*(v + 1)**2/5
Let q(f) = -1. Let n(c) = 18*c**2 - 13*c - 1. Let h(u) = 2*n(u) - 6*q(u). Factor h(w).
2*(2*w - 1)*(9*w - 2)
Let i = -28 + 63. Let s be (20/i)/((-3)/(-7)). Determine f so that -5/3*f**2 + s*f**5 + 8/3*f**4 - 1/3*f + 1/3 + 1/3*f**3 = 0.
-1, 1/2
Let n = -82/141 - -31571/705. Let i = n - 44. Factor -2/5*k + 1/5 + i*k**2.
(k - 1)**2/5
Let x(g) = -18*g**4 - 80*g**3 + 50*g**2 + 72*g - 36. Let f(v) = 18*v**4 + 79*v**3 - 51*v**2 - 72*v + 35. Let r(p) = 4*f(p) + 5*x(p). Let r(i) = 0. Calculate i.
-5, -1, 2/3
Factor -2/3*x + 2/3*x**5 + 4/3*x**4 + 0 - 4/3*x**2 + 0*x**3.
2*x*(x - 1)*(x + 1)**3/3
Let r(c) be the third derivative of -c**6/510 + c**5/102 + c**4/51 - c**3/17 - 21*c**2. Determine l so that r(l) = 0.
-1, 1/2, 3
Let c = -2/67 - -140/201. Suppose 5*m - 61 + 46 = 0. Factor 2/3*l**2 - 2/3*l**4 + 0 - 2/3*l**5 + c*l**m + 0*l.
-2*l**2*(l - 1)*(l + 1)**2/3
Factor 0 + 1/5*x**5 - 4/5*x**2 - x**4 + 8/5*x**3 + 0*x.
x**2*(x - 2)**2*(x - 1)/5
Let c(o) be the second derivative of 1/40*o**5 + 0 + 1/4*o**3 - 1/4*o**2 - o - 1/8*o**4. Factor c(x).
(x - 1)**3/2
Let z(w) be the third derivative of w**7/420 - w**6/180 - w**5/30 - w**3/2 + w**2. Let l(a) be the first derivative of z(a). Factor l(o).
2*o*(o - 2)*(o + 1)
Let y(r) = -r**2 + 10*r - 4. Let l(d) = -d. Let w = 2 - 4. Let j = w - -3. Let u(n) = j*y(n) + 6*l(n). Factor u(x).
-(x - 2)**2
Let w(i) be the third derivative of -i**11/665280 - i**10/302400 - i**5/60 - 9*i**2. Let l(o) be the third derivative of w(o). Determine h, given that l(h) = 0.
-1, 0
Let m(b) be the second derivative of 9*b**6/50 - b**4/20 + b. Factor m(d).
3*d**2*(3*d - 1)*(3*d + 1)/5
Factor 158*o**2 - 5 - 203*o**2 + 0 - 30*o.
-5*(3*o + 1)**2
Find s, given that 1/4*s**3 - 7/4*s - 1 - 1/2*s**2 = 0.
-1, 4
Let n(g) = -g**3 - 7*g**2 - 6*g + 2. Let y be n(-6). Determine u so that 6/7*u + 4/7 + 2/7*u**y = 0.
-2, -1
Suppose f**4 + f**3 - 3*f**3 + 0*f**4 = 0. Calculate f.
0, 2
Solve -1 + 3*p**2 - 2*p**2 + p**5 + 1 - p**4 - p**3 = 0 for p.
-1, 0, 1
Let o(f) be the second derivative of 1/48*f**4 + 1/4*f**2 + 0 + 3*f + 1/8*f**3. Factor o(m).
(m + 1)*(m + 2)/4
Let u = -1200 - -1200. Determine c so that u*c + 1/5*c**3 + 1/5*c**2 + 0 = 0.
-1, 0
Let c(o) be the third derivative of o**6/280 - 3*o**5/140 + 3*o**4/56 - o**3/14 + 2*o**2. Determine j, given that c(j) = 0.
1
Let k = -37 - -39. Let j(x) be the first derivative of -x**2 + 1/3*x**3 + x + k. Factor j(n).
(n - 1)**2
Let f(n) be the second derivative of 5*n - 1/9*n**3 + 2/9*n**2 + 1/54*n**4 + 0. Factor f(m).
2*(m - 2)*(m - 1)/9
Let j = -5 + 8. Let p be (-20)/15*j*-1. Suppose 0*n**3 + 0 + 2/7*n**2 - 2/7*n**p + 0*n = 0. What is n?
-1, 0, 1
Suppose 23 = 2*u - 5*o, u - 3*o - 13 = -0*o. Determine s, given that -1/4*s**u + 1/2*s**3 + 0 - 1/4*s**2 + 0*s = 0.
0, 1
Let r = 13 - 12. Let f(x) be the first derivative of 0*x + r - 1/8*x**2 + 1/12*x**3. Factor f(b).
b*(b - 1)/4
Let s(l) be the second derivative of -l**5/40 + l**4/12 - l. Factor s(f).
-f**2*(f - 2)/2
Let u be (33/(-621))/(6/(-18)). Let g = u + 4/23. Factor -4/3 - g*h**2 - 4/3*h.
-(h + 2)**2/3
Let r(y) be the second derivative of -y**5/90 - y**4/6 + 7*y**3/9 - 11*y**2/9 - 29*y. Factor r(q).
-2*(q - 1)**2*(q + 11)/9
Let l be (-2)/(-9) + (-6)/27. Let l - 4*k**2 - k**5 - k + 0 - 6*k**3 - 4*k**4 = 0. Calculate k.
-1, 0
Let h(i) = -3*i + 20. Let y be h(6). Suppose -x - 13 = 4*k - 8*k, 0 = y*x + k - 10. Factor b**2 + 1/3 + 1/3*b**x + b.
(b + 1)**3/3
Let z = 18 + -14. Determine c, given that -z + 3*c**2 - c**2 - c**4 + 3 = 0.
-1, 1
Let n(k) be the second derivative of 1/6*k**4 + 0*k**3 - 1/10*k**5 - 1/15*k**6 + 0 + 0*k**2 - 4*k + 1/21*k**7. Factor n(x).
2*x**2*(x - 1)**2*(x + 1)
Let c(s) be the second derivative of -s**4/32 - 3*s**3/16 - 10*s. Factor c(v).
-3*v*(v + 3)/8
Factor -4/3 + 1/6*o**3 - 5/2*o - o**2.
(o - 8)*(o + 1)**2/6
Let k(m) = 4*m**3 + 2 + 3*m**3 - 7*m**2 - 6*m**3. Let z be k(7). Factor 6*s**4 - 3*s + z*s**2 + 3*s + 6*s**3 + 2*s**5.
2*s**2*(s + 1)**3
Let t(p) = p**2 - p. Let m(r) = 3*r**2 - 8*r. Let h(c) = -m(c) + 4*t(c). Find y such that h(y) = 0.
-4, 0
Let x(s) = 6*s**3 + s**2 - 6*s - 6. Let g(u) = u**3 - u - 1. Let d = 10 - 14. Let f = d + 2. Let i(w) = f*x(w) + 10*g(w). Factor i(r).
-2*(r - 1)*(r + 1)**2
Let t(j) be the first derivative of j**5/20 - j**4/8 - 2*j**3/3 - 4. Solve t(y) = 0.
-2, 0, 4
Let s(b) be the second derivative of -1/15*b**3 + 0 + 0*b**2 + 1/15*b**4 + 2*b. Factor s(h).
2*h*(2*h - 1)/5
Factor -2/5*d**3 - 4/5*d - 2*d**2 + 16/5.
-2*(d - 1)*(d + 2)*(d + 4)/5
Suppose -1 - 11 = -2*j. Let h(x) be the second derivative of -2*x - 1/75*x**j + 0 + 0*x**3 + 1/30*x**4 + 0*x**5 + 0*x**2. Factor h(n).
-2*n**2*(n - 1)*(n + 1)/5
Let p(b) = 4*b**2 + 5*b - 4. Let s be (1 + -3)*(-18)/12. Let c(v) = 2*v**2 + 3*v - 2. Let u(z) = s*p(z) - 5*c(z). Factor u(i).
2*(i - 1)*(i + 1)
Let y(m) be the third derivative of -m**7/70 - m**6/10 - m**5/4 - m**4/4 + 10*m**2. Factor y(o).
-3*o*(o + 1)**2*(o + 2)
Let z = -3 + 8. Suppose -z*o + 8 = -2*d - 6, -d + 23 = 5*o. Factor 0*t - t**4 + d*t**3 + 3*t**2 - 2*t - 2*t**3 + 2 - 3*t.
-(t - 1)**3*(t + 2)
Let u(a) = -a**4 - a**2 - a + 1. Let b(r) = -9*r**4 - 5*r**2 - 5*r + 5. Let h(p) = -b(p) + 5*u(p). Factor h(w).
4*w**4
Let w = -16 + 12. Let f be (-2 + w)/((-12)/8). What is g in 0*g - 7/4*g**f - 1/2*g**2 + 0 + 9/4*g**3 = 0?
0, 2/7, 1
Let r = -12/23 + 47/46. Let s(t) be the first derivative of 1/2*t**2 - 1 - 1/6*t**3 - r*t. Suppose s(i) = 0. Calculate i.
1
Let l(o) be the first derivative of 3/2*o**2 + 2 - 2*o - 1/3*o**3. Find b, given that l(b) = 0.
1, 2
Let y(z) = z**3 + z**2 - 1. Let t(h) = -7*h**3 + h**2 + 24*h + 24. Let c(m) = 5*t(m) + 40*y(m). Let c(o) = 0. Calculate o.
-4, -1
Let f(x) be the first derivative of -x**2/2 + 2*x + 3. Let r be f(0). Suppose -3*i + 6*i**2 - r - 1 + 5*i**3 + i**3 - 3*i**5 - 3*i**4 + 0*i**5 = 0. Calculate i.
-1, 1
Let q(b) = -b**3 + 5*b**2 + 2*b - 7. Let g = -13 + 18. Let n be q(g). Factor -2 - 1 + a**2 + a + n.
a*(a + 1)
Let a(o) = -o**2 + 6*o - 6. Let b be a(3). Let 0*r**2 - b*r**2 - 7*r**3 + 4*r**3 - r + 0*r**2 - r**4 = 0. Calculate r.
-1, 0
Let r(y) be the second derivative of -y**6/120 - y**5/60 + y**4/6 + 2*y**3/3 + 2*y**2 + 5*y. Let l(v) be the first derivative of r(v). Solve l(c) = 0 for c.
-2, -1, 2
Let n = -423 + 13537/32. Let z(v) be the third derivative of n*v**4 - v**2 + 0 - 1/80*v**5 - 1/160*v**6 + 1/280*v**7 + 0*v**3 + 0*v. Factor z(m).
3*m*(m - 1)**2*(m + 1)/4
Let c(n) be the first derivative of -n**8/420 + n**7/420 + n**6/180 - n**3 - 1. Let z(v) be the third derivative of c(v). Factor z(f).
-2*f**2*(f - 1)*(2*f + 1)
Let g(f) be the first derivative of -f**5/5 + f**4/2 + f**3 - 2*f**2 - 4*f - 8. Factor g(r).
-(r - 2)**2*(r + 1)**2
Let k = -23 - -26. Let y(l) be the first derivative of 1/12*l**k - 2 - 1/16*l**4 + 0*l**2 + 0*l. Factor y(q).
-q**2*(q - 1)/4
Let j(s) = 20*s**4 + 38*s**3 + 44*s**2 - 2*s. Let p(o) = 7*o**4 + 13*o**3 + 15*o**2 - o. Let t(y) = 5*j(y) - 14*p(y). Factor t(m).
2*m*(m + 1)**2*(m + 2)
Suppose 8*d**3 + 2*d**2 - d - 2*d**3 - 2 - 5*d + 0*d = 0. Calculate d.
-1, -1/3, 1
Factor -2/9*m**2 + 4/9 + 2/9*m.
-2*(m - 2)*(m + 1)/9
Let g(o) be the second derivative of 1/12*o**3 + 0 - 1/4*o**2 + 3*o - 1/40*o**5 + 1/24*o**4. Find s, given that g(s) = 0.
-1, 1
Factor 0*m**2 - 1/5*m**3 + 1/5*m + 0.
-m*(m - 