q*d + 2/5*d**2 = 0. Calculate d.
-1
Let g(r) be the third derivative of r**8/336 + r**7/30 + 3*r**6/20 + 11*r**5/30 + 13*r**4/24 + r**3/2 + 3*r**2. Factor g(u).
(u + 1)**4*(u + 3)
Let c(p) = -p**2. Let d(i) = -5*i**2 - 12*i - 4. Suppose 0*b + b = 1. Let z(w) = b*d(w) + 4*c(w). Find a, given that z(a) = 0.
-2/3
Let z be (1*(-4)/(-18))/((-3)/(-1)). Let r(c) be the first derivative of -z*c**3 + 2/9*c**2 - 2/9*c + 3. Solve r(h) = 0 for h.
1
Let d(k) = -5*k**5 + 2*k**4 - 6*k**3 - 2*k**2 + 5*k - 6. Let c(z) = -4*z**5 + 2*z**4 - 5*z**3 - 2*z**2 + 4*z - 5. Let m(j) = 6*c(j) - 5*d(j). Factor m(h).
h*(h - 1)*(h + 1)**3
Find c, given that 2/13*c**2 - 2/13*c**3 + 0 + 0*c = 0.
0, 1
Let r(b) be the third derivative of -b**6/840 + b**4/14 + 5*b**3/6 - 4*b**2. Let s(a) be the first derivative of r(a). Factor s(l).
-3*(l - 2)*(l + 2)/7
Factor -12/11*r + 2/11 + 18/11*r**2.
2*(3*r - 1)**2/11
Factor -3/4*k**3 + 3/4*k**2 + 0*k + 0.
-3*k**2*(k - 1)/4
Let i(o) be the second derivative of -o**6/10 + 9*o**5/20 - o**4/4 - 3*o**3/2 + 3*o**2 + 10*o. Factor i(h).
-3*(h - 2)*(h - 1)**2*(h + 1)
Factor -1/3*o**2 + 2/3*o - 1/3.
-(o - 1)**2/3
Let b = -16/39 - -1/13. Let q = 2/3 + b. Factor 9*o**3 - q - 9*o**2 + 3*o.
(3*o - 1)**3/3
Solve 5/2*m - 3 - 1/2*m**2 = 0.
2, 3
Let v(s) be the third derivative of -s**7/945 - s**6/108 - 7*s**5/270 - s**4/36 + 12*s**2. Solve v(m) = 0.
-3, -1, 0
Let g(w) = -w**3 - w + 1. Let y(v) = 2*v**3 - 6*v**2 + 22*v - 14. Let a(i) = 4*g(i) + y(i). Factor a(u).
-2*(u - 1)**2*(u + 5)
Factor 5*k**5 - 3*k**5 + 121*k**3 - 119*k**3 - 4*k**5.
-2*k**3*(k - 1)*(k + 1)
Let 10/11*q**3 - 2/11*q**4 - 4/11 - 18/11*q**2 + 14/11*q = 0. What is q?
1, 2
Let k be (-24)/(-10) - (-9)/15. Suppose -7 - 2 = -k*u. Determine p, given that 4*p + 5*p**2 + p + u*p**2 - 2 + p = 0.
-1, 1/4
Let x be (-27)/(-12) - (-2)/(-8). Solve 2/3*j**x - 4*j + 6 = 0 for j.
3
Let k = -13 + 11. Let i(u) = u**2 + 1. Let s(y) = -3*y**3 + 2*y**2 + 9*y + 8. Let t(p) = k*i(p) + s(p). Factor t(m).
-3*(m - 2)*(m + 1)**2
Suppose -1/3*n**2 - 3*n + 10/3 = 0. Calculate n.
-10, 1
Let q be (-3)/6 + (-15)/(-6). Let m(i) = 3*i**4 - 2*i**q - i**4 + 0*i**2. Let w(y) = -4*y**4 + y**3 + 3*y**2. Let l(a) = -5*m(a) - 2*w(a). Factor l(c).
-2*c**2*(c - 1)*(c + 2)
Let b be (-14)/8*16/(-6). Suppose 30 = -67*r + 82*r. Factor -b*n**r + 8/3 - 4/3*n**3 - 8/3*n.
-2*(n + 2)**2*(2*n - 1)/3
Let y(f) be the third derivative of 1/120*f**4 + 0*f + 0*f**3 - 7/600*f**6 - 2*f**2 - 2/525*f**7 - 1/150*f**5 + 0. Suppose y(q) = 0. What is q?
-1, 0, 1/4
Let m be (-3)/(((-1)/(-1))/(-1)). Let o(g) = -4*g**2 - g - 3. Let j(u) = u**2 + 1. Let b(q) = m*j(q) + o(q). Solve b(z) = 0 for z.
-1, 0
Determine m, given that -4/3*m**3 + 2/3 - 11/3*m + 13/3*m**2 = 0.
1/4, 1, 2
What is b in 6/7*b - 2/7*b**2 - 4/7 = 0?
1, 2
Let u(f) be the second derivative of f**6/75 + f**5/50 - f**4/5 - 4*f**3/15 + 8*f**2/5 - 2*f - 12. Find s, given that u(s) = 0.
-2, 1, 2
Let n(y) be the second derivative of y**6/10 - y**4/4 + 12*y. Let n(i) = 0. What is i?
-1, 0, 1
Let l(r) be the second derivative of 0 + 1/90*r**4 + 0*r**3 + 3*r + 1/150*r**5 + 0*r**2. Factor l(s).
2*s**2*(s + 1)/15
Let a(s) = 2*s**2 - 2*s. Let h be a(2). Let y(t) be the second derivative of 1/30*t**h - 1/5*t**2 + 0 + 0*t**3 + 2*t. Factor y(m).
2*(m - 1)*(m + 1)/5
Let p be 7 - (1 + -3)*-1. Let d(m) be the second derivative of -1/10*m**p - 4*m**2 - 8/3*m**3 + 0 - 3*m - 5/6*m**4. Factor d(z).
-2*(z + 1)*(z + 2)**2
Factor -18*l**3 + 9*l**3 + 3*l + 3*l**3 + 3*l**5.
3*l*(l - 1)**2*(l + 1)**2
Let v(p) = -22*p**3 - 12*p**2 + 14*p. Let h(c) = -7*c**3 - 4*c**2 + 5*c. Let r(i) = 10*h(i) - 3*v(i). Factor r(u).
-4*u*(u - 1)*(u + 2)
Let t(d) = 20*d**2 - 7*d - 27. Let u(v) = 7*v**2 - 2*v - 9. Let y(i) = 4*t(i) - 11*u(i). Suppose y(q) = 0. Calculate q.
-1, 3
Suppose 6 = 2*c - 4*s, -4*c + s - 5*s - 36 = 0. Let k(w) = 2*w**2 + 8*w - 7. Let n be k(c). Suppose 0 + 0*v - 2/9*v**n - 4/9*v**2 = 0. Calculate v.
-2, 0
Let j(s) be the second derivative of -s**6/30 - s**5/4 - s**4/4 + 3*s**3/2 - 2*s + 3. Factor j(c).
-c*(c - 1)*(c + 3)**2
Factor 10*h - 3*h**2 - 22*h - h**2 - 8.
-4*(h + 1)*(h + 2)
Let d(v) be the third derivative of -v**7/560 - v**6/80 - 3*v**5/160 - 14*v**2. Factor d(x).
-3*x**2*(x + 1)*(x + 3)/8
Let h(u) be the third derivative of u**5/60 - u**3/6 - 5*u**2. Factor h(x).
(x - 1)*(x + 1)
Let f(s) = s**3 + 4*s**2 + 5*s + 5. Let y be f(-2). Suppose -4*r = -20, 0 = -2*t - y*t + 4*r - 5. Factor 4/5 - 2*a**t + 24/5*a**2 - 18/5*a.
-2*(a - 1)**2*(5*a - 2)/5
Let y be 11 + 6/(-2) - (-6)/(-3). Let z(q) be the first derivative of -q**3 + 4 - 3/2*q**2 + y*q. Factor z(k).
-3*(k - 1)*(k + 2)
Let i(r) be the third derivative of r**8/84 + 8*r**7/105 + r**6/6 + 2*r**5/15 - 16*r**2. Let i(n) = 0. Calculate n.
-2, -1, 0
Suppose -5*v + 0*v = -40. Let a be 2/7 - v/(-70). Determine y, given that -6/5*y**3 + 0 - a*y**5 + 0*y + 6/5*y**4 + 2/5*y**2 = 0.
0, 1
Let z(j) be the first derivative of 1 - 2*j + 2/3*j**3 + j**4 - 2*j**2. Find x, given that z(x) = 0.
-1, -1/2, 1
Determine u so that -12/11 - 34/11*u - 28/11*u**2 - 6/11*u**3 = 0.
-3, -1, -2/3
Suppose 4*b - 7*b - 51 = 0. Let c = 21 + b. Factor -1/2*j**c + 0 + 1/2*j**5 + 0*j + 0*j**3 + 0*j**2.
j**4*(j - 1)/2
Let m be (-4 - -1)*8/(-3). Let h(q) be the first derivative of -14*q**3/3 + 6*q - 6. Let z(j) = 9*j**2 - 4. Let o(w) = m*z(w) + 5*h(w). Factor o(a).
2*(a - 1)*(a + 1)
Suppose 4*b = -t + 20, -2*b - 3 = -11. Factor 2*x + 1/4*x**2 + t.
(x + 4)**2/4
Suppose -53*h = -62*h + 36. Factor 1/2 - 2*i**3 + 1/2*i**h + 3*i**2 - 2*i.
(i - 1)**4/2
Let z(m) be the third derivative of 0 - 2*m**2 + 1/16*m**5 - 1/40*m**7 - 9/160*m**6 + 9/32*m**4 + 0*m + 1/4*m**3. Let z(w) = 0. What is w?
-1, -2/7, 1
Factor -2/7 + 1/7*a**2 - 1/7*a.
(a - 2)*(a + 1)/7
Let f = 43/87 + 5/29. Suppose 4*i + 6 + f*i**2 = 0. Calculate i.
-3
Factor -13*l**3 + 6*l**4 + 12*l**2 - 7*l**3 - l**3 + 12*l.
3*l*(l - 2)**2*(2*l + 1)
Find b such that 0 - 1/5*b - 1/5*b**2 + 1/5*b**4 + 1/5*b**3 = 0.
-1, 0, 1
Suppose 2*s - 6 = -0. Let v(r) = 4*r**4 - 8*r**4 + 3*r**2 + r**4 - 12*r + 3*r**s. Let k(z) = z**4 - z**2 - z. Let x(u) = 9*k(u) - v(u). Factor x(y).
3*y*(y - 1)*(y + 1)*(4*y - 1)
Let n(f) = -1 - f**2 + f**2 + f**2. Let m(l) = -10*l - 8. Let d(i) = m(i) - 4*n(i). Let d(h) = 0. Calculate h.
-2, -1/2
Let k(b) = -7*b**5 + b**4 + 4*b**3 - b**2 + 3. Let w(r) = 6*r**5 - r**4 - 4*r**3 + r**2 - 2. Let o(m) = 2*k(m) + 3*w(m). Let o(d) = 0. What is d?
-1, 0, 1/4, 1
Solve 39*g**2 + g**3 - 256*g + 247*g - 4*g**3 - 39*g**4 + 12*g**5 = 0 for g.
-1, 0, 1/4, 1, 3
Factor 24*l + 4*l**4 - 8*l + 27*l**2 - 4*l - 4 + 19*l**3 - 4*l.
(l + 1)*(l + 2)**2*(4*l - 1)
Let i be (10/20)/((-7)/(-12)). Factor -i*u - 2/7*u**2 - 4/7.
-2*(u + 1)*(u + 2)/7
Let f(v) = -3*v**2 + 7*v + 12. Let r(x) = -11*x**2 + 29*x + 49. Let b(m) = -9*f(m) + 2*r(m). Find w such that b(w) = 0.
-1, 2
Let z(p) = 6*p**3 - 6*p**2 + 3*p - 1. Let u be z(1). Let -4/3 + 2/3*m**u + 2/3*m = 0. What is m?
-2, 1
Suppose 4*h = -6 + 18. Factor 4*v**h - 2*v**4 - 3 - 12*v + 5 + 8*v.
-2*(v - 1)**3*(v + 1)
Let d(y) be the first derivative of -y**6/33 - 2*y**5/11 - 3*y**4/11 + 8*y**3/33 + 8*y**2/11 - 6. Factor d(a).
-2*a*(a - 1)*(a + 2)**3/11
Let l(g) be the first derivative of -2*g**5/5 - 3*g**4/2 - 2*g**3/3 + 3*g**2 + 4*g + 15. Find o such that l(o) = 0.
-2, -1, 1
Let t be 3 + 0/(-5 - -3). Factor -4 + 2*a**t + 3*a**2 - 6*a**3 - 2*a + 4*a**2 + 3.
-(a - 1)**2*(4*a + 1)
Let w(t) be the third derivative of -1/9*t**3 + 1/18*t**4 - 1/90*t**5 + t**2 + 0 + 0*t. Factor w(b).
-2*(b - 1)**2/3
Let i(c) = -c**4 - 2*c**3. Let o(y) = -y**4 - y**3. Let f(n) = 2*i(n) - 3*o(n). Solve f(u) = 0 for u.
0, 1
Let t(x) be the second derivative of 1/50*x**5 + 1/10*x**2 - 3*x - 1/15*x**3 + 0 + 0*x**4 - 1/150*x**6. What is z in t(z) = 0?
-1, 1
Let t(q) = -12*q**5 - 14*q**4 + 2*q**3 + 8*q**2 - 2. Let z(g) = g**4 - g**3 - 1. Let i(v) = -t(v) + 2*z(v). Solve i(b) = 0.
-1, 0, 2/3
Let q(o) be the third derivative of 0 - 1/420*o**7 + 1/240*o**6 + 0*o**3 + 0*o**5 + 0*o + 0*o**4 - 6*o**2. Suppose q(g) = 0. What is g?
0, 1
Let t(a) be the first derivative of 3*a**6/2 + 3*a**5 - 15*a**4/4 - 5*a**3 + 3*a**2 + 7. Suppose t(v) = 0. What is v?
-2, -1, 0, 1/3, 1
Determine h, given that 13*h - 25 - 2*h**2 + h**2 - 3*h = 0.
5
Let k(u) be the second 