 5*i + 3 = 18. Factor 1/3 + 7/6*o + 7/6*o**2 + 1/3*o**i.
(o + 1)*(o + 2)*(2*o + 1)/6
Let i(f) be the second derivative of f**6/1080 - f**5/180 + f**4/72 - f**3/2 - 3*f. Let x(p) be the second derivative of i(p). Factor x(u).
(u - 1)**2/3
Let h(n) = -3*n**3 + 16*n**2 + n - 2. Let u(a) = a**3 + a**2 + a. Let g(o) = -h(o) + 4*u(o). Factor g(j).
(j - 1)**2*(7*j + 2)
Let g(v) be the second derivative of 1/5*v**5 + 1/6*v**4 + 0*v**2 + 0*v**3 + 4*v + 0 + 1/15*v**6. Suppose g(j) = 0. What is j?
-1, 0
Solve 3/4*n**3 + 1/2*n**2 - 2 - 3*n = 0.
-2, -2/3, 2
Suppose -3 + 15/4*r - 3/4*r**2 = 0. Calculate r.
1, 4
Suppose -2*j - 4*v = 3*j + 14, -3*j - 7 = v. Let r be 2 + 0 - (j - -1). Factor 8/7 + 48/7*o + 6*o**2 - 14*o**r.
-2*(o - 1)*(7*o + 2)**2/7
Let q be 16/(-540)*-5*-6. Let y = q + 14/9. Determine z so that -2/3*z**3 - y*z + 4/3*z**2 + 0 = 0.
0, 1
Suppose 3*a + 0*a - 5*v = -25, 0 = -5*a - v + 5. Suppose -7*o + 12*o - 15 = a. Factor -2/7*l - 4/7*l**2 - 2/7*l**o + 0.
-2*l*(l + 1)**2/7
Let f be 34/12 + 2/(-6). Let q = -325 - -651/2. Find d such that -2*d**4 - 3/2*d**3 + 3/2*d - q + f*d**2 = 0.
-1, 1/4, 1
Let a be (-286)/(-77) - 4/(-14). Factor 88/9*s + 50/9*s**3 - 8/9*s**a - 16/9 - 12*s**2.
-2*(s - 2)**3*(4*s - 1)/9
Let t(r) be the second derivative of r**4/42 - 2*r**3/7 + r. Suppose t(h) = 0. Calculate h.
0, 6
Suppose 4*h = 3*k + 22, 0*h = -2*h + 4*k + 16. Let a(d) be the first derivative of 0*d**3 + 1/8*d**h - 2 + 0*d - 1/4*d**2. Factor a(c).
c*(c - 1)*(c + 1)/2
Let w(h) be the third derivative of h**5/90 - 7*h**4/36 + 37*h**2. Factor w(k).
2*k*(k - 7)/3
Let c be 2 - (-1)/(-2)*-4. Solve 2*a**5 - 2*a**4 + 0*a**5 - 4*a**5 + 2*a - 2*a**4 + c*a**2 = 0.
-1, 0, 1
Suppose -1 = 2*g - 4*g - 5*s, 7 = g - 4*s. Solve -3*b**g + 3*b + 0*b**2 + 2*b**2 + b**2 - 6 + 3*b**2 = 0.
-1, 1, 2
Let b(q) be the first derivative of 0*q**2 + 3/10*q**4 + 0*q + 1 + 2/15*q**3 + 6/25*q**5 + 1/15*q**6. Factor b(f).
2*f**2*(f + 1)**3/5
Let s(h) be the third derivative of 2*h**2 + 2/21*h**3 - 1/210*h**5 + 0*h + 1/84*h**4 + 0. Determine x, given that s(x) = 0.
-1, 2
Factor -14 - 5*d**2 + 28 - 14 + 25*d.
-5*d*(d - 5)
Suppose -7*h = -4*h - 21. Solve -13 + h + 7 - z**2 = 0.
-1, 1
Let j be -1*8/(-12)*3. Let v be 5 - (4/j + -1). Determine g so that 6/11*g**v + 0*g + 2/11*g**2 + 2/11*g**5 + 6/11*g**3 + 0 = 0.
-1, 0
Suppose -5*h + 0*y - 2 = -y, 2*h + 8 = 4*y. Factor 0*w**3 + 2*w**2 - 2/3*w**4 - 4/3*w + h.
-2*w*(w - 1)**2*(w + 2)/3
Let c(f) be the first derivative of -2*f**2 - 2*f**3 + 0*f**4 + 0*f + 2/5*f**5 + 1. Determine z so that c(z) = 0.
-1, 0, 2
Let d(x) be the second derivative of 3*x**5/20 - 3*x**4/4 + x**3 - 2*x. Solve d(a) = 0 for a.
0, 1, 2
Let s(v) = v**3 + 10*v**2 + 8*v - 7. Let c be s(-9). Find o such that -2*o**2 + 2*o**2 - o**c = 0.
0
Let a = 1101 + -1101. Suppose 2/3*m**2 + 4/3*m + a = 0. What is m?
-2, 0
Let p(k) be the third derivative of 1/30*k**5 - 3*k**2 + 0*k**4 + 0*k + 0*k**3 + 0. Suppose p(z) = 0. What is z?
0
Let c(a) be the second derivative of 3*a**5/4 + 19*a**4/4 + 8*a**3 - 6*a**2 - 19*a. Factor c(i).
3*(i + 2)**2*(5*i - 1)
Let g(i) be the first derivative of 2*i**3/15 - i**2/5 - 4*i/5 - 16. Solve g(d) = 0 for d.
-1, 2
Let r be (-2)/3*11/(-22). Factor 0*a**2 + 0 - r*a**3 + 0*a.
-a**3/3
Let i be (14/12)/7*(0 + 4). Determine x, given that -i*x**2 + 0*x + 0 + 5/3*x**3 = 0.
0, 2/5
Let n(l) be the first derivative of -l**6/2340 + l**5/260 - l**4/78 - 4*l**3/3 - 1. Let h(d) be the third derivative of n(d). Determine w, given that h(w) = 0.
1, 2
Let w(f) be the second derivative of -1/30*f**6 + 0 + 0*f**3 + 0*f**4 + f + 0*f**5 + 0*f**2. Factor w(t).
-t**4
Let v(a) = 6*a + 3. Let c(f) = f**2 + 11*f + 5. Let p(h) = 3*c(h) - 5*v(h). Solve p(o) = 0.
-1, 0
Suppose -3*q + 4*q = 0. Suppose q = -4*t - f - 4, 0 + 8 = -5*t - 2*f. Factor -i - i**2 + 2*i**2 + t*i**3 + i**2 - i**3.
-i*(i - 1)**2
Let f be (5/(-4))/(1/(-4)). Factor -i**2 - 2*i - 4 + 2*i + f.
-(i - 1)*(i + 1)
Factor 0 + 0*f - 3/5*f**2.
-3*f**2/5
Let 25/2*k**2 + 5/2 + 15*k = 0. Calculate k.
-1, -1/5
Let z be 1/5 + 3/(-15). Let h be (z - -3) + -1 + 12. Let h + 2*f**3 - 9*f**2 + f**3 - 2 = 0. Calculate f.
-1, 2
Let r(o) = -5*o**3 + 4*o**2 + 7*o - 6. Let z(w) = w**3 - w**2 - w + 1. Let d(v) = -v - 1. Let i be d(-2). Let a(k) = i*r(k) + 6*z(k). Factor a(j).
j*(j - 1)**2
Let n(g) be the second derivative of g**10/105840 - g**9/26460 + g**8/23520 - g**4/12 + 3*g. Let z(m) be the third derivative of n(m). Factor z(s).
2*s**3*(s - 1)**2/7
Suppose -5*y + 52 = -3*w + 4*w, 3*w - 6 = 0. Factor -12*l - y*l**2 - 18/5.
-2*(5*l + 3)**2/5
Let y(m) be the third derivative of -5*m**8/336 + 2*m**7/21 - m**6/4 + m**5/3 - 5*m**4/24 + m**2 + 2. Factor y(u).
-5*u*(u - 1)**4
Factor -2 - 10*n**3 + 8*n**4 - 2*n - 4*n + 5*n - 6*n**2 + 11*n.
2*(n - 1)**2*(n + 1)*(4*n - 1)
Let 2/3*w - 1/6*w**3 - 2/3 + 1/6*w**2 = 0. What is w?
-2, 1, 2
Let t be 4/18 - -6*8/108. Determine v, given that t*v**2 + 8/3 + 8/3*v = 0.
-2
Suppose -2*a - s + 2*s = -3, 4 = 4*s. Let w(b) be the second derivative of -5*b - 1/60*b**5 + 1/18*b**3 + 0*b**4 + 0*b**a + 0. Factor w(n).
-n*(n - 1)*(n + 1)/3
Let r(g) be the third derivative of -g**8/1848 + 2*g**7/1155 - g**5/165 + g**4/132 - 6*g**2. Factor r(q).
-2*q*(q - 1)**3*(q + 1)/11
Let z(d) be the first derivative of -d**4/40 + d**3/30 + d**2/20 - d/10 - 25. Find y, given that z(y) = 0.
-1, 1
Suppose 3*g + 4 = 4*u, -u = -0 - 4. Let m(v) be the second derivative of -1/180*v**6 + 1/72*v**g + 0*v**2 + 0 + 1/36*v**3 - v - 1/120*v**5. Factor m(r).
-r*(r - 1)*(r + 1)**2/6
Let t(z) be the second derivative of -1/6*z**3 + 1/20*z**5 - z**2 - 6*z + 0 + 1/6*z**4. Determine a so that t(a) = 0.
-2, -1, 1
Suppose -5*v + 2*p + 36 = 0, -p + 0*p - 27 = -4*v. Suppose 3 = 3*s - v. Factor -2/3*y**2 - 2*y**s + 0 - 2*y**4 + 0*y - 2/3*y**5.
-2*y**2*(y + 1)**3/3
Let x(w) = 17*w + 10*w**2 - 10*w**2 - 8 + 17*w**2. Let f(p) = 4*p**2 + 4*p - 2. Let c(d) = -26*f(d) + 6*x(d). Factor c(y).
-2*(y - 1)*(y + 2)
Let a = -4/47 - -75/329. Solve -a*n**4 + 2/7*n**3 - 1/7 - 1/7*n**5 + 2/7*n**2 - 1/7*n = 0.
-1, 1
Let a = 35 + -33. Let m(t) be the first derivative of -2*t**2 - 14/3*t**3 - a + 0*t. Factor m(j).
-2*j*(7*j + 2)
Factor -4*v + v**2 - 2 - 3 - 1 + 9.
(v - 3)*(v - 1)
Let q(n) be the third derivative of n**5/660 - 2*n**3/33 - 19*n**2. Factor q(k).
(k - 2)*(k + 2)/11
Let z be 4/(-3) + 1 + 1. Let m = 135 - 131. Find b, given that -1/3*b**m - 1/3 - 1/3*b**5 + z*b**3 - 1/3*b + 2/3*b**2 = 0.
-1, 1
Let m(r) = -13*r**5 - r**4 + 9*r**3 + 5*r**2 - 5*r. Let w(p) = -20*p**5 - 2*p**4 + 14*p**3 + 8*p**2 - 8*p. Let n(f) = -8*m(f) + 5*w(f). Factor n(l).
2*l**3*(l - 1)*(2*l + 1)
Let n(k) = 2*k**2 - 3*k + 4. Let x(y) = y**2 + y. Let h(v) = -3*n(v) + 3*x(v). Solve h(w) = 0.
2
Suppose 4*l = 16, 4*x - 4*l - l = 0. Let f(u) = u**2 + 3*u - 6. Let m be f(-5). Solve 2/9*y**m + 2/9 - 2/9*y + 4/9*y**3 - 4/9*y**2 - 2/9*y**x = 0.
-1, 1
Suppose 7*v - 6 = 5*v. Factor -d - d + 0*d**3 - 5*d**v + 3*d**3 - 4*d**2.
-2*d*(d + 1)**2
Let j(g) be the first derivative of -19*g**3 + 51*g**2/2 - 12*g - 7. Let t(s) = 14*s**2 - 13*s + 3. Let n(l) = -2*j(l) - 9*t(l). Factor n(c).
-3*(c - 1)*(4*c - 1)
Let -j - 3/5*j**3 - 1/5 - 7/5*j**2 = 0. Calculate j.
-1, -1/3
Let x = 17 + -20. Let j(i) = 3 - 3*i - 3*i**2 + 2*i**2 + 4*i**4 + 4*i**2 + i**3. Let p(f) = -f**4 - f**2 + f - 1. Let z(n) = x*p(n) - j(n). Factor z(k).
-k**3*(k + 1)
Determine n, given that 1 + 2*n + 3 - n**2 - 5 = 0.
1
Let j(d) be the third derivative of d**8/1680 - 2*d**7/525 + d**6/120 - d**5/150 + 12*d**2. Factor j(t).
t**2*(t - 2)*(t - 1)**2/5
Suppose 0 = -q + 2*q - 2. Let -q - 6*b**3 + 0*b**4 + b**3 + 9*b**2 - b**4 - 6*b**4 + 5*b = 0. What is b?
-1, 2/7, 1
Suppose 2*c = 2 + 10. Let l = -5 + c. Factor 1 + l - n**2 + 0 + n.
-(n - 2)*(n + 1)
Factor -2/3*s**2 + 2*s - 2*s**3 + 2/3.
-2*(s - 1)*(s + 1)*(3*s + 1)/3
Suppose 0 = 7*r + 7*r - 2*r. Factor r*z**2 + 1/4*z**4 + 0 + 0*z**3 + 0*z.
z**4/4
Let p(m) = -3*m - 2. Let y be p(-2). Solve -4*q + 7 - 11 + 6 - 2*q**4 + y*q**3 = 0 for q.
-1, 1
Let n(b) be the first derivative of b**8/240 + 8*b**7/525 + 11*b**6/600 + b**5/150 + b**2 + 2. Let z(y) be the second derivative of n(y). Factor z(l).
l**2*(l + 1)**2*(7*l + 2)/5
Let u(f) be the second derivative of -f**3/6 + 7*f**2 + 7*f. Let a be u(14). Factor 0 - 2*m