- 1)*(c + 1)/9
Let m(i) be the second derivative of i**4/4 + 4*i**3 + 24*i**2 - 16*i. Factor m(u).
3*(u + 4)**2
Find p such that 180*p**3 - 24*p + 28*p - 96*p**2 - 100*p**4 + 12*p = 0.
0, 2/5, 1
Let c be ((-99)/110)/(78/(-10)). Let r = c - -37/130. Let 4/5 - 6/5*x + r*x**2 = 0. What is x?
1, 2
Suppose 0 = r - 0*d - 2*d, 0 = 2*r + 4*d - 8. Let h(a) = -a**3 - 3*a**2 - 3*a. Let o be h(-2). Let -6*z**r + 6 + o + 0 - z + 9*z = 0. Calculate z.
-2/3, 2
Let j(a) be the second derivative of -a**6/195 + a**5/26 - 3*a**4/26 + 7*a**3/39 - 2*a**2/13 - 6*a. Factor j(s).
-2*(s - 2)*(s - 1)**3/13
Let z be 24/56 + 6/(-42). Suppose 6/7 + 2/7*o**3 - z*o - 6/7*o**2 = 0. Calculate o.
-1, 1, 3
Suppose 2*v + 3 = 11. Suppose -14 = -v*o - 6. Determine d so that -2*d**2 + 0*d**2 + d**o - 6 + 4*d**2 + 3*d = 0.
-2, 1
Suppose 133 = 2*q + 39. Let z = 189/4 - q. Factor 1/2*k**2 + 1/4*k**5 - 1/2*k**4 + 0 + 0*k**3 - z*k.
k*(k - 1)**3*(k + 1)/4
Let n be (388/(-28))/(132/14). Let v = n + 18/11. Factor -v - 1/2*a - 1/2*a**2 - 1/6*a**3.
-(a + 1)**3/6
Let c be 2 + -4 + (1 - -1). Suppose c = 3*u + u - 8. Determine s so that 14*s**u - 11*s + 0*s + 4 - 7*s = 0.
2/7, 1
Suppose -130/3*n - 2/15*n**5 - 34/15*n**4 - 116/3*n**2 - 212/15*n**3 - 50/3 = 0. Calculate n.
-5, -1
Let n(s) = 2*s + s**2 + 0 + 6*s**2 - s**3 - 4 + s**2. Let r be n(8). Find i, given that -4*i + 12*i**3 + 5*i - r*i**2 + 2*i = 0.
0, 1/2
Let y(d) = -2*d**3 + 36*d**2 - 2*d + 38. Let o be y(18). Factor -4/3*q**o + 4/3 + 2/3*q - 2/3*q**3.
-2*(q - 1)*(q + 1)*(q + 2)/3
Factor 3*x**2 + 3*x**2 - 2*x**2 + 4*x.
4*x*(x + 1)
Let g(b) be the first derivative of -4/3*b**3 + 0*b**2 + 1/2*b**4 + 0*b - 1. Determine y, given that g(y) = 0.
0, 2
Let v(y) = -6*y**3 + 60*y**2 + 39*y. Let g(x) = -x**3 + 12*x**2 + 8*x. Let s(k) = -21*g(k) + 4*v(k). Let s(c) = 0. Calculate c.
-2, 0
Let 4*u**5 - 2*u - u + 12*u**2 + 4*u**3 - 12*u**4 - 5*u = 0. What is u?
-1, 0, 1, 2
Let u(j) = -j**2 - 4*j + 3. Let n be u(-5). Let x(s) = -s**3 + s + 1. Let y(i) = 10*i**4 + 46*i**3 + 56*i**2 + 14*i - 2. Let w(a) = n*x(a) - y(a). Factor w(d).
-2*d*(d + 2)**2*(5*d + 2)
Suppose 7*r = 3*r + 40. Factor -9*w + 0*w**3 - r*w**2 + w - 4*w**3 - 2.
-2*(w + 1)**2*(2*w + 1)
Let z(o) be the second derivative of o**6/360 - o**5/120 - 5*o**3/6 + 2*o. Let b(u) be the second derivative of z(u). Suppose b(x) = 0. What is x?
0, 1
Let t(b) be the second derivative of -b**4/48 - b**3/6 - 3*b**2/8 + b + 25. Factor t(q).
-(q + 1)*(q + 3)/4
Determine y so that -2/3*y**4 + 4/3*y - 4/3*y**3 + 8/3*y**2 - 2 = 0.
-3, -1, 1
Let j(u) = 4*u**2 - 1. Let r be j(1). Let i(x) be the third derivative of -x**2 - 1/96*x**4 + 0*x + 0*x**r + 0 + 1/240*x**5. Factor i(g).
g*(g - 1)/4
Let b(j) be the third derivative of -j**6/660 + j**5/165 - j**4/132 + 8*j**2. Find o such that b(o) = 0.
0, 1
Let q(f) be the first derivative of -f**6/40 - f**5/20 + f**4/8 + f**3/2 - 3*f**2/2 + 2. Let w(a) be the second derivative of q(a). Let w(t) = 0. Calculate t.
-1, 1
Solve -k + 20*k**2 + k - 5*k**3 - 7*k - 8*k = 0 for k.
0, 1, 3
Suppose 0*u + 12 = -2*u - 3*a, 5*a = -20. Suppose r + 1 - 3 = u. Factor -2/9 - 8/9*h**r + 10/9*h.
-2*(h - 1)*(4*h - 1)/9
Let z be 2/3 - (-152)/24. Solve 2*k**3 + 2*k**4 + 2*k**2 - z*k**3 + 9*k**3 = 0.
-1, 0
Let a(t) be the first derivative of -t**6/60 + t**5/60 - 5*t**2/2 - 5. Let z(b) be the second derivative of a(b). Find d such that z(d) = 0.
0, 1/2
Let g(r) be the third derivative of -r**6/210 + r**4/14 - 4*r**3/21 - 25*r**2. Solve g(o) = 0.
-2, 1
Let f be (-6)/(-4) - (-3)/(12/(-5)). Let -f*y**5 + 0*y**2 + 1/2*y**3 + 0*y**4 - 1/4*y + 0 = 0. Calculate y.
-1, 0, 1
Suppose -r + 0*r + 133 = -4*z, 2 = 2*r. Let c be 28/30 - z/(-55). Solve m + 1/3*m**3 + m**2 + c = 0.
-1
Let v(w) be the second derivative of -w**10/151200 - w**9/75600 - w**4/12 - w. Let d(k) be the third derivative of v(k). Factor d(n).
-n**4*(n + 1)/5
Suppose 5*h - 5 = 10. Solve 2*c**5 + 10*c**4 + 4*c**2 - 2*c**4 - c**h + 11*c**3 = 0 for c.
-2, -1, 0
Let i(z) be the first derivative of -z**6/10 + 9*z**5/25 - 3*z**4/10 - 2*z**3/5 + 9*z**2/10 - 3*z/5 + 16. Determine n, given that i(n) = 0.
-1, 1
Suppose -2*d + 5*c = 11 + 6, -c = -5*d - 8. Let f = 3 + d. Find g, given that -2*g**3 - g**2 - g**3 + f*g**3 = 0.
-1, 0
Factor 2*c**3 + 2*c**3 + 16*c**2 - 111*c + 123*c.
4*c*(c + 1)*(c + 3)
Let d be (-1)/(-2) - 66/(-60). Let f(l) be the first derivative of -d*l**5 + 0*l**2 + 0*l - 7/4*l**4 + 1 - 2/3*l**3 - 1/2*l**6. Let f(o) = 0. What is o?
-1, -2/3, 0
Let u(f) = -4*f**2 - 8*f**2 + 13*f**2. Let o(r) = 2. Let v(y) = o(y) - 2*u(y). Suppose v(t) = 0. Calculate t.
-1, 1
Let d be (-3)/4 - 22/(-8). Let r = d - -1. Determine a, given that 7/4*a**5 + 0 + 9/4*a**4 - 9/4*a**2 - 1/2*a - 5/4*a**r = 0.
-1, -2/7, 0, 1
Let s(i) = -11*i - 20. Let q be s(-2). Suppose 0 + 2*v**q + 1/2*v = 0. Calculate v.
-1/4, 0
Let b(i) = 5*i**2 + 29*i - 1. Let s(k) = -2*k**2 - 10*k. Let f(u) = -4*b(u) - 11*s(u). Factor f(o).
2*(o - 2)*(o - 1)
Let p(s) be the second derivative of s**7/14 - s**6/10 - 3*s**5/20 + s**4/4 + 33*s. Factor p(y).
3*y**2*(y - 1)**2*(y + 1)
Let c(j) be the second derivative of -j**4/3 - 32*j**3/3 - j + 19. Solve c(r) = 0.
-16, 0
Suppose -k + 12 = 3*u - u, 5*u - 25 = 0. Factor -2*s**5 - 6*s**4 - 128*s**k + 126*s**2 - 9*s**3 + 3*s**3.
-2*s**2*(s + 1)**3
Determine n, given that 3/2*n**2 + 1/4*n**4 - n + 1/4 - n**3 = 0.
1
Solve 0 + 2/3*u**3 + 2/9*u**4 - 10/9*u**2 + 4/9*u - 2/9*u**5 = 0 for u.
-2, 0, 1
Let x(g) = g**2 + g. Let t be ((-2)/(-3))/((-1)/(-3)). Let d(k) = -18*k**2 + k + 141 - 143 - 21*k. Let b(i) = t*d(i) + 22*x(i). Factor b(j).
-2*(j + 1)*(7*j + 2)
Let p(a) be the second derivative of -a**5/4 - 25*a**4/6 - 40*a. What is k in p(k) = 0?
-10, 0
Let i(n) be the third derivative of n**7/1155 + 7*n**6/660 + 17*n**5/330 + 17*n**4/132 + 2*n**3/11 + 30*n**2. Determine g, given that i(g) = 0.
-3, -2, -1
Find q, given that 4*q**3 - 8/5*q**2 + 0*q - 16/5*q**4 + 0 + 4/5*q**5 = 0.
0, 1, 2
Suppose 0*j = 3*j - 9. Suppose 3*w - 2*b - 16 = 0, 3*w - 11 = -3*b + 10. Factor -25/2*t**4 - 15*t**j - 2 + 11/2*t**2 + w*t.
-(t + 1)**2*(5*t - 2)**2/2
Let a(j) be the first derivative of 1/12*j**4 + 0*j**3 + 2 - 1/6*j**2 + 0*j. Suppose a(k) = 0. What is k?
-1, 0, 1
Suppose -b + 2*r - 4 = 0, -2*b + 4*r = -4*b + 16. Let z(k) be the second derivative of -3/4*k**5 - k**b - 2*k - 13/6*k**4 - 13/6*k**3 + 0. Factor z(w).
-(w + 1)*(3*w + 1)*(5*w + 2)
Let u(b) = 10*b**3 + 2*b**2 - 5*b - 6. Let h(y) = -3*y**2 + 3*y + 3 + 2 + y - 11*y**3. Let j(l) = 6*h(l) + 5*u(l). Suppose j(z) = 0. Calculate z.
-1/4, 0
Factor d**3 + 52*d - 3*d**3 + 6*d**2 - 56*d.
-2*d*(d - 2)*(d - 1)
Let c(a) = a**3 + 3*a**2 + 2*a - 2. Let f be c(-4). Let u = -23 - f. Factor 0*t**2 - 1/2*t + 0 + 1/2*t**u.
t*(t - 1)*(t + 1)/2
Let r(q) = 9*q**3 - q. Suppose 5 = 3*a + 2. Let c be r(a). Solve 4*k**2 + 24*k - 18*k**2 + 0 + c = 0 for k.
-2/7, 2
Let c(a) = -a**3 - a**2 + a + 1. Let p(y) = 2*y**3 + 4*y**2 - 5*y - 1. Let j(v) = -6*c(v) + 2*p(v). Factor j(r).
2*(r - 1)*(r + 2)*(5*r + 2)
Factor t**5 - 1/5*t - 4/5*t**3 + 8/5*t**4 - 2*t**2 + 2/5.
(t - 1)*(t + 1)**3*(5*t - 2)/5
Suppose 0*h - 2/3*h**3 - 2/9*h**4 - 4/9*h**2 + 0 = 0. What is h?
-2, -1, 0
Let j be 1*(4 + 1/(2/(-8))). Let z(f) be the first derivative of 4/39*f**3 - 2/13*f + 0*f**2 - 2/65*f**5 - 3 + j*f**4. Factor z(g).
-2*(g - 1)**2*(g + 1)**2/13
Factor 1/3*w**3 + 0 + 1/3*w**4 - 1/3*w**5 - 1/3*w**2 + 0*w.
-w**2*(w - 1)**2*(w + 1)/3
Let x(k) = k**2 - 3*k - 14. Let g be x(6). Suppose -5*s + 3*s = 3*n - 12, 5*s = g*n + 7. Factor -1/2*u**3 - 1/2*u**n + 1/2*u + 1/2.
-(u - 1)*(u + 1)**2/2
Let a(m) be the first derivative of 4*m**3/3 + 2*m**2 - 24*m - 7. Suppose a(b) = 0. What is b?
-3, 2
Let g(l) be the second derivative of -l**4/60 + l**2/10 - l. Determine n so that g(n) = 0.
-1, 1
Let n(i) be the third derivative of i**5/80 - i**4/4 + 2*i**3 + 4*i**2. Factor n(f).
3*(f - 4)**2/4
Let y = 14 + -10. Suppose 5*j - 7 = y*a, 2*j = -3*a - j + 15. Find k, given that -26*k**4 + 9*k**2 + a*k - 12*k**3 - 3*k**2 - 12*k**5 + 2*k = 0.
-1, -2/3, 0, 1/2
Let u(f) be the second derivative of f**8/336 + 2*f**2 + 4*f. Let j(k) be the first derivative of u(k). Factor j(v).
v**5
Let x(d) = -d + 1. Let z(u) = -5*u + 4. Let b(t) = -3*x(t) + z(t). Let k be b(-1). Let 6*w**k - 5*w - 2*w**2 - 4