 1/12*r**3 + 0*r**2 + 4 + 0*r. Suppose d(m) = 0. What is m?
0
Let t(c) = -5*c**5 - c**4 - 6*c**3 - 6*c**2. Let y(z) = z**5 + z**3 + z**2. Let q(o) = 2*o + 6. Let x be q(-6). Let s(f) = x*y(f) - t(f). Factor s(a).
-a**4*(a - 1)
Let c(k) be the first derivative of k**4/26 + 10*k**3/39 + 7*k**2/13 + 6*k/13 - 11. Factor c(i).
2*(i + 1)**2*(i + 3)/13
Let m(x) be the third derivative of x**8/20160 - x**7/2520 + x**6/720 - x**5/360 + x**4/4 - 6*x**2. Let j(g) be the second derivative of m(g). Solve j(z) = 0.
1
Let g(i) = -i**3 + i**2 + i. Let s(a) = -a**3 + 3*a**2. Let x(n) = 6*g(n) - 3*s(n). Suppose x(q) = 0. Calculate q.
-2, 0, 1
Let a(q) = 3*q**5 + 2*q**3 - 5*q**2 + 5*q - 5. Let n(u) = -u**5 - u**3 + 2*u**2 - 2*u + 2. Let v(x) = 6*a(x) + 15*n(x). Factor v(f).
3*f**3*(f - 1)*(f + 1)
Let d(b) = -6*b**3 - 5*b**2 - 4*b - 5. Let j = 6 + 0. Let a(l) = 7*l**3 + 6*l**2 + 5*l + 6. Let t(c) = j*d(c) + 5*a(c). Factor t(p).
-p*(p - 1)*(p + 1)
Suppose -5*f - 3*b - 120 = 0, -2*b = 2*f - 3*f - 37. Let u = -51/2 - f. Factor -1/2 - 1/2*l**3 - u*l**2 - 3/2*l.
-(l + 1)**3/2
Let z be ((-4)/(-20))/((-1)/(-4)). Factor -2/5*j**2 - z*j**3 - 2/5*j**4 + 0 + 0*j.
-2*j**2*(j + 1)**2/5
Let k(t) be the second derivative of -t**4/78 + t**3/39 + 11*t. Solve k(d) = 0 for d.
0, 1
Let v(u) be the third derivative of 0*u**4 + 0 + 0*u**3 - 1/120*u**6 + 0*u**5 + 3*u**2 + 0*u. Let v(h) = 0. What is h?
0
Let i be (141/(-45) + 3)*-3. Let g = 2 - -1. Factor 2/5*j + 0 - 4/5*j**2 + i*j**g.
2*j*(j - 1)**2/5
Let r(s) = 11*s**3 + 33*s**2 + 3*s - 9. Let j(m) = 6*m**3 + 16*m**2 + 2*m - 4. Let d(w) = 5*j(w) - 2*r(w). Find k, given that d(k) = 0.
-1, 1/4
Suppose -5*c - 4*r = -6*r, -2*c = 5*r. Factor c - 1/4*w**2 + 1/4*w**5 + 0*w - 3/4*w**4 + 3/4*w**3.
w**2*(w - 1)**3/4
Let a(o) = -2*o - 3 + 2*o**3 - o**3 + 2*o**2 - 3*o. Let r be a(-3). Find u such that 4*u**2 - 8*u**2 + 2*u + r*u**3 - u**3 = 0.
0, 1
Let i be 36*(-12)/(-80) + -5. Let y(s) = s**3 + 3*s**2 + 2*s + 2. Let p be y(-2). Factor -i - 2/5*b**p - 4/5*b.
-2*(b + 1)**2/5
Suppose -f + 8 = f. Suppose 0*x = f*x. Solve -6/7*s**3 + 8/7*s**4 + x*s - 2/7*s**2 + 0 = 0.
-1/4, 0, 1
Let t(a) be the third derivative of -a**6/30 - a**5/10 + a**3/3 - 7*a**2. Let t(u) = 0. Calculate u.
-1, 1/2
Suppose 0 = -m - 5*q + 15, -2*m + 6 = 2*m + 2*q. Factor 3*d**4 + 2*d**3 - 2*d**4 + m*d**4 + d**2.
d**2*(d + 1)**2
Let w(c) = 5*c**2 + 10*c - 11. Let o(i) = -10*i**2 - 20*i + 21. Let t(j) = -4*o(j) - 9*w(j). Find p, given that t(p) = 0.
-3, 1
Let g be (-23)/(-7) - (-2)/(-7). Factor 2*y**3 - y**2 + y**3 - 2*y**g - 2*y**3.
-y**2*(y + 1)
Let r(w) be the first derivative of -4 + 9/8*w**4 - 1/3*w**3 + 5/12*w**6 + 0*w**2 - 6/5*w**5 + 0*w. What is l in r(l) = 0?
0, 2/5, 1
Let v(o) be the second derivative of o**5/4 + 5*o**4/4 - 5*o**3/6 - 15*o**2/2 + 10*o. What is d in v(d) = 0?
-3, -1, 1
Let x be 205/(-371) - (-52)/91. Let v = x - -261/212. Suppose -3/4*a**2 + v*a + 1/2 = 0. What is a?
-1/3, 2
Let u(l) be the third derivative of -1/10*l**5 + 0*l**3 + 0*l + 2*l**2 + 0 + 1/40*l**6 + 1/8*l**4. Factor u(r).
3*r*(r - 1)**2
Let t(r) be the second derivative of 1/20*r**5 + 0*r**3 - 1/12*r**4 - 8*r + 0*r**2 + 0. Let t(j) = 0. Calculate j.
0, 1
Factor 7*l**3 - 3*l**3 + 8*l + 12*l**2 - 140 + 140.
4*l*(l + 1)*(l + 2)
Let n(b) be the second derivative of -1/40*b**5 + 1/4*b**3 + 0 + 0*b**4 + b + 1/2*b**2. Factor n(m).
-(m - 2)*(m + 1)**2/2
Let x(v) = 2*v**3 - 10*v**2 - 20*v - 14. Let r(q) = -5*q**3 + 31*q**2 + 60*q + 41. Let u(o) = 6*r(o) + 17*x(o). Factor u(d).
4*(d + 1)**2*(d + 2)
Let q(i) be the third derivative of -i**6/720 - i**5/40 - 3*i**4/16 - i**3/6 - 5*i**2. Let z(h) be the first derivative of q(h). Factor z(d).
-(d + 3)**2/2
Let k(w) be the second derivative of 6*w + 0*w**2 - 1/12*w**3 + 1/12*w**4 + 0 - 1/40*w**5. Determine d, given that k(d) = 0.
0, 1
Let o(p) be the third derivative of -p**5/80 - 2*p**2. Determine n, given that o(n) = 0.
0
Factor -3*t - 3*t - 9 - 4*t**2 + 0*t + 3*t**2.
-(t + 3)**2
Let q be (4*2/50)/((-21)/(-210)). Factor 6/5*a**2 + 28*a**3 - 8*a - 98/5*a**4 - q.
-2*(a - 1)**2*(7*a + 2)**2/5
Factor 16*a**2 + a - 3*a**3 + 6*a - 21*a - 9*a + 6.
-(a - 3)*(a - 2)*(3*a - 1)
Determine j so that 2*j**5 + 4*j**2 + 17*j**3 + 21*j**3 - 44*j**3 = 0.
-2, 0, 1
Let u(d) = -d - 8. Let x be u(-11). What is k in -45*k**x - 33*k**4 - 27*k**2 + 16*k**5 - 12*k**5 - 6*k - 13*k**5 = 0?
-1, -2/3, 0
Let d be ((-12)/(-8))/3 + (-1)/4. Factor -1/4*u**2 - 1/4*u**3 + 1/4*u + d.
-(u - 1)*(u + 1)**2/4
Let f(c) be the first derivative of -c**8/3360 - c**7/840 + c**6/720 + c**5/120 - 2*c**3/3 - 5. Let z(b) be the third derivative of f(b). What is s in z(s) = 0?
-2, -1, 0, 1
Factor -2/3*h**3 + 0 - 2/3*h**2 + 2/3*h + 2/3*h**4.
2*h*(h - 1)**2*(h + 1)/3
Let v(p) be the second derivative of -p**6/15 - 2*p**5/5 + p**4/2 + 10*p**3/3 - 8*p**2 + 17*p + 3. Factor v(n).
-2*(n - 1)**2*(n + 2)*(n + 4)
Let a(y) = y**3 + 7*y**2 + 7*y + 9. Let q be a(-6). Let x(n) be the first derivative of 1 - 1/2*n**4 - 3*n**2 + 2*n**q + 2*n. Suppose x(h) = 0. What is h?
1
Let c be 46/14 + (-30)/105. Suppose 0*v - 2*v**5 - 2/3*v**c + 10/3*v**4 - 2/3*v**2 + 0 = 0. Calculate v.
-1/3, 0, 1
Let z(j) be the third derivative of -j**6/220 + j**5/330 + j**4/66 + 5*j**2. Let z(d) = 0. Calculate d.
-2/3, 0, 1
Let w = -2238/5 - -448. Let w*u**2 + 0 - 4/5*u = 0. Calculate u.
0, 2
Let h(x) be the first derivative of x**3 - 27*x**2/2 + 42*x + 19. Factor h(s).
3*(s - 7)*(s - 2)
Suppose 0 = x - 6*x + 20. Let d be 18/5 + x/10. Factor t**d - t + 6*t**2 - 5*t + 1 - 4*t**3 + 2*t.
(t - 1)**4
Factor -2/5*m**4 + 0*m - 2/5*m**2 + 4/5*m**3 + 0.
-2*m**2*(m - 1)**2/5
Let p(s) be the first derivative of -1/10*s**6 + 3/25*s**5 + 3/20*s**4 - 1/5*s**3 + 0*s**2 + 0*s - 2. Factor p(y).
-3*y**2*(y - 1)**2*(y + 1)/5
Suppose 0 - 10/7*r**5 + 6/7*r**3 - 2*r**2 + 2*r**4 + 4/7*r = 0. Calculate r.
-1, 0, 2/5, 1
Suppose -4*f = -c - 6, -f = c + 4*f - 21. Let b(t) = t**4 + 10*t**3 + 12*t**2 - 2*t + 7. Let x(k) = -k**3 - k**2 + k - 1. Let q(m) = c*x(m) + b(m). Factor q(y).
(y + 1)**4
Let g(c) be the first derivative of -3*c**5/25 + 2*c**3/5 - 3*c/5 - 19. Solve g(j) = 0 for j.
-1, 1
Suppose -6*a + 26 - 14 = 0. Solve 0 + 2/5*n**3 + 0*n + 0*n**a - 2/5*n**4 = 0.
0, 1
Let s be 2/10 + (-26)/5. Let y = 8 + s. Factor -4*z**3 + 2*z**5 - y*z + 6*z - z.
2*z*(z - 1)**2*(z + 1)**2
Let s = 14/13 - -89/26. Let w(l) be the first derivative of 6*l - 3/4*l**4 + 0*l**3 + s*l**2 - 1. Solve w(d) = 0.
-1, 2
Solve -2/3*k - 4*k**2 + 0 + 14/3*k**3 = 0.
-1/7, 0, 1
Determine f so that 10*f**2 + 11*f**2 - 4*f + 10*f**2 - 27*f**2 = 0.
0, 1
Let m(q) = 2*q**4 + 15*q**3 + 24*q**2 + 17*q + 3. Let p(w) = 4*w**4 + 29*w**3 + 48*w**2 + 35*w + 7. Let l(h) = 5*m(h) - 3*p(h). Determine d so that l(d) = 0.
-3, -1
Let j be (0 + 2)/(-2)*5. Let n = 9 + j. Suppose -4/5*a**n - 4/5*a**3 + 2/5*a**5 + 4/5 + 16/5*a**2 - 14/5*a = 0. What is a?
-2, 1
Let y = 0 + 3. Suppose 2*z - 5*s - 13 = z, 0 = 3*z + 3*s - y. Factor 2*h + 3*h**z - 4*h**4 - 1 + 5*h**2 + 0 - 5*h.
-(h - 1)**2*(h + 1)*(4*h + 1)
Factor 14*o**5 - 17*o**5 - o**4 - 5*o**4.
-3*o**4*(o + 2)
Let n(d) be the first derivative of d**3/6 + d**2 - 5*d/2 + 32. Factor n(f).
(f - 1)*(f + 5)/2
Let r(z) = z**2 - z + 1. Let o(h) = -2*h**2 - 23*h + 166. Let w(a) = -o(a) - 3*r(a). Suppose w(i) = 0. What is i?
13
Let j be 1/2*6/1. Suppose -w - v = j*v + 13, 3*v = 3*w - 21. Factor -2/13*b**4 + 0*b**2 + 4/13*b**w + 0 - 2/13*b**5 + 0*b.
-2*b**3*(b - 1)*(b + 2)/13
Let r be (8/32)/((-3)/(-8)). Let t(p) be the third derivative of -1/40*p**6 + 0*p + 1/60*p**5 + 0 + r*p**3 - p**2 + 1/3*p**4. Find h, given that t(h) = 0.
-1, -2/3, 2
Let l(o) be the second derivative of -o**4/114 + o**3/57 + 2*o**2/19 - 9*o. Factor l(y).
-2*(y - 2)*(y + 1)/19
Suppose -64*j - 20 = -74*j. Factor 2/3*f**j + 1/3*f - 1/3*f**3 - 2/3.
-(f - 2)*(f - 1)*(f + 1)/3
Let g(w) = 7*w**4 - w**2. Let v(f) = -f + 1. Let d be v(-5). Let o(q) = 15*q**4 - 2*q**2. Let x(y) = d*o(y) - 13*g(y). Suppose x(s) = 0. Calculate s.
-1, 0, 1
Factor c**2 + 0*c**2 - 2*c**2 + 0*c**2 + 4.
-(c - 2)*(c + 2)
Suppose -2*n + 6*n - 8 = 0. Factor -3*x - 5*x**2 + 2*x**n + 5*x - 5*x.
-3*x*(x + 1)
Factor -1/5*u**3 + 1/5*u + 1/5*u**2 - 1/5.
-(u - 1)**2*(u + 1)/5
Suppose -2*y + 8 = 2*y. Factor -4*i**3 + 2*i**2 + 4 + 6*i**y - 10*i + 2*i**3.
-2