*d**4 + 27*d**3 - 78*d**2 - 39*d - 27. Let n(o) = 2*b(o) + 27*g(o). Factor n(p).
-3*p*(p - 1)*(p + 1)**3
Suppose -4*y = -0*y - 8. Suppose -y*r**4 + 9 + r**4 + 2*r**3 - 9 - r**5 = 0. Calculate r.
-2, 0, 1
Let p = -864 + 992. Let j = 41 - -87. Suppose j*z**4 + 48*z**2 - p*z**3 - 8*z + 1/2 = 0. What is z?
1/4
Let r = 11 + -219/20. Let w(s) be the third derivative of 4*s**2 + 0*s**3 + 0 + 0*s + 0*s**6 - 1/350*s**7 + 3/100*s**5 - r*s**4. Solve w(a) = 0 for a.
-2, 0, 1
Suppose 4 = -4*m + 2*q + 2*q, -8 = -2*q. Factor -m*x**3 + 4*x**2 - x**3 + 2*x**4 - x**4 + 0*x**4.
x**2*(x - 2)**2
Let -5*h**2 + 9 + 12*h + 2*h**2 - 18*h = 0. Calculate h.
-3, 1
Let z(a) be the second derivative of -a**6/10 - 9*a**5/20 - 3*a**4/4 - a**3/2 - 9*a. Factor z(t).
-3*t*(t + 1)**3
Let z be (19/15 + -1)*10/4. Let o(b) be the second derivative of -3/5*b**5 - 4/15*b**6 + 0*b**2 - z*b**4 + 0 - 1/21*b**7 - 1/3*b**3 - b. Factor o(m).
-2*m*(m + 1)**4
Let a(r) = r - 7. Let y be a(10). Find u such that 25*u**2 - u**2 - 14*u + 4*u - 8*u - 10*u**y + 4 = 0.
2/5, 1
Let w be 260/24*(12/5)/3. What is p in w*p**3 + 8/3*p + 0 + 4*p**4 + 2/3*p**5 + 8*p**2 = 0?
-2, -1, 0
Let p(r) be the second derivative of 0*r**6 + 0*r**2 - 1/40*r**5 - 5*r + 0*r**3 + 0 + 1/84*r**7 + 0*r**4. Determine k so that p(k) = 0.
-1, 0, 1
Let x(w) be the third derivative of w**5/240 + w**4/24 + w**3/6 + 7*w**2. Factor x(g).
(g + 2)**2/4
Let s(l) be the first derivative of -l**4/22 - 6*l**3/11 - 24*l**2/11 - 40*l/11 - 43. Factor s(p).
-2*(p + 2)**2*(p + 5)/11
Suppose 4*x - 58 = 5*k - 3, 5*x + 2*k = 44. Suppose 3*j = -2*j + x. Factor -1/3*s + 1/3*s**3 + 1/3*s**j - 1/3.
(s - 1)*(s + 1)**2/3
Let u be (-3)/((-3)/(-6)*-3). Suppose 0 = m + u*m. Determine n, given that -6*n + 1 + m*n**3 + 9*n**2 - 4*n**3 + 0 = 0.
1/4, 1
Let m = 6 + -14. Let x(c) = c**2 + 8*c + 2. Let s be x(m). Let 4*y**2 + 0*y**s - 2*y**4 + y**2 - 2 - y**2 = 0. Calculate y.
-1, 1
Suppose -8*x + 12*x = -144. Let d be (x/30)/((-2)/5). Solve 0*g + 0 + 2/3*g**2 + 1/3*g**d = 0 for g.
-2, 0
Let w be (-1)/(-1) - -1 - -2. Solve 1 + x**2 + w*x - x - x = 0 for x.
-1
Suppose -2*k - 2 = 2*j - 20, 2*k - 22 = -j. Suppose -5*l = -3*t - k, 5*l + t + 3*t - 6 = 0. Factor -o - 3*o - o**l + 2 + 3*o.
-(o - 1)*(o + 2)
Let y(v) = -3*v**5 - 16*v**4 - 11*v**3 - 6*v**2 - 4. Let d(h) = -3*h**5 - 15*h**4 - 12*h**3 - 6*h**2 - 3. Let m(s) = -4*d(s) + 3*y(s). Factor m(a).
3*a**2*(a + 1)**2*(a + 2)
Let p(m) be the third derivative of 2*m**7/315 - m**6/360 - m**5/15 - 5*m**4/72 + m**3/9 + 30*m**2. Factor p(r).
(r - 2)*(r + 1)**2*(4*r - 1)/3
Let u(h) = 33*h**4 - 48*h**3 + 69*h**2 + 21*h + 21. Let x(c) = 8*c**4 - 12*c**3 + 17*c**2 + 5*c + 5. Let r(i) = 5*u(i) - 21*x(i). Suppose r(w) = 0. Calculate w.
0, 2
Suppose -4 = d + 2*c, -c - 2 = d - 1. Let u(k) be the second derivative of 0*k**3 - 1/6*k**4 + 0 + k**d + k. Factor u(t).
-2*(t - 1)*(t + 1)
Let l be (-26)/(-10) + (-2)/(-5). Let r(d) = 4*d - 8. Let a be r(3). Factor -2*n**3 - n**a + 8*n**l - 4*n**4 + 2*n**4 - 3*n**2.
-3*n**2*(n - 1)**2
Let n be (-15)/(-300)*(-10)/(-84). Let g(b) be the second derivative of 0 - n*b**7 - 3/80*b**5 + b + 0*b**2 + 1/40*b**6 + 0*b**3 + 1/48*b**4. Factor g(w).
-w**2*(w - 1)**3/4
Let y(l) be the third derivative of l**10/75600 + l**9/9450 + l**8/3360 + l**7/3150 - l**4/12 - 2*l**2. Let x(i) be the second derivative of y(i). Factor x(v).
2*v**2*(v + 1)**2*(v + 2)/5
Let s(w) be the first derivative of w**6/42 - 3*w**5/35 + 3*w**4/28 - w**3/21 + 8. Factor s(q).
q**2*(q - 1)**3/7
Let p be (8/(-18))/(34/(-51)). Let q(d) be the second derivative of -1/6*d**4 - d**2 + d + 0 - p*d**3. Factor q(o).
-2*(o + 1)**2
Let x be 1*2*(-1 + 7). Let s = -10 + x. Suppose 2/3*h**3 - 2/3*h**s - 2/3*h + 2/3 = 0. Calculate h.
-1, 1
Let u(i) be the first derivative of -2*i**6/9 + 4*i**5/3 - 3*i**4 + 28*i**3/9 - 4*i**2/3 + 8. Suppose u(m) = 0. Calculate m.
0, 1, 2
Let g(b) = -2*b**3 + 15*b**2 - 13*b + 11. Let y(d) = d**3 - 8*d**2 + 7*d - 6. Let m(n) = 6*g(n) + 11*y(n). Find r, given that m(r) = 0.
0, 1
Let j(u) be the first derivative of 135*u**3 - 45*u**2 + 5*u + 29. Find f such that j(f) = 0.
1/9
Let v = -3 - -6. Suppose 4*g + g - 5*u - 30 = 0, -v*g + 5*u = -26. Determine m, given that m**g + 2*m**3 + 0 + m**4 + 0 = 0.
-1, 0
Let f = 286 - 1427/5. Factor -f*r**4 + 3/5*r**2 + 3/5*r**3 - 3/5*r + 0.
-3*r*(r - 1)**2*(r + 1)/5
Let i be -1 + (-6)/(-2) + 1. Let y = 2 - 0. Suppose -17*t**2 - y*t**i + 17*t**2 = 0. What is t?
0
Let s(i) be the first derivative of -i**4/3 + 2*i**2/3 - 30. Solve s(g) = 0.
-1, 0, 1
Suppose i - 2*b = -0*i + 12, 3*b + 12 = 0. Suppose 11 = i*a - 1. Factor u**a + 1/4*u**4 + 0*u + 0 + u**2.
u**2*(u + 2)**2/4
Suppose 3*x - 22 = r, 3*r = -5*x - 2*r + 70. Let u = -9 + x. Factor 0*m + 1/3*m**2 + u.
m**2/3
Suppose -4*c + 37 - 21 = 0. Suppose -4*y = -5*j - 5, 3*j = -c*y + 27 + 2. Factor -j*h + 2/3 + 7/3*h**2.
(h - 1)*(7*h - 2)/3
Let u(d) = -3*d**3 + 8*d**2 - 10*d + 10. Let s(r) = -10*r**3 + 25*r**2 - 29*r + 31. Let f(i) = 4*s(i) - 14*u(i). Factor f(j).
2*(j - 2)**3
Suppose -2*s + 6 = s. Factor 2*k - 16 + 4 + 3*k**2 - s*k.
3*(k - 2)*(k + 2)
Let j(y) be the second derivative of -2*y**5/35 - 3*y**4/14 - 2*y**3/21 - 23*y. Factor j(m).
-2*m*(m + 2)*(4*m + 1)/7
Let a be 2/(-5) + (-10)/(-25). Let n(w) be the second derivative of 1/2*w**4 + a - 2*w - 1/2*w**2 - 1/4*w**3 - 7/40*w**5. Suppose n(m) = 0. What is m?
-2/7, 1
Let d = -15 - -19. Factor l**4 + 4*l**d + 15*l**5 + l**4.
3*l**4*(5*l + 2)
Suppose 0*n = -n + 4. Suppose o = 5*o - n. Let -6*s + 5*s - 2*s**2 + s**2 + s**3 + o = 0. Calculate s.
-1, 1
Let g(d) be the first derivative of d**4/5 + d**3/15 - 2*d**2/5 - d/5 - 35. Factor g(x).
(x - 1)*(x + 1)*(4*x + 1)/5
Find q such that 0*q - 1/3*q**4 + 0 + 0*q**3 + 1/3*q**5 + 0*q**2 = 0.
0, 1
Let f(b) = 2*b**2 + 2*b - 4. Let q(k) = 2*k - 3. Let g(j) = 3*j - 4. Let w(x) = -3*g(x) + 4*q(x). Let s(p) = f(p) + 4*w(p). What is d in s(d) = 0?
-1, 2
Suppose 5*q = q. Let s(z) be the third derivative of 1/90*z**6 + 0*z**4 + 0*z**3 - 1/90*z**5 + 0*z - 1/315*z**7 + q - z**2. Determine o so that s(o) = 0.
0, 1
Let a = -6 + 4. Let f be -1*(-1 + -4 - a). Factor z + 0*z**2 + 0*z**2 - z**f.
-z*(z - 1)*(z + 1)
Let n(r) be the second derivative of r**4/8 - r**3/2 + 18*r. Factor n(g).
3*g*(g - 2)/2
Let z(i) = -i. Let l(u) = 5*u**2 - 4*u. Let h(g) = l(g) - 4*z(g). Factor h(y).
5*y**2
Let z(i) = -i**2 + 2*i + 2. Let h be z(2). Let h*x**3 + x - 12*x**2 + 2*x**3 + 3*x + x**3 = 0. Calculate x.
0, 2/5, 2
Suppose -2*r + u + 31 = 0, u + 2 + 1 = 0. Suppose -2*f = -4*v + 4, 0*f = 2*f + 5*v - r. Determine c so that 2/3*c**3 + 2*c**f + 2/3 + 2*c = 0.
-1
Let k be 1/4*0 + 1*2. Suppose -1/4*n**k + 0 - 1/2*n = 0. What is n?
-2, 0
Let a = 67/237 - -4/79. Find g such that -2/3*g**2 + 0 - a*g**3 - 1/3*g = 0.
-1, 0
Let a = 10 + -5. Suppose p = y + 2*y + 10, -4*p = a*y - 6. Factor 0 - 1/4*d**2 - 9/4*d**p + 0*d + 3/2*d**3.
-d**2*(3*d - 1)**2/4
Factor 1/2*k**2 - 4*k + 8.
(k - 4)**2/2
Let o(i) be the second derivative of -2*i + 1/15*i**5 + 0 + 0*i**3 - 1/12*i**4 - 1/2*i**2 - 1/60*i**6. Let r(j) be the first derivative of o(j). Factor r(a).
-2*a*(a - 1)**2
What is r in 26*r + 14*r + 46*r**2 + r**3 + 13*r**3 + 8 = 0?
-2, -1, -2/7
Find y, given that 411*y + 3*y**2 - 23*y**2 + 90 - 106*y - 15*y**2 = 0.
-2/7, 9
Let k(i) be the third derivative of i**5/390 + i**4/156 + 2*i**2. Factor k(g).
2*g*(g + 1)/13
Factor d + 2*d**3 + d - 6*d - 2*d**2.
2*d*(d - 2)*(d + 1)
Let z(h) be the first derivative of h**5/20 + h**4/8 - h**2/2 + 3. Let r(d) be the second derivative of z(d). Suppose r(p) = 0. What is p?
-1, 0
Factor 9/5*k + 6/5 - 6/5*k**2.
-3*(k - 2)*(2*k + 1)/5
Let x be (-4)/(-32) - (-100)/224. What is d in 2/7*d**2 - x + 2/7*d = 0?
-2, 1
Let r(p) = p**3 - 26*p**2 + 24*p + 27. Let h be r(25). Let -1/2*a**h - 9/2 + 3*a = 0. What is a?
3
Let j(t) be the first derivative of 1/2*t**2 - 3 + 0*t**3 - 1/12*t**4 + 3*t. Let m(n) be the first derivative of j(n). Determine b, given that m(b) = 0.
-1, 1
Let t(i) = -i**3 - 6*i**2 - 2*i - 9. Let m be t(-6). Let p(z) be the first derivative of 2/9*z**m + 0*z - 2 + 1/9*z**2. Factor p(j).
2*j*(3*j + 1)/9
Let f(z) be the third derivative of 2*z**7/105 + z**6/120 - z**5/5 - 11*z**4/24 - z**3/3 + 7*z**2. Factor f(x).
(x - 2)*(x + 1)**2*(4*x + 1)
Let i(p) = -p**2