*3*(y + 1)/2
Let u(a) be the second derivative of a**6/180 - a**4/36 + a**2/12 + 2*a - 45. Factor u(v).
(v - 1)**2*(v + 1)**2/6
Let j(w) be the first derivative of -3/4*w**4 - 4*w**3 + 2 + 0*w - 6*w**2. Factor j(b).
-3*b*(b + 2)**2
Let i(p) = 6*p**5 - 12*p**4 - 12*p**3 + 68*p**2 - 50*p + 4. Let l(x) = x**5 - x**4 - x**2 + x + 1. Let v(s) = i(s) - 4*l(s). Determine u, given that v(u) = 0.
-3, 0, 1, 3
Let x be (2/3*9)/((-8721)/(-1197)). Solve -32/17*u**3 + 0 + 22/17*u**2 - 4/17*u + x*u**4 = 0 for u.
0, 2/7, 1
Let g(b) be the second derivative of b**4/24 + 5*b**3/12 - 3*b**2/2 + 67*b + 2. Determine u so that g(u) = 0.
-6, 1
Let f = 5 + 4. Let y be ((-26)/18 - -1)/((-3)/f). Factor -14/3*p + y - 6*p**2.
-2*(p + 1)*(9*p - 2)/3
Let d be ((-60)/15)/((1 + -3)/8). Factor o**3 + 63*o + 47*o**2 - 65 - 30*o**2 - d.
(o - 1)*(o + 9)**2
Let d(h) = 2*h**2 + 55*h - 403. Let f(t) = 25*t**2 + 715*t - 5240. Let i(c) = -40*d(c) + 3*f(c). Factor i(k).
-5*(k - 5)*(k + 16)
Let r(h) be the third derivative of 0 + 9*h**2 + 1/138*h**4 - 8/69*h**3 + 0*h + 1/690*h**5. Suppose r(w) = 0. What is w?
-4, 2
Let d(x) be the second derivative of 5*x**8/336 - x**7/42 - 15*x**2/2 - 3*x. Let j(i) be the first derivative of d(i). Factor j(m).
5*m**4*(m - 1)
Let q(b) = -9*b**2 - 74*b. Let c(s) = -3*s**2 - 24*s. Let d(i) = -17*c(i) + 6*q(i). Determine m, given that d(m) = 0.
-12, 0
Let u be (1 + -1)*(-67 + 66). Factor 2/3*w + u + 2/3*w**3 + 4/3*w**2.
2*w*(w + 1)**2/3
Let u = 73/46 - 123/92. Factor -1/4 + u*n**2 - 1/4*n**3 + 1/4*n.
-(n - 1)**2*(n + 1)/4
Let z(k) = -2*k**5 - k**4 - 4*k**3 + 4*k**2 - 3*k + 3. Let m(f) = -f**5 - f**3 + f**2 - f + 1. Let r(c) = -3*m(c) + z(c). Factor r(t).
t**2*(t - 1)**2*(t + 1)
Let m(x) be the first derivative of 0*x - x**2 + 1/5*x**5 - 1/3*x**3 + 1/2*x**4 + 8. Factor m(r).
r*(r - 1)*(r + 1)*(r + 2)
Let r be 7/(-70)*(-15980)/(-8). Let n = r + 201. Determine s so that -2*s + 1 + n*s**2 - 1/4*s**3 = 0.
1, 2
Let j be (14/(-784)*12)/((-24)/14). Let v(g) be the first derivative of j*g**4 + 0*g**2 + 0*g**3 + 0*g + 8. Factor v(d).
d**3/2
Suppose -2 = 2*d - 8. Solve -6*t**5 - 7*t**3 + 12*t**d + 10*t**2 + 5*t**3 - 4*t - 10*t**4 = 0 for t.
-2, -1, 0, 1/3, 1
Let a = -22 - -116/5. Let y(n) be the first derivative of -a*n**3 - 7/10*n**4 - 1 + 0*n - 2/5*n**2. Determine l, given that y(l) = 0.
-1, -2/7, 0
Let a(q) = -q + 159*q**2 - 160*q**2 + q. Let h(v) be the first derivative of -7*v**3/3 + 3*v**2/2 - 2*v + 3. Let w(m) = -6*a(m) + h(m). Factor w(n).
-(n - 2)*(n - 1)
Let b(g) = -5*g + 9. Let d be b(-5). Let p = -12 + d. Factor -5*v**4 + 4*v**3 - 11*v**4 - 10*v**5 + p*v**5.
4*v**3*(v - 1)*(3*v - 1)
Suppose -5*m = -r - 9, -5*m + 7 = r - 4. Let d(x) = 2*x + 2. Let p be d(4). Factor 64*a**2 + 13*a**3 - 64*a + 80*a**2 - 111*a**3 + p*a**m + 8.
-2*(a - 1)*(7*a - 2)**2
Let h(k) = -k - 7. Let q be h(-9). Factor -9*n**3 + 4*n - 3 + 9 + 5*n**3 + 2 - 8*n**q.
-4*(n - 1)*(n + 1)*(n + 2)
Let k(d) = -33*d**3 - 68*d**2 - 40*d - 2. Let i(y) = 65*y**3 + 135*y**2 + 80*y + 5. Let m(l) = 3*i(l) + 5*k(l). Factor m(q).
5*(q + 1)**2*(6*q + 1)
Let h(v) = 6*v + 67. Let z be h(-11). Suppose 5*i + p = 14, 2*i = -p + 6 - z. Let -2*s**2 - 2*s**i - 2/3*s - 2/3*s**4 + 0 = 0. Calculate s.
-1, 0
Let w be (1 - (-30)/4) + 4. Let g = -221/18 + w. Suppose 0*l + 8/9 + g*l**3 - 2/3*l**2 = 0. What is l?
-1, 2
Let o(n) be the third derivative of -7/100*n**5 - 3/10*n**4 + 0 + 9*n**2 + 2/5*n**3 + 0*n. Suppose o(f) = 0. Calculate f.
-2, 2/7
Let q(p) = 3*p**2 - 2*p - 12. Suppose 0 - 2 = -l. Let w(h) = 3*h**2 - 3*h - 12. Let r(v) = l*w(v) - 3*q(v). Factor r(g).
-3*(g - 2)*(g + 2)
Let h(j) = -j**2 + 14*j - 42. Let q be h(5). Suppose 16 = 5*d + q*d. Let 0*s + 0 + 1/6*s**d = 0. Calculate s.
0
Suppose 3*w - 4*f - 7 = 0, 22 - 55 = -5*w - 4*f. Suppose -v + 4*t = -14, 0 = -3*v + 8*v + 5*t + w. Factor -6*h**v + 8*h**2 - 4 + h**2 + h**2.
4*(h - 1)*(h + 1)
Let -768/7*n**2 - 6/7*n**4 - 416/7 + 184/7*n**3 + 1056/7*n = 0. Calculate n.
2/3, 2, 26
Let q(s) be the third derivative of -s**5/240 + s**4/96 + s**3/12 + 64*s**2. Determine b so that q(b) = 0.
-1, 2
Let c(a) be the second derivative of -a**6/10 + 27*a**5/20 + 100*a. Factor c(b).
-3*b**3*(b - 9)
Let v = -2300 + 2302. Factor -2/11*u + 2/11*u**v - 4/11.
2*(u - 2)*(u + 1)/11
Let h(x) be the first derivative of -3*x**5/20 + 9*x**4/16 + x**3/4 - 9*x**2/8 - 134. Solve h(k) = 0.
-1, 0, 1, 3
Factor 1/7*h**5 + 4/7*h**4 - 4/7*h**2 - 3/7*h + 2/7*h**3 + 0.
h*(h - 1)*(h + 1)**2*(h + 3)/7
Let b(c) be the first derivative of -6*c**2 + 5*c**4 + 8/3*c**3 - 10 + 0*c. Factor b(l).
4*l*(l + 1)*(5*l - 3)
Let y(g) = 5*g - 33. Suppose -3*j + 28 = j. Let q be y(j). Factor -2/7*p - 2/7*p**q + 4/7.
-2*(p - 1)*(p + 2)/7
Let a(n) be the first derivative of -n**6/9 - 77*n**5/30 - 379*n**4/24 - 373*n**3/9 - 145*n**2/3 - 52*n/3 + 647. Determine w so that a(w) = 0.
-13, -2, -1/4
Let k be 1 - (1 - -4 - 4). Let a(f) be the third derivative of 0*f + 4*f**2 + 1/20*f**5 + 0*f**4 + 0*f**3 + k. Determine z, given that a(z) = 0.
0
Let l(n) = -n**3 + 3*n**2 + 5*n + 3. Let k be l(4). Let m(w) = 2*w - 14. Let z be m(k). Factor z + 2*h**2 + 3/2*h + 1/2*h**3.
h*(h + 1)*(h + 3)/2
Let a = -13 - -24. Let q(x) = x**3 - 11*x**2 + x - 2. Let w be q(a). Solve 17*d**2 + 0*d**3 + 18*d + 4*d**2 - w*d**3 = 0.
-2/3, 0, 3
Factor -2/9*b**5 - 28/9*b**3 + 4/9 - 2*b + 4/3*b**4 + 32/9*b**2.
-2*(b - 2)*(b - 1)**4/9
Let d(j) = 18*j**2 - 852*j**3 + 851*j**3 + 2*j - 18*j - 15. Let n be d(17). Suppose 4/3*o + 2*o**n + 0 + 2/3*o**3 = 0. Calculate o.
-2, -1, 0
Let r(m) = -12*m**3 + 12*m**2 + 24*m - 24. Let c(q) = 2*q**3 - q**2 - q. Let w(v) = 4*c(v) + r(v). Suppose w(d) = 0. Calculate d.
-2, 1, 3
Let b = -28405/9 - -3157. Factor -1/9*g**3 - 10/9*g**2 - b*g + 1/9*g**4 + 0.
g*(g - 4)*(g + 1)*(g + 2)/9
Let t(d) be the first derivative of d**5/16 - 5*d**4/12 + 19*d - 15. Let i(l) be the first derivative of t(l). Factor i(n).
5*n**2*(n - 4)/4
Suppose -2/9*t**2 + 8 + 0*t = 0. What is t?
-6, 6
Let u be ((-7)/5)/((-64)/(-80)). Let d = 13/4 + u. Find s, given that -1 + d*s - 1/2*s**2 = 0.
1, 2
Suppose -47*k + v = -43*k - 5, -18 = k - 3*v. Factor 0 - 1/4*t**k - 3/4*t**2 - 1/2*t.
-t*(t + 1)*(t + 2)/4
Let s(z) be the third derivative of 0*z**5 - 2*z**2 + 0*z**3 - 1/1680*z**8 - 1/600*z**6 + 0*z + 1/525*z**7 + 0 + 0*z**4. Find j, given that s(j) = 0.
0, 1
Let i(a) be the second derivative of a**5/40 + 11*a**4/24 - a**3/12 - 11*a**2/4 + 6*a + 6. Factor i(r).
(r - 1)*(r + 1)*(r + 11)/2
Let o be 6 - (-116)/(0 - -4). Let g be (3 + o/(-10))*-4. Factor -1 + 3*q - 9/4*q**g.
-(3*q - 2)**2/4
Factor -9/4*k**2 + 6 - 3/4*k**3 + 9/2*k.
-3*(k - 2)*(k + 1)*(k + 4)/4
Let r(m) be the third derivative of -m**5/150 + m**4/30 + 16*m**3/5 + 140*m**2. Solve r(f) = 0 for f.
-6, 8
Let a(t) = -5*t - 14 + 2*t + 6*t + 2. Let d be a(6). Factor -2 - 14*z**2 - d*z - z**3 - z**3 + 8*z**2.
-2*(z + 1)**3
Let l(t) be the first derivative of 4*t**3/3 - 4*t**2 + 3. Factor l(s).
4*s*(s - 2)
Let g = 173 - 173. Let d(o) be the second derivative of 0 - 1/5*o**5 - 1/5*o**6 + g*o**4 - 1/21*o**7 - 6*o + 0*o**2 + 0*o**3. Suppose d(f) = 0. What is f?
-2, -1, 0
Let o be (6 - 10)/((-6)/21). Suppose -5 = 3*j - o. Factor -2*d**4 - 7*d**3 - 4*d**3 + 12*d**j + d**4.
-d**3*(d - 1)
Let d = -19/339 - -1093/1356. Factor -d*a - 1/2*a**2 + 0 + 1/4*a**3.
a*(a - 3)*(a + 1)/4
Suppose -2*u**5 - 74*u**3 - 554*u**4 - 22*u**3 + 530*u**4 - 128*u**2 = 0. Calculate u.
-4, 0
Let q(a) be the first derivative of -17 + 3/16*a**4 - 1/20*a**5 + 0*a**2 - 1/6*a**3 + 0*a. Determine x, given that q(x) = 0.
0, 1, 2
Let x(y) = y**3 + y**2 + 5*y - 1. Let w(n) = n**3 + n**3 + 68*n - 32*n - 30*n. Suppose 0 = -4*z - 0*z + 12. Let h(u) = z*w(u) - 4*x(u). Factor h(f).
2*(f - 2)*(f - 1)*(f + 1)
Find c such that 6/5*c**5 + 0 - 8/5*c - 4*c**4 + 14/5*c**3 + 8/5*c**2 = 0.
-2/3, 0, 1, 2
What is v in 4/5*v**2 - 4/5*v**4 + 0 - 2/5*v + 2/5*v**5 + 0*v**3 = 0?
-1, 0, 1
Let x(o) be the third derivative of 0*o**5 + 0*o**6 + 0*o**3 + 0*o**4 + o**2 - 1/245*o**7 + 0 + 0*o - 1/392*o**8. Factor x(r).
-6*r**4*(r + 1)/7
Let f(w) = 8*w - 3 + 4*w**2 - 4 - 5 + 4. Let v(k) = -3*k**2 - 5*k + 5. Let l(u) = 5*f(u) + 8*v(u). Factor l(s).
-4*s**2
Let r(n) be the third derivative of n**6/160 + 13*n**5/120 + 2*n**4/3 + 4*n**3/3 + 4*n**2 + 115. Solve r(f) = 0 for f