 Suppose 0*a = a - 2*y + k, -3*a - 5*y + 31 = 0. Factor 0 + 2/3*n - 10/3*n**a - 8/3*n**4 + 16/3*n**3.
-2*n*(n - 1)*(2*n - 1)**2/3
Let r(c) = 4*c**3 - 16*c**2 - 7*c - 63. Let v(n) = -n**3 + 5*n**2 + 2*n + 21. Let d(j) = 2*r(j) + 7*v(j). Let h(u) be the first derivative of d(u). Factor h(o).
3*o*(o + 2)
Factor 6*p + 21 + 3/7*p**2.
3*(p + 7)**2/7
Let u(m) be the first derivative of -m**5/570 - 15*m**2/2 - 32. Let c(b) be the second derivative of u(b). Factor c(a).
-2*a**2/19
Let z(k) = k**4 - 5*k**3 - k**2 + 7*k + 6. Let t(b) = -b**4 - b**2 - b - 1. Let u(f) = 2*t(f) + z(f). Factor u(c).
-(c - 1)*(c + 1)**2*(c + 4)
Let k(o) be the second derivative of o**6/270 - 11*o**5/360 + o**4/12 - 8*o**3/3 + 13*o. Let h(c) be the second derivative of k(c). Factor h(j).
(j - 2)*(4*j - 3)/3
Let y be (-6)/9 - (-1700)/30. Let h be 16/12*(y/44 + -1). Factor -6/11*t + 2/11*t**2 + h.
2*(t - 2)*(t - 1)/11
Let c(b) be the third derivative of -9/160*b**6 + 1/8*b**4 + 1/5*b**5 + 0*b**3 - 14*b**2 + 0*b + 0. Determine n so that c(n) = 0.
-2/9, 0, 2
Let t(j) be the second derivative of -j**6/30 + 7*j**5/5 - 13*j**4/2 + 38*j**3/3 - 25*j**2/2 - 240*j. Factor t(d).
-(d - 25)*(d - 1)**3
Let n(j) = j**3 - 14*j**2 - 15*j. Suppose 3*o - 30 = 15. Let d be n(o). Factor -1/4*y**3 - 1/2*y**4 - 1/4*y**5 + 0*y + 0 + d*y**2.
-y**3*(y + 1)**2/4
Let f(r) = -68*r + 682. Let d be f(10). Factor -3/2*q**3 + 1/2*q**4 + 0 - q + 1/2*q**5 - 5/2*q**d.
q*(q - 2)*(q + 1)**3/2
Let t be ((-12)/3)/(-3 + 1). Let g(f) = 7*f**2 - t*f**3 - f**3 - 2*f + 3 - 4*f. Let r(h) = -h**3 + h**2 + 1. Let j(k) = g(k) - r(k). Factor j(y).
-2*(y - 1)**3
Let n be (-1 - (-8)/7) + 1824/21. Suppose 2 = -86*x + n*x. What is s in -2/7*s - 4/7 + 2/7*s**x = 0?
-1, 2
Let t(z) = z**3 - z. Let p(y) = 5*y**4 - 35*y**3 + 60*y**2 - 45*y + 15. Let d(s) = -p(s) - 5*t(s). Solve d(w) = 0 for w.
1, 3
Let i = -106/51 + 22/51. Let w = 73/34 + i. Factor 0*s + 1/2 - w*s**2.
-(s - 1)*(s + 1)/2
Let t(g) be the first derivative of -g**6/21 - 12*g**5/35 + 5*g**4/7 + 104*g**3/21 - 15*g**2 + 100*g/7 - 69. Determine d, given that t(d) = 0.
-5, 1, 2
Suppose s - 4*v = -13 - 2, 2*v - 20 = -2*s. Let a(x) be the second derivative of -4/105*x**6 - 6*x + 0 + 0*x**2 + 3/70*x**s + 0*x**3 - 1/84*x**4. Factor a(p).
-p**2*(2*p - 1)*(4*p - 1)/7
Factor -49 - 7*b**2 - 279 + b**2 + 68 - 45*b + 11*b**2.
5*(b - 13)*(b + 4)
Factor 333/2*c**2 + 219/4 + 3/4*c**4 + 57*c**3 + 165*c.
3*(c + 1)**3*(c + 73)/4
Let i(s) be the first derivative of 2/21*s**3 - 7 - 18/7*s + 1/14*s**4 - 9/7*s**2. Let i(w) = 0. What is w?
-3, -1, 3
Suppose -240/13*g + 288/13 - 46/13*g**2 - 2/13*g**3 = 0. Calculate g.
-12, 1
Let l(t) be the first derivative of 3*t**5/80 + t**4/16 - 10*t + 13. Let m(g) be the first derivative of l(g). Factor m(z).
3*z**2*(z + 1)/4
Suppose 5*m + 21 = -4*i, -73 = 5*i - 5*m - 13. Let h = i + 13. Suppose -2/3*n**3 - 2/3*n**h + 2/3*n**2 + 0*n + 0 + 2/3*n**5 = 0. What is n?
-1, 0, 1
Let k(t) = t**2 + 4*t + 1. Let w be k(-3). Let d be (-6)/(-9)*(1 - w). Determine y, given that 0*y**2 - 2*y**5 - 7*y**2 + d*y**3 + 7*y**2 = 0.
-1, 0, 1
Suppose 21*x = -0*x + 126. Let i(c) be the first derivative of -2*c**2 - 2/5*c**5 - 3/2*c**4 + 2 + 0*c + 10/3*c**3 + 1/3*c**x. Solve i(q) = 0 for q.
-2, 0, 1
Let c(p) be the first derivative of -2*p**3/9 - 50*p**2/3 - 1250*p/3 - 4. Factor c(q).
-2*(q + 25)**2/3
Let j(m) be the first derivative of -1/6*m**4 - 5*m + 3 + 2*m**2 - 1/3*m**3. Let k(g) be the first derivative of j(g). What is s in k(s) = 0?
-2, 1
Solve -12/7*i**3 + 16/7*i + 0 + 88/7*i**2 - 22/7*i**5 - 10*i**4 = 0.
-2, -2/11, 0, 1
Let b be (54/10 - 3)/(152/190). Factor 10/13*u**2 + 2/13*u**b + 6/13*u + 0 - 2/13*u**4.
-2*u*(u - 3)*(u + 1)**2/13
Let i(x) be the first derivative of 4/7*x**3 - 15/7*x**4 + 5/7*x**6 + 15/7*x**2 + 39 - 6/35*x**5 - 6/7*x. Suppose i(j) = 0. Calculate j.
-1, 1/5, 1
Suppose -7*l**2 + 9*l**2 - l**3 + 18 - 5*l**2 - 7*l - 7*l**2 = 0. Calculate l.
-9, -2, 1
Let w be (10/(-25)*5)/((-95)/152). Find s such that -1/5*s**2 - 64/5 - w*s = 0.
-8
Suppose 3*a - 2*x + 45 = 4*a, 4*a + 2*x = 198. Factor -3*j**5 + 66*j**2 + 18 - 12*j**4 + a*j - 19*j**2 - 5*j**2.
-3*(j - 2)*(j + 1)**3*(j + 3)
Suppose -330*x + 474 = -186. Suppose -121/2 - 11*z - 1/2*z**x = 0. Calculate z.
-11
Let a(g) be the second derivative of 5*g**7/42 - 23*g**6/3 + 359*g**5/2 - 1650*g**4 + 3375*g**3/2 + 16875*g**2 - 2*g + 109. Factor a(v).
5*(v - 15)**3*(v - 2)*(v + 1)
Let d(g) be the second derivative of -g**4/6 + 52*g**3 - 155*g**2 - 152*g. Solve d(o) = 0.
1, 155
Factor -5/3*m**2 + 1/6*m**3 - 2/3*m + 1/6*m**5 + 2/3*m**4 + 4/3.
(m - 1)**2*(m + 2)**3/6
Let h(m) = -m**3 + m**2 - m + 34. Let f be h(0). Determine j, given that 14*j - 5*j**3 - 21*j**2 - f*j - 4*j**2 = 0.
-4, -1, 0
Let n(i) be the third derivative of -i**8/8400 + i**7/1400 - i**6/1800 - 35*i**4/24 + 27*i**2. Let j(f) be the second derivative of n(f). Factor j(r).
-r*(r - 2)*(4*r - 1)/5
Let y = -865 + 870. Let c(m) be the third derivative of 0 - m**2 - 1/40*m**y + 0*m + 1/4*m**4 - m**3. Factor c(p).
-3*(p - 2)**2/2
Let u(k) be the third derivative of -k**6/240 + 3*k**5/40 - 5*k**4/16 - 25*k**3/12 - 2*k**2 + 143*k. Let u(h) = 0. What is h?
-1, 5
Let h(v) = 3*v - 10. Let n be h(4). Solve m**5 + 7 - 5*m**3 + 4*m**4 - n*m**5 + 2*m**2 - 7 = 0 for m.
0, 1, 2
Let v(p) = p**2 - 4*p + 2. Let d be v(4). Let i be 26/299 + (-56)/(-414). What is n in 5/9*n**3 + 0 - i*n - 1/3*n**d = 0?
-2/5, 0, 1
Let q = 483 - 483. Let y(m) be the first derivative of q*m + 0*m**2 - 7 + 2/27*m**3. Factor y(z).
2*z**2/9
Find k such that 2*k**4 - 4*k**4 + 6*k**3 - 12*k**3 + 5*k**4 + 3*k**5 = 0.
-2, 0, 1
Let k = -20327 + 101637/5. Let 2*g**4 - 14/5*g**3 - 8/5 + 16/5*g - 2/5*g**5 - k*g**2 = 0. Calculate g.
-1, 1, 2
Let o(l) be the second derivative of l**5/4 + 25*l**4 + 1595*l**3/2 + 4205*l**2 - 559*l. Factor o(h).
5*(h + 2)*(h + 29)**2
Let q(p) be the first derivative of 0*p**3 + 1/22*p**4 - 3/11*p**2 - 10 + 4/11*p. Let q(l) = 0. Calculate l.
-2, 1
Suppose 4*m - 10*m + 30 = 0. Suppose 0 = 3*y + m*y. Solve y - 8/7*z**2 + 2/7*z = 0 for z.
0, 1/4
Let t(r) be the first derivative of -2*r**6/3 - 148*r**5/5 - 248*r**4 - 1856*r**3/3 + 384. Let t(v) = 0. Calculate v.
-29, -4, 0
Let a be ((28/(-15))/(-14))/((-4)/(-3)). Let f(z) be the first derivative of 0*z + a*z**2 - 4 + 1/15*z**3. Factor f(k).
k*(k + 1)/5
Suppose 6*r = -9*r + 30. Suppose -f - r + f**3 - 1 + 1746*f**2 - 1743*f**2 = 0. Calculate f.
-3, -1, 1
Determine u, given that 22/5*u + 23/5 - 1/5*u**2 = 0.
-1, 23
Let y be (1/5)/(((-7)/(-140))/(3/5)). Solve 4*n**2 - 28/5*n - 4/5*n**3 + y = 0 for n.
1, 3
Let y = 16 - 14. Let p be ((-11)/5 - -3)/((-12)/(-10)). Factor -2/3 + p*s**y + 0*s.
2*(s - 1)*(s + 1)/3
Let o(g) = g**2 + 3*g - 1. Let j(w) = -7*w**2 - 79*w + 132. Let b(a) = -j(a) - 6*o(a). Factor b(m).
(m - 2)*(m + 63)
Suppose -9*w + 10*w = -5*u + 19, -23 = -5*u - 2*w. Factor 0*y**2 + 1/3*y**5 - y**4 + 2/3*y**u + 0*y + 0.
y**3*(y - 2)*(y - 1)/3
Let m(o) = 25*o**5 - 20*o**4 - 25*o**3 - 80*o**2 + 80. Let b(c) = -c**5 + 2*c**4 - c**2 + c. Let t(s) = -20*b(s) - m(s). What is d in t(d) = 0?
-4, -2, -1, 1, 2
Factor 2/9*n**2 + 28/9 - 10/3*n.
2*(n - 14)*(n - 1)/9
Let g = -11/5 - -92/35. Let o(j) be the first derivative of 0*j + 9 - 3/35*j**5 + 0*j**4 + g*j**2 + 3/7*j**3. Suppose o(s) = 0. Calculate s.
-1, 0, 2
Let m(c) be the first derivative of -5 - 4/3*c**2 - 1/4*c**6 + 0*c - 16/3*c**3 - 28/15*c**5 - 5*c**4. Factor m(q).
-q*(q + 2)**3*(9*q + 2)/6
Let t = 5955/7 + -850. Determine j, given that -2/7 - 4/7*j**2 - t*j - 1/7*j**3 = 0.
-2, -1
Suppose -15*d + 6*d = 153. Let w = d - -53/3. Solve 8/3*l + 8/3 + w*l**2 = 0.
-2
Let n(d) be the first derivative of -4*d**5 + 25*d**4/4 + 35*d**3/3 - 5*d**2 - 21. What is r in n(r) = 0?
-1, 0, 1/4, 2
Suppose 12 = -4*t, -d - t + 5*t + 10 = 0. Let o be (-18)/(-9) - (-1 - d)*-1. Determine u so that 1/3*u**o - 1/3*u**4 - 1/3*u**5 + 0 + 0*u + 1/3*u**2 = 0.
-1, 0, 1
Factor -8*o - 2*o**5 + 364*o**2 + 4*o**4 - 19*o**3 + 25*o**3 - 372*o**2.
-2*o*(o - 2)**2*(o + 1)**2
Let q(p) be the third derivative of -p**8/1008 + 8*p**7/315 - 29*p**6/360 + 7*p**5/90 + 4*p**2 - 18. Factor q(a).
-a**2*(a - 14)*(a - 1)**2/3
Let y be (1 - -3)*30/12. Factor -12*k - y - 1 + 3*k**2 + 11.
3*k*(k - 4)
Let -6*o**3 - 4*o**2 - 3*o**4 - 11*o