. Let q(z) = -z**3 - z - 1. Let j(w) = 2*q(w) - t(w). Factor j(s).
-s*(s - 1)*(s + 1)
Let y(i) be the third derivative of i**5/120 + 133*i**4/24 + 17689*i**3/12 - 260*i**2 + 1. Factor y(p).
(p + 133)**2/2
Let z(g) = -6*g**3 - 10*g**2 - 5*g - 1. Let k(f) = -24*f**3 - 40*f**2 - 19*f - 3. Let n be (-2 + 0)/(2/(-22)). Let l(a) = n*z(a) - 6*k(a). Factor l(r).
4*(r + 1)**2*(3*r - 1)
Let b(y) be the second derivative of -y**8/560 + y**7/350 + y**6/100 - 21*y**2/2 + 4*y. Let r(u) be the first derivative of b(u). Let r(p) = 0. What is p?
-1, 0, 2
Let o = -111/5 - -112/5. Factor 1/5*z**2 - 1/5 + o*z - 1/5*z**3.
-(z - 1)**2*(z + 1)/5
Let w be ((-928)/(-348))/((-28)/(-6)). Determine s, given that 0*s + 1/7*s**2 - w = 0.
-2, 2
Let k = 31 + -29. Let q(d) be the third derivative of 4/9*d**3 + 0*d + 7*d**k + 7/90*d**6 + 1/6*d**4 + 0 - 4/15*d**5. Factor q(l).
4*(l - 1)**2*(7*l + 2)/3
Suppose 0 = 4*v + 20, 3*g - 6*v + 4*v = 19. Suppose -5*i + 40 = g*y, 5*i + 9 = 34. Suppose 44*c**3 - 8*c - y*c**2 + c**3 - 9*c**3 + 33*c**2 = 0. Calculate c.
-1, 0, 2/9
Let z(l) be the first derivative of -l**5/540 + 5*l**4/216 - l**3/9 + 21*l**2 - 8. Let b(f) be the second derivative of z(f). Factor b(k).
-(k - 3)*(k - 2)/9
Let q = -44 + 52. Suppose q*p - 7*p = 2. Factor 0 + 0*x**p - 1/2*x**3 + 0*x.
-x**3/2
Let g(i) be the second derivative of 0 + 4*i**2 + i**4 + 8*i - 1/10*i**5 - 3*i**3. Factor g(t).
-2*(t - 4)*(t - 1)**2
Let z(t) = -2*t**2 - 91*t - 471. Let r be z(-6). Let 3/2*a**2 + 0*a + r*a**5 + 0 - 3*a**3 - 3/2*a**4 = 0. Calculate a.
-1, 0, 1/2, 1
Let t = 103/6 - 35/3. Let j = -3 + t. Factor 2 - 7/2*u**3 + 3/2*u**5 + 21/2*u**2 - j*u**4 - 8*u.
(u - 1)**3*(u + 2)*(3*u - 2)/2
Let j be (-58)/(-377) + (-24)/(-13). Find v, given that 8/9 - 98/9*v**3 - 64/9*v + 154/9*v**j = 0.
2/7, 1
Let o = -1703 + 1705. Factor 0 + 1/2*d**3 - o*d**2 - 5/2*d.
d*(d - 5)*(d + 1)/2
Let k(c) = 20*c**4 - 32*c**3 - 4*c**2 + 8*c + 8. Suppose -h + 7 = -1. Let r(y) = y**2 - 1. Let x(i) = h*r(i) + k(i). Factor x(d).
4*d*(d - 1)**2*(5*d + 2)
Let w be (-3)/(-3) - ((-2)/4 + 9 + -8). What is k in -w*k**3 + 45/2*k**2 + 3375/2 - 675/2*k = 0?
15
Let k be 0/(10/10*(-8)/(-2)). Let 1/4*j**3 + 0*j**2 - 1/4*j**4 + 0*j + k = 0. Calculate j.
0, 1
Let x(l) = -l**2 - 5*l - 4. Let k be x(-2). What is s in 37*s**k - 22*s**2 - 18*s**2 = 0?
0
Factor -1058/5 - 92/5*s - 2/5*s**2.
-2*(s + 23)**2/5
Let u = 50 - 50. Find a such that 1/2*a**3 + u + 9/2*a - 3*a**2 = 0.
0, 3
Let d(w) be the first derivative of 5 - 8/3*w**2 + 2/15*w**5 + 8/3*w**3 + 2*w - w**4. Let x(f) be the first derivative of d(f). Factor x(a).
4*(a - 2)**2*(2*a - 1)/3
Let n be -3*-5*(-3)/45. Let t be (-3 + -2)*n*1. Factor -4 + 12*m + 0 - t - 3 - 3*m**2.
-3*(m - 2)**2
Let r(l) be the second derivative of -4*l + 0 - 1/60*l**6 + 1/12*l**3 + 1/36*l**4 - 1/60*l**5 + 1/12*l**2 - 1/252*l**7. Solve r(q) = 0.
-1, 1
Let h be 1953/(-310) + 13/2. Factor h*z**2 + 0*z + 0.
z**2/5
Let d be 2/(2*-1)*(-26 + 23). Let b(t) be the first derivative of -5/2*t**2 - 1/4*t**4 - 4/3*t**3 - 2*t - d. Factor b(j).
-(j + 1)**2*(j + 2)
Let l = -185413/6 - -84364811/2730. Let y = l - 8/65. Factor -y*c + 2/7*c**2 + 2/7.
2*(c - 1)**2/7
Let c(l) be the first derivative of -3/5*l - 1/10*l**2 + 3 + 1/20*l**4 + 1/5*l**3. Suppose c(a) = 0. What is a?
-3, -1, 1
Let w(d) = -d**5 - 4*d**4 - 2*d**3 + d - 1. Let h(o) = -427*o**2 - 1 + o + 427*o**2 - o**4. Let u(y) = 4*h(y) - 4*w(y). Let u(g) = 0. Calculate g.
-2, -1, 0
Let w(r) be the first derivative of -12*r**5/35 + 7*r**4 - 56*r**3/3 - 8*r**2/7 + 32*r + 146. Let w(c) = 0. What is c?
-2/3, 1, 2, 14
Let y = -784 - -787. Let t(i) be the first derivative of -9/5*i**2 - 4 + 0*i - 1/10*i**4 + 4/5*i**y. Suppose t(n) = 0. Calculate n.
0, 3
Let k(v) = -28*v**2 + 2*v - 3. Let u be k(2). Let y be 5/(-2)*(-4 + u/(-30)). Suppose 3/4*s**2 - 3/4*s**3 - 3/4 + y*s = 0. What is s?
-1, 1
Let x(h) be the first derivative of 2*h**5/45 - 41*h**4/18 + 364*h**3/9 - 2156*h**2/9 - 5488*h/9 + 3. Factor x(f).
2*(f - 14)**3*(f + 1)/9
Find b such that 65/4*b**2 + 0 - 45*b - 5/4*b**3 = 0.
0, 4, 9
Let j(h) be the third derivative of -h**10/453600 + h**8/60480 - h**5/6 + 7*h**2. Let s(i) be the third derivative of j(i). Factor s(l).
-l**2*(l - 1)*(l + 1)/3
Let u(f) be the third derivative of 6*f**7/385 - 61*f**6/220 + f**5/11 - 139*f**2. What is p in u(p) = 0?
0, 1/6, 10
Suppose 507*x = 516*x - 18. Let s(i) be the second derivative of 0 + 8*i + 1/15*i**6 + 1/4*i**4 - 1/12*i**3 - 9/40*i**5 + 0*i**x. Factor s(z).
z*(z - 1)**2*(4*z - 1)/2
Let v(b) = 22*b**2 - 42*b + 124. Let a(h) = -27*h**2 + 41*h - 125. Let j(p) = 4*a(p) + 5*v(p). Determine x so that j(x) = 0.
3, 20
Let b(h) be the third derivative of -h**6/160 + h**5/16 - 7*h**4/32 + 3*h**3/8 + 11*h**2 - 4*h. Solve b(u) = 0 for u.
1, 3
Let w be (2 - 3/6)/((-2)/(-12)). Suppose 4*u + 7 + 5 = 0, -u + w = 3*t. Let -15*i**2 + 63/4*i**t + 3/2*i**3 + 0 - 27/4*i**5 + 6*i = 0. What is i?
-1, 0, 2/3, 2
Let z(p) be the third derivative of -p**8/70560 - p**7/8820 + p**6/840 - 3*p**5/20 + 5*p**2. Let d(i) be the third derivative of z(i). Factor d(a).
-2*(a - 1)*(a + 3)/7
Factor 68/21 - 2/21*g**2 + 10/7*g.
-2*(g - 17)*(g + 2)/21
Let z(j) be the third derivative of 2 - 2/27*j**3 + 1/108*j**4 - 5*j**2 + 0*j + 1/270*j**5. Suppose z(c) = 0. What is c?
-2, 1
Let q(b) = 5*b**3 - 38*b**2 + 89*b - 32. Let x(l) = 5*l**3 - 35*l**2 + 90*l - 30. Let t(g) = -5*q(g) + 4*x(g). Factor t(a).
-5*(a - 8)*(a - 1)**2
Let y(t) = t**2 - 14*t + 27. Let q be y(12). Suppose m**3 + 4*m**q + 0 - 10*m**2 + 0 = 0. What is m?
0, 2
Let w be (1 + 0)/(2/10). Suppose -f + w*v + 102 = 3*f, 0 = -4*f - 2*v + 116. Let -n**2 + n**2 + 29*n**4 - f*n**4 = 0. What is n?
0
Let z(q) be the second derivative of q**6/180 - 11*q**5/120 + 4*q**4/9 - 7*q**3/9 - 385*q. Suppose z(s) = 0. Calculate s.
0, 2, 7
Suppose 5*p - 5*o + 9 + 36 = 0, 0 = -5*p - 4*o - 36. Let q be (-2 - 9/6)*p/56. Factor 0 - q*l**2 - 3/2*l.
-l*(l + 3)/2
Let h = 10037/4 + -2509. Factor -h*c**2 + c + 0.
-c*(c - 4)/4
Let j = 189 + -184. Let u(b) be the first derivative of -16/3*b**3 + 0*b + 5 + j*b**4 - 8/5*b**5 + 2*b**2. Suppose u(p) = 0. What is p?
0, 1/2, 1
Let k(w) be the third derivative of w**8/84 + 26*w**7/105 - 29*w**6/30 + w**5 + 580*w**2. Solve k(y) = 0.
-15, 0, 1
Let d be (-5)/((-7 - -9)/(-2)). Let n(a) be the second derivative of 0 + a**3 + 12*a - 1/2*a**4 + 1/10*a**d - a**2. Factor n(t).
2*(t - 1)**3
Suppose -7*p - 4 = -4*p - 5*f, 2 = f. Suppose 3*i = -2*r + 9, -2*i - 1 = -2*r + 3. Factor p*c**2 + 2/9*c + 0 + 16/3*c**r + 32/9*c**4.
2*c*(c + 1)*(4*c + 1)**2/9
Let n(h) be the first derivative of -h**3/3 + h**2/2 + 6*h + 133. Factor n(c).
-(c - 3)*(c + 2)
Let u(z) be the third derivative of -z**7/70 - 2*z**6/15 - 23*z**5/60 - 5*z**4/12 + 34*z**2 - 1. Factor u(b).
-b*(b + 1)**2*(3*b + 10)
Let k = 452 + -31639/70. Let v(z) be the third derivative of -3*z**2 + 0*z**4 + 0*z**3 + 0 + 0*z**6 + 0*z**5 - k*z**7 + 0*z. Factor v(y).
-3*y**4
Solve -5/2*s**2 + 4*s - 2 + 1/2*s**3 = 0 for s.
1, 2
Let f(u) be the second derivative of u**7/840 - u**6/480 - u**5/480 + 5*u**3/6 + 3*u. Let s(k) be the second derivative of f(k). Factor s(p).
p*(p - 1)*(4*p + 1)/4
Factor -5/3 + 23/6*i - 5/2*i**2 + 1/6*i**4 + 1/6*i**3.
(i - 2)*(i - 1)**2*(i + 5)/6
Let n(s) = 7*s**2 + 3*s - 4. Let c(l) be the first derivative of l**3 + l**2/2 - 2*l + 13. Let p(t) = -9*c(t) + 4*n(t). Factor p(g).
(g + 1)*(g + 2)
Let x = -105 - -106. Let b(d) be the first derivative of 9/7*d**2 + 4/7*d + x + 2/3*d**3. Factor b(r).
2*(r + 1)*(7*r + 2)/7
Let i be ((-15)/10)/(6/(-28)). Let q(t) be the second derivative of 0*t**2 + 0*t**3 - 1/15*t**6 - 3*t + 0*t**4 - 4/21*t**i + 0*t**5 + 0. Factor q(b).
-2*b**4*(4*b + 1)
Let o(v) = 2*v - 8. Let h be o(6). Factor -2*s**5 - s**5 + 3*s**4 + 3*s**h - 6*s**2 + 0*s**5 + 3*s.
-3*s*(s - 1)**3*(s + 1)
Let z(d) = 5*d**4 + 2*d**3 - 21*d**2 + 16*d - 11. Let n(h) = 6*h**4 + 2*h**3 - 22*h**2 + 14*h - 12. Let s(r) = 3*n(r) - 4*z(r). What is p in s(p) = 0?
-4, 1
Let n(p) = p**2 + 2*p + 3. Let x be n(-2). Let u(c) be the first derivative of c - 1/3*c**x - 7/8*c**4 + 2 + 7/4*c**2. Find m such that u(m) = 0.
-1, -2/7, 1
Let h(q) = 6*q**2 + 6*q - 3. Let r(y) = 17*y**2 + 18*y - 8. Let t(o) = -8*h(o) + 3*r(o). Let t(k) = 0. Calculate k.
-2, 0
Suppose 0 =