be 336/540 - 4/p. Factor -h*d**2 + 4/9*d - 2/9.
-2*(d - 1)**2/9
Factor -7*k - 11*k + 18790 - 18838 + 3*k**2.
3*(k - 8)*(k + 2)
Let v be 9/12*2 + (-867)/18. Let r = -44 - v. Determine a so that -2/3*a + 0 - r*a**2 - 2*a**3 = 0.
-1, -1/3, 0
Let n(f) be the third derivative of f**6/60 + 7*f**5/30 - 5*f**4/6 - 16*f**3/3 + 3*f**2 + 4. Factor n(q).
2*(q - 2)*(q + 1)*(q + 8)
Let l(i) = -4*i**3 - 42*i**2 - 26*i + 6. Let b(y) = -8*y**3 - 85*y**2 - 51*y + 13. Let m(u) = 6*b(u) - 13*l(u). Suppose m(s) = 0. Calculate s.
-8, -1, 0
Let w(a) = 13*a**2 - 25*a**2 + 14*a**2 + a - 6. Let t be w(-4). Determine o so that -24*o - 4 + o**2 + t*o + o**2 = 0.
-1, 2
Suppose -4*j = 3*l + 20, -l + 0*j + 15 = -3*j. Suppose 0 = v - 2*v - 4*k + 4, -3*k + 3 = l. What is u in v + 0*u - 3/7*u**3 + 0*u**2 - 1/7*u**4 = 0?
-3, 0
Let g(n) be the second derivative of -3*n**5/20 + 7*n**4/4 - 7*n**3 + 12*n**2 - 56*n. Factor g(i).
-3*(i - 4)*(i - 2)*(i - 1)
Determine d, given that 33/7*d - 3/7*d**3 + 12/7*d**4 - 6/7 - 36/7*d**2 = 0.
-2, 1/4, 1
Suppose 0 = 55*i - 54*i - 5*q + 13, 3 = q. Factor -2/3*d**i - 8/3 - 10/3*d.
-2*(d + 1)*(d + 4)/3
Let s(o) be the second derivative of o**6/60 + o**5/10 + 5*o**4/24 + o**3/6 + o - 14. Solve s(b) = 0.
-2, -1, 0
Let q(i) be the third derivative of i**8/84 - 4*i**7/105 - 7*i**6/30 - 4*i**5/15 - 144*i**2. Determine a so that q(a) = 0.
-1, 0, 4
Let q(v) = -v**3 + 10*v**2 - 30*v + 15. Let d(t) = -t - 1. Let s(c) = 3*d(c) - q(c). Factor s(k).
(k - 6)*(k - 3)*(k - 1)
Let w(y) be the first derivative of y**6/120 + y**5/15 + y**4/6 - 11*y**2/2 - 6. Let u(k) be the second derivative of w(k). Factor u(t).
t*(t + 2)**2
Let f(q) = q**2 - 13*q - 9. Let u(y) be the first derivative of y**3/3 - y**2/2 - y + 13. Let l(c) = -f(c) + 5*u(c). Factor l(g).
4*(g + 1)**2
Let o(l) = l + 2. Let y be o(3). Suppose 2*r - r - y = 0. Determine u, given that -3*u**5 - r*u**5 - 13*u**3 - 20*u**4 - 4*u**2 - 3*u**3 = 0.
-1, -1/2, 0
Let c(t) be the third derivative of 3/224*t**8 + 0 + 17/210*t**7 + 1/48*t**4 + 0*t - 1/6*t**3 + 1/5*t**5 - 5*t**2 + 23/120*t**6. Determine a so that c(a) = 0.
-1, 2/9
Factor 12*j + 0*j**2 - j + 2*j**2 + 5*j.
2*j*(j + 8)
Let q(y) be the first derivative of -9*y**5/20 + 13*y**4/4 - 8*y**3 + 6*y**2 + 4*y + 17. What is s in q(s) = 0?
-2/9, 2
Let w(r) be the first derivative of 0*r + 1/12*r**4 + 1/2*r**2 - 1/60*r**5 - 1/6*r**3 + 4. Let i(t) be the second derivative of w(t). Factor i(y).
-(y - 1)**2
Let s(p) be the second derivative of -p**4/4 + 5*p**3 + 36*p**2 + 313*p. Solve s(x) = 0 for x.
-2, 12
Let 1/3*d**2 - 106/3*d + 2809/3 = 0. What is d?
53
Let k(q) be the second derivative of -7*q**7 - 203*q**6/10 + 9*q**5/10 + 191*q**4/4 + 46*q**3 + 18*q**2 + 52*q + 1. Suppose k(g) = 0. Calculate g.
-3/2, -1, -2/7, 1
Let q(y) be the third derivative of y**6/120 - 11*y**5/60 + 13*y**4/8 - 15*y**3/2 - 58*y**2. Find l such that q(l) = 0.
3, 5
Let v(u) be the second derivative of u**8/10080 + u**7/105 + 2*u**6/5 + 48*u**5/5 + 4*u**4/3 - 5*u - 4. Let q(n) be the third derivative of v(n). Factor q(z).
2*(z + 12)**3/3
Let v(o) be the second derivative of -o**5/80 - o**4/4 - 7*o**3/8 - 5*o**2/4 - 41*o. Solve v(y) = 0 for y.
-10, -1
Let a(i) be the first derivative of 8 - 2/105*i**5 + 0*i + 0*i**2 + 0*i**3 - 1/42*i**4. Factor a(v).
-2*v**3*(v + 1)/21
Let w(t) be the second derivative of 0 + 0*t**2 - 1/12*t**4 - 14*t + 1/10*t**5 - 1/30*t**6 + 0*t**3. Determine o, given that w(o) = 0.
0, 1
Let v(n) be the third derivative of -n**7/3360 - n**6/240 - n**5/40 + 5*n**4/8 - 7*n**2. Let o(w) be the second derivative of v(w). Let o(u) = 0. What is u?
-2
Let h(j) be the second derivative of -5/24*j**4 + 5/3*j**3 - 7*j - 1/6*j**5 + 0 + 7*j**2 + 1/24*j**6. Let k(r) be the first derivative of h(r). Factor k(l).
5*(l - 2)*(l - 1)*(l + 1)
Let v = 41 + -41. Factor v*y**2 - 23*y**3 + 4*y**2 + 25*y**3.
2*y**2*(y + 2)
Let w = -25 + 31. Let m be 8*(-4)/8 + w. Factor 3/4 + 3/4*g**m + 3/2*g.
3*(g + 1)**2/4
Determine c so that -7 + 11 - 3 + 5*c**2 - 1 - 80*c = 0.
0, 16
Let t be 99064/(-4636) + 23 + -1. Determine j so that 14/19*j**3 - 34/19*j**2 + 34/19*j - 2/19*j**4 - t = 0.
1, 2, 3
Let r(q) be the second derivative of -q**5/5 - 8*q**4/3 - 32*q**3/3 + q + 2. Factor r(g).
-4*g*(g + 4)**2
Find c, given that 32/11 - 32/11*c**2 - 24/11*c - 6/11*c**3 = 0.
-4, -2, 2/3
Solve 68*a**2 - 86/3*a**3 + 10/3*a**4 - 64/3 - 64/3*a = 0.
-2/5, 1, 4
Let o(a) = 3*a**2 + 567*a - 18. Let v(u) = u**2 + 140*u - 4. Let i(z) = 2*o(z) - 9*v(z). Solve i(l) = 0 for l.
-42, 0
Suppose -3*j = -4*j + 5. Suppose -6 - 3 = -3*z + 5*t, 0 = -2*z + j*t + 6. Factor -13 - 2 + 4*p**2 + p**3 - 16*p - 1 + z*p**3.
4*(p - 2)*(p + 1)*(p + 2)
Let n be (-3*104/12)/1. Let u(m) = -4*m**2 + 8*m - 1. Let y(c) = -17*c**2 + 33*c - 3. Let o(g) = n*u(g) + 6*y(g). Factor o(v).
2*(v - 4)*(v - 1)
Suppose 2*y + 21 = 65. Let g be 2/11 - 1*(-106)/y. Find z, given that -1/6*z**4 + 1/6*z**2 + 0*z - 1/6*z**3 + 1/6*z**g + 0 = 0.
-1, 0, 1
Let x(q) be the third derivative of -q**7/1260 + 11*q**6/180 - 161*q**5/120 - 11*q**4/36 + 121*q**3/9 + 598*q**2. Let x(o) = 0. What is o?
-1, 1, 22
Let c(y) be the first derivative of -y**4/20 - y**3/3 + 4*y**2/5 + 12*y/5 - 38. Factor c(l).
-(l - 2)*(l + 1)*(l + 6)/5
Let i(p) be the second derivative of p**6/240 + 11*p**5/160 + 11*p**4/32 + 37*p**3/48 + 7*p**2/8 + 325*p. Solve i(k) = 0 for k.
-7, -2, -1
What is j in 56*j**2 + 116 - 219 + 57 + j - j**3 - 10*j**2 = 0?
-1, 1, 46
Let f = -68 + 76. Find g such that 8 + 4*g**3 - f*g**2 - 3*g + g - 2*g**3 + 0*g = 0.
-1, 1, 4
Let y = 257/8 - -773/24. Let b = y - 64. Factor -2/3*k + b*k**2 + 0.
k*(k - 2)/3
Let j be 189/35*30/36. Factor -5/2*r**3 - 3*r**2 + j*r + 1.
-(r - 1)*(r + 2)*(5*r + 1)/2
Factor 2/7*w + 4/7*w**2 - 4/7 - 2/7*w**3.
-2*(w - 2)*(w - 1)*(w + 1)/7
Factor 2/3*c**4 + 0 + 6*c**3 + 40/3*c**2 + 8*c.
2*c*(c + 1)*(c + 2)*(c + 6)/3
Let h(r) be the first derivative of -r**5 + 25*r**4 + 110*r**3/3 - 50*r**2 - 105*r - 735. Let h(z) = 0. Calculate z.
-1, 1, 21
Let v(z) be the third derivative of 0 - 7*z**2 - 1/15*z**5 + 1/30*z**6 + 2/105*z**7 - 1/84*z**8 + 0*z + 0*z**4 + 0*z**3. Solve v(b) = 0 for b.
-1, 0, 1
Let y(n) be the first derivative of -n**6/9 + 4*n**5/75 + 3*n**4/5 - 32*n**3/45 - n**2/3 + 4*n/5 + 81. Determine o so that y(o) = 0.
-2, -3/5, 1
Suppose s = -4*c + 9 + 2, 0 = -4*s + 12. Suppose -21 = -5*k - b - b, c*b - 6 = 0. Suppose -24*l**2 + 10*l**2 - 2*l + 9 + 9*l**2 - l**k - l = 0. What is l?
-3, 1
Let o be 6/2*(-22)/(-33). Factor -14*y**o - 5*y**3 + 5*y - 10*y + 4*y**2.
-5*y*(y + 1)**2
Let s(d) be the first derivative of 2*d**3/51 - 42*d**2/17 - 86*d/17 - 208. Factor s(n).
2*(n - 43)*(n + 1)/17
Let c be (17 + (-1125)/66)/(4/(-22)). Find x, given that -4 - 9/4*x**2 - c*x**3 - 6*x = 0.
-4, -1
Let g(w) = -w**5 - 23*w**4 + 4*w**3 + 20*w**2 + 3. Let y(c) = c**5 + 24*c**4 - 5*c**3 - 20*c**2 - 4. Let o(p) = 4*g(p) + 3*y(p). Factor o(b).
-b**2*(b - 1)*(b + 1)*(b + 20)
Let l(d) be the first derivative of d**4/4 - 5*d**3/3 - 13*d**2/2 - 7*d - 228. Factor l(r).
(r - 7)*(r + 1)**2
Find x such that 2/3*x**3 + 0 + 0*x - 4/3*x**4 + 2*x**2 = 0.
-1, 0, 3/2
Let f be (-68)/(-32) - ((-10)/(-2) + (-351)/72). Suppose 1/5*n**5 - 2/5*n**4 + 0*n**f + 0*n + 1/5*n**3 + 0 = 0. What is n?
0, 1
Suppose -3*m + 2*m = 2*a - 6, 2*m + 7*a - 18 = 0. Solve -10/3*d + 25/3 + 1/3*d**m = 0.
5
Let j(f) be the first derivative of 3*f**4/10 + 3*f**3/5 - 3*f**2/2 - 18*f/5 - 88. Solve j(t) = 0.
-2, -1, 3/2
Let l(y) be the third derivative of -y**8/588 - 2*y**7/49 - 8*y**6/35 + 64*y**5/105 + 62*y**2 + 1. Factor l(k).
-4*k**2*(k - 1)*(k + 8)**2/7
Let z(y) = 2*y**3 + 9*y**2 + 6*y + 8. Let r be z(-4). Let l(m) be the first derivative of -1/4*m**2 + r*m - 1/6*m**3 + 6. Solve l(j) = 0.
-1, 0
Let n(j) be the first derivative of j**6/2 - 48*j**5/5 + 63*j**4/2 - 40*j**3 + 39*j**2/2 - 208. Factor n(p).
3*p*(p - 13)*(p - 1)**3
Suppose 58 + 98 = 4*d. Suppose -5*j + 4*p = -0*j - 130, -p = 2*j - d. Factor -213*r**2 + 11*r**5 - 2*r + 18*r**3 - 3*r**5 + j*r**4 + 215*r**2.
2*r*(r + 1)**3*(4*r - 1)
Let h(k) = 40*k - 20. Let t(d) = -2*d**2 + d. Let w(p) = -h(p) - 5*t(p). Let w(j) = 0. Calculate j.
1/2, 4
Let s(w) be the second derivative of -w**5/100 + w**4/12 + 13*w**3/30 + 7*w**2/10 + 47*w. Factor s(y).
-(y - 7)*(y + 1)**2/5
L