 Let o(r) = -6*a(r) - 5*w(r). Find n such that o(n) = 0.
21
Let y(x) be the third derivative of 169*x**7/525 - 13*x**6/100 - 7*x**5/10 - 5*x**4/12 + 66*x**2. Factor y(a).
2*a*(a - 1)*(13*a + 5)**2/5
Determine m, given that -111 + 221 - 25*m + 5*m**2 - 113 - 67 = 0.
-2, 7
Solve -13/3*v**2 + 55/3*v + 1/3*v**3 - 25 = 0.
3, 5
Let f = 40526/8445 + 2/1689. What is s in 0 + f*s**4 + 8/5*s**2 - 22/5*s**3 - 1/5*s - 9/5*s**5 = 0?
0, 1/3, 1
Let g(l) be the first derivative of 3*l**5/25 - 21*l**4/20 - 22. Factor g(n).
3*n**3*(n - 7)/5
Let n(c) = 2*c - 7*c - 2 + 2*c. Let s be n(-2). Factor -y**4 + 4*y**3 + y**s + 2*y**4 + 2*y**2.
2*y**2*(y + 1)**2
Let z = 93/16 + 431/80. Let g(q) be the first derivative of 8/3*q**6 + z*q**5 + q + 43/3*q**3 - 5 + 11/2*q**2 + 73/4*q**4. Determine j so that g(j) = 0.
-1, -1/4
Let l = 38 + -35. Factor 6*n**2 + 282*n**4 + 3*n**3 - 3 - 285*n**4 + l.
-3*n**2*(n - 2)*(n + 1)
Let w(a) be the first derivative of 4*a**3/21 - 10*a**2/7 + 24*a/7 + 73. What is h in w(h) = 0?
2, 3
Suppose 3*s + 4*v = 327, s - 5*v = -v + 93. Let c be ((-6)/s*-10)/(6/14). Factor 10/3*x**2 + 2/3*x**4 - 8/3*x**3 + 0 - c*x.
2*x*(x - 2)*(x - 1)**2/3
Let u = -558/65 + 122/13. Let d be (45/25)/(2/4). Determine a so that 0 + d*a**2 + u*a = 0.
-2/9, 0
Let r(m) = -3 - 12*m + 0 - 6*m**2 - 6*m. Let i(g) = -5*g**2 - 19*g - 2. Let x(d) = -3*i(d) + 4*r(d). What is s in x(s) = 0?
-1, -2/3
Let u = -3620 - -10865/3. Suppose 10/3*p**3 + 0*p + 5/3*p**2 + 0 + u*p**4 = 0. Calculate p.
-1, 0
Let g(n) be the third derivative of n**11/665280 + n**10/302400 - n**9/60480 + 7*n**5/30 - 28*n**2. Let i(f) be the third derivative of g(f). Factor i(r).
r**3*(r - 1)*(r + 2)/2
Suppose 147/4*a**2 - 9 - 111/4*a**4 + 9/8*a**5 + 33/2*a**3 - 141/8*a = 0. Calculate a.
-1, -1/3, 1, 24
Let q = -11 - -18. Factor q*s**2 + 4*s - 3*s**2 - 8*s**2.
-4*s*(s - 1)
Factor 20*f - 46*f**3 - 26*f**2 - 14 + 3*f + 23*f + 48*f**3 - 8.
2*(f - 11)*(f - 1)**2
Let j be 2 + -6 - (-1)/((-1)/(-11)). Suppose j*f = -3*f. Suppose -22/9*g**4 - 8/9*g**5 + 0 - 10/9*g**3 + f*g + 4/9*g**2 = 0. What is g?
-2, -1, 0, 1/4
Suppose 48 = 4*z - 0*h - 3*h, 5*z + h = 41. Let s be (-3 - -35)/(-3 + z). Factor s*l + 2/3*l**2 + 32/3.
2*(l + 4)**2/3
Let o be 76/(-8)*152/12. Let k = 121 + o. Let -k - 1/3*r**2 + r = 0. What is r?
1, 2
Let b(h) be the second derivative of -1/42*h**4 - 15*h + 0 + 3/7*h**2 + 2/21*h**3. Find a, given that b(a) = 0.
-1, 3
Solve -74/7*n**3 + 48/7*n**2 - 32/7 + 2*n**4 + 104/7*n = 0 for n.
-1, 2/7, 2, 4
Solve 3*z - 3*z - 17*z**3 - 16*z + 18 + z**3 + 2*z**4 - 32*z + 44*z**2 = 0.
1, 3
Let y(b) be the first derivative of 5*b**4/6 + 214*b**3/9 + 14*b**2 + 342. Factor y(r).
2*r*(r + 21)*(5*r + 2)/3
Let f(c) = 351*c - 9477. Let i be f(27). Suppose 8 = 4*w - 4. Factor -1/2 + 3/4*h + i*h**2 - 1/4*h**w.
-(h - 1)**2*(h + 2)/4
Let s = 15 - 8. What is w in 4*w**3 + 33*w**2 - 6*w - s*w**3 - 42*w**2 = 0?
-2, -1, 0
Let w = -190 + 210. Suppose -2*f = 8*f - w. Let 2/5*m + 2/5*m**f - 2/5 - 2/5*m**3 = 0. Calculate m.
-1, 1
Let x(b) be the second derivative of b**7/210 + 7*b**6/150 + b**5/50 - 7*b**4/15 - 4*b**3/5 + 87*b + 3. Suppose x(g) = 0. Calculate g.
-6, -2, -1, 0, 2
Let h(i) be the third derivative of 5*i**8/336 - i**7/14 + i**6/12 + i**5/6 - 5*i**4/8 + 5*i**3/6 - 36*i**2 + 3*i. Factor h(l).
5*(l - 1)**4*(l + 1)
Let g(a) be the second derivative of 0 + 0*a**5 + 1/21*a**4 - 1/70*a**6 + 0*a**2 + 0*a**3 - 4*a + 1/294*a**7. Factor g(d).
d**2*(d - 2)**2*(d + 1)/7
Let n(y) be the second derivative of y**7/70 + y**6/40 - y**5/10 + 9*y**2/2 + 16*y. Let w(j) be the first derivative of n(j). Suppose w(x) = 0. What is x?
-2, 0, 1
Let y be 24/(-20) + 0 + (-124)/(-20). Determine r, given that 0 + 0*r**2 + 12/13*r**4 - 2/13*r**y - 18/13*r**3 + 0*r = 0.
0, 3
Let f(i) = i - 1. Let w(h) = -h + 1. Let t(r) = -6*f(r) - 5*w(r). Let z(o) = -5*o**2 + 14*o - 9. Let s(n) = -4*t(n) - z(n). Factor s(u).
5*(u - 1)**2
Suppose 0 = 7*s - 4*s - x - 10, s + x = 10. Suppose -s*o + o = -8. Find n, given that 0*n + 21/2*n**4 + 0 - 8*n**3 + 2*n**o - 9/2*n**5 = 0.
0, 2/3, 1
Let u = 9 - 6. Factor 5*s**5 + 29*s + 45*s**u - 29*s + 20*s**2 + 30*s**4.
5*s**2*(s + 1)**2*(s + 4)
Let m(f) be the third derivative of -f**8/3360 - f**7/2520 - 13*f**4/24 + 3*f**2. Let n(v) be the second derivative of m(v). Factor n(d).
-d**2*(2*d + 1)
Factor -1 + 3/8*n**2 + 3/4*n - 1/8*n**3.
-(n - 4)*(n - 1)*(n + 2)/8
Suppose 0 = v + 4*g - 7, -6*v + 4*v - g = -7. Suppose 2*n = -3*n - 3*p + 13, -11 = -v*n - 5*p. Factor 5*z**2 - z**2 - z**n + 4*z + 2*z.
3*z*(z + 2)
Let x(l) be the third derivative of l**6/120 + l**5/4 + 3*l**4 + 18*l**3 - 11*l**2. Factor x(i).
(i + 3)*(i + 6)**2
Let y be -1 - 1238/(-8) - 5. Let p = y + -148. What is w in -p*w - 1/2 - 1/4*w**2 = 0?
-2, -1
Let q be 154/28*(0 + 32/44). Suppose 3/2*x**3 + 2*x**2 - 2*x - 2*x**q + 0 + 1/2*x**5 = 0. Calculate x.
-1, 0, 1, 2
Let o(j) = 3*j**2 + 5*j - 3. Let q(l) = -5*l**2 - 5*l + 4. Let x(z) = 6*o(z) + 5*q(z). Factor x(p).
-(p - 1)*(7*p + 2)
Let c(i) be the third derivative of i**6/300 + 7*i**5/150 + i**4/4 + 3*i**3/5 - 7*i**2. Factor c(s).
2*(s + 1)*(s + 3)**2/5
Let p(x) be the third derivative of 0*x**4 + 0*x**3 + 0*x - 5/336*x**8 - 1/24*x**6 + 0*x**5 + 19*x**2 + 0 + 1/21*x**7. Factor p(a).
-5*a**3*(a - 1)**2
Let x(l) = l**3 + l**2 + 2*l**2 + 3*l + 2*l**2. Let v be x(-4). Let 9*t - t**v + 7 - 34 + 39*t**3 + 69*t**2 + 5*t**4 + 2*t**4 = 0. What is t?
-3, -1, 1/2
Let r be (-12)/(-102) + 78087/1683. Let d = r - 139/3. Determine p, given that -d*p**2 + 0 - 6/11*p = 0.
-3, 0
Factor -536*o + 81*o + 9*o**2 - 4*o**2 + 35*o + 8820.
5*(o - 42)**2
Let c be (-30)/8*(-89)/445. Factor -3/2*q + c*q**2 + 3/4.
3*(q - 1)**2/4
Let z = 11 + -15. Let x(n) = 3*n**3 + 6*n**2 + 6*n - 3. Let k(f) = -3*f**3 - 5*f**2 - 6*f + 4. Let i(d) = z*x(d) - 3*k(d). Solve i(q) = 0 for q.
-2, -1, 0
Let x(w) be the first derivative of 0*w**5 - 15/4*w**4 + 0*w**2 + 0*w - 10/3*w**3 + 5/6*w**6 + 15. Determine k, given that x(k) = 0.
-1, 0, 2
Let s(q) = 2*q**3 + 2*q**2 + q. Let o(j) = -5*j**3 - 14*j**2 + 22*j. Let v(d) = -2*o(d) - 4*s(d). Suppose v(x) = 0. What is x?
-12, 0, 2
Let g = -2421 + 2424. Factor 0*d + d**2 + 0 - 1/3*d**g.
-d**2*(d - 3)/3
Let t(n) = n**3 - 10*n**2 + 5*n + 7. Let b(a) = -3*a**3 + 11*a**2 - 4*a - 8. Let c(w) = 3*b(w) + 4*t(w). Factor c(m).
-(m - 1)*(m + 2)*(5*m + 2)
Let o be (-2)/25 + 119/1400. Let b(m) be the third derivative of 0 - 7*m**2 + 0*m - 1/50*m**5 + 0*m**3 + o*m**6 + 1/350*m**7 + 0*m**4. Factor b(y).
3*y**2*(y - 1)*(y + 2)/5
Let u(i) = 2*i**3 + 116*i**2 - 112*i - 3. Let q be u(1). Let -9/7*d**q + 0 - 5/7*d**4 - 1/7*d**5 - d**2 - 2/7*d = 0. What is d?
-2, -1, 0
Suppose 2*r - 4*p = 34, 0 = 5*r + 6*p - p - 145. Let n = -22 + r. Factor 2*x**4 - x**4 + 47*x**n - 5*x**5 - 52*x**3 - 11*x**4.
-5*x**3*(x + 1)**2
Let t(s) = 2*s**2 - 13*s + 1. Let m(o) = o**2 - 6*o + 1. Suppose k - 2*k = -13. Suppose 2*y - k = 7. Let n(a) = y*m(a) - 4*t(a). Find l such that n(l) = 0.
1, 3
Suppose 4*t = 2*t + 4. Let a = -7/29 - -107/203. Factor -2/7 + a*u**t + 0*u.
2*(u - 1)*(u + 1)/7
Find n, given that -8/5*n + 0 + 1/5*n**2 = 0.
0, 8
Let u(m) be the third derivative of 1/1620*m**6 + 0*m**5 + 3*m**2 + 0*m - 1/108*m**4 - 1/2*m**3 + 0. Let x(l) be the first derivative of u(l). Factor x(d).
2*(d - 1)*(d + 1)/9
Let p(o) be the second derivative of -o**6/180 + o**5/20 + 7*o**4/72 - 78*o. Let p(m) = 0. What is m?
-1, 0, 7
Let t = -215/6 - -36. Suppose -d = -n + 5 - 1, -5*d = -4*n + 20. What is s in 1/6*s - 1/6*s**3 - t*s**2 + n + 1/6*s**4 = 0?
-1, 0, 1
Let l(o) be the second derivative of o**5/360 + o**4/12 + 11*o**3/36 - 15*o**2/2 - 41*o. Let d(c) be the first derivative of l(c). Factor d(k).
(k + 1)*(k + 11)/6
Let d(s) be the third derivative of s**6/420 - s**5/35 - 9*s**4/28 + 15*s**2 - 9*s. Factor d(b).
2*b*(b - 9)*(b + 3)/7
Suppose 4*a = 2*l - 30, -2*l = -a - a - 34. Find j such that j**2 + 0*j**2 - 8*j + 0*j**2 - l + 3*j**3 + 23 = 0.
-2, 2/3, 1
Solve -2/11*c**3 - 16/11*c**2 + 18/11*c + 0 = 0 for c.
-9, 0, 1
Find c such that 0 - 13/6*c**2 - 7/6*c - 35/6*c**4 + 17/2*c**3 + 2/3*c**5 = 0.
-1/4, 0, 1, 7
Let g(p) be the second derivative of 0 + 5/2*p**3 + 0*p**2 - 25/12*p**4 - 11/4*p**5 - 1/2*p**6 - 13*p. Solve g(y) = 0.
-3, -1, 0, 1/3
Let l(d) be the first derivative of -2 