given that 10*n - 18*n**2 + 5*n**2 - n**2 + 37 - 12 + 15*n**2 = 0.
-5
Let w(n) be the third derivative of n**7/2100 - n**6/150 + 11*n**5/600 + n**4/30 - n**3/5 + 459*n**2. What is z in w(z) = 0?
-1, 1, 2, 6
Let o(q) be the first derivative of 14*q**3/27 - 38*q**2/3 + 64*q/9 + 66. Solve o(m) = 0 for m.
2/7, 16
Let c(w) be the third derivative of -w**7/210 - w**6/15 - 7*w**5/20 - 3*w**4/4 + 8*w**2 - 5. Factor c(m).
-m*(m + 2)*(m + 3)**2
Let t(o) be the first derivative of 2*o**3/33 + 27*o**2/11 + 52*o/11 - 297. Factor t(b).
2*(b + 1)*(b + 26)/11
Let n = -967 + 971. Suppose 0 - 4/5*x**2 + 4/5*x**n - 4/5*x**5 + 4/5*x**3 + 0*x = 0. What is x?
-1, 0, 1
Let n(a) = a**3 - 22*a**2 + 25*a - 84. Let j be n(21). Let v(f) be the first derivative of 12*f**4 + 11*f**3 + j*f - 8 + 3*f**2 + 21/5*f**5. Solve v(u) = 0.
-1, -2/7, 0
Let g(k) = k**3 - 3*k**2 + 3*k - 3. Let a(j) = j - 1. Let d(c) = 6*a(c) - 2*g(c). Suppose d(z) = 0. What is z?
0, 3
Find d such that -d**2 - 12/5*d - 4/5 = 0.
-2, -2/5
Let u(i) = -15*i**2 + 42*i - 43. Let w(k) = -8*k**2 + 24*k - 22. Let f(v) = -6*u(v) + 11*w(v). Find p such that f(p) = 0.
-4, -2
Suppose 20 = 4*z - 3*g, 5*z + 8 = z - 4*g. Let h be -1*(-3 + z)*4. Factor b**2 + 4*b**4 + 6*b**3 - h*b**2 - 7*b**4.
-3*b**2*(b - 1)**2
Let l(g) be the third derivative of -g**7/490 + g**6/35 - 9*g**5/70 + 2*g**4/7 - 5*g**3/14 + 474*g**2. Let l(h) = 0. Calculate h.
1, 5
Let k(x) = -36 + 21 - 64 - x**2 + 18*x + 0*x**2. Let q(p) = -p**2 + 18*p - 78. Let c(r) = 3*k(r) - 2*q(r). Factor c(i).
-(i - 9)**2
Let o be 2*-1 - (-3 + -1). Suppose 3*j - 289 = -14*j. Find m such that 8*m - 9*m**2 + j*m**2 - 12*m**o = 0.
0, 2
Let y be 4/(1896/478) - 2/10. Let s = y - 2/237. Factor -4/5 - 1/5*b**2 - s*b.
-(b + 2)**2/5
Suppose 4*u**2 - 1706*u + 547*u + 564*u + 563*u + 48 = 0. Calculate u.
2, 6
Let j be (3 + (6 - 4))*-1. Let r(z) = z**2 + 5*z + 5. Let d be r(j). Factor -21*b**4 + 6*b**3 + 12*b**4 + 3*b**d - 9*b**5.
-3*b**3*(b + 2)*(2*b - 1)
Let 324*w**2 - 297*w**5 - 193*w**3 + 10*w**4 - 37*w**4 + 293*w**5 - 59*w**3 - 41*w**4 = 0. Calculate w.
-9, 0, 1
Let h(u) be the first derivative of -2*u**3/3 - 13*u**2 - 24*u + 235. Let h(w) = 0. Calculate w.
-12, -1
Let g(l) be the third derivative of -l**5/150 + 23*l**4/60 - 14*l**3/5 - 130*l**2 + l. Factor g(y).
-2*(y - 21)*(y - 2)/5
Let a be (-3)/12*2*-2. Let w be 8/1*a/4. Suppose -w*q + 2*q + 2 - q**2 + 2*q - 3 = 0. What is q?
1
Let 5*v**2 + 6971 - 1280*v + 14793 + 60156 = 0. Calculate v.
128
Let n = -3066 - -3068. Suppose -12/5 + 12/5*i - 3/5*i**n = 0. Calculate i.
2
Find k, given that 13 + 3*k**3 - 52*k**2 + 26 - 311*k + 58*k**2 - 45*k**2 + 308*k = 0.
-1, 1, 13
Let l(p) = p**3 - 2*p**2 - 10*p + 21. Let c be l(3). Let c*n + 1/8*n**2 + 0 = 0. Calculate n.
0
Let v(c) be the first derivative of 3*c**2 + 14 + 2/3*c**3 + 4*c. Suppose v(n) = 0. What is n?
-2, -1
Solve 3/4*t**3 - 21/2*t**2 + 3/8*t**4 + 69/4*t - 63/8 = 0 for t.
-7, 1, 3
Suppose -y + g - 181 = 0, -y - 5*g - 22 = 177. Let d = -184 - y. Factor 2/5*v**2 + d + 6/5*v.
2*v*(v + 3)/5
Let a be -2*(1335/135 - 10). Suppose 8/3 - a*d**2 + 16/9*d - 2/9*d**3 = 0. What is d?
-2, 3
Factor 42*z**2 - 65*z**2 + 18*z + 20*z**2.
-3*z*(z - 6)
Let b(j) = -3*j**3 + 23*j**2 + 51*j + 35. Let d(x) = -2*x**3 + 12*x**2 + 26*x + 18. Let f(l) = 6*b(l) - 10*d(l). Factor f(a).
2*(a + 1)*(a + 3)*(a + 5)
Let s(t) be the second derivative of -t**6/75 + 13*t**5/50 - t**4/3 - 8*t**3/5 + 503*t. Find k, given that s(k) = 0.
-1, 0, 2, 12
Suppose -3*p = 2*i + 56, -p + 5*p = -3*i - 75. Let k be (2256/p)/(2/(-6)). Factor 4*a**5 + 4*a + 376*a**4 - k*a**4 - 8*a**3.
4*a*(a - 1)**2*(a + 1)**2
Let c(p) = 4*p**5 - 6*p**4 + 18*p**3 + 22*p**2 + 6*p. Let m(v) = 2*v**4 - v**3 - v**5 + 2*v**2 - 3*v**2 - v**4. Let l(t) = -2*c(t) - 12*m(t). Factor l(s).
4*s*(s - 3)*(s + 1)**3
Let t(u) be the third derivative of u**5/36 - 5*u**4/72 - 10*u**3/3 - 11*u**2 + 5. Solve t(a) = 0 for a.
-3, 4
Let c(t) be the first derivative of 0*t + 20 - 5/18*t**3 + 1/24*t**4 + 1/3*t**2. Suppose c(i) = 0. What is i?
0, 1, 4
Let t(j) be the third derivative of -1/112*j**8 - j**6 + 0 - 4*j**5 - 1/7*j**7 + 0*j + 15*j**2 - 16*j**3 - 10*j**4. Suppose t(a) = 0. What is a?
-2
Let m(b) be the second derivative of b**6/120 - 53*b**5/20 + 5723*b**4/24 - 1855*b**3/2 + 11025*b**2/8 + 192*b. Factor m(q).
(q - 105)**2*(q - 1)**2/4
Solve -800*r**2 - 980 + 70*r + 795*r**2 + 70*r = 0 for r.
14
Let x(y) be the third derivative of -y**6/40 + y**5/8 - y**4/8 + 49*y**2 - 2*y. Factor x(r).
-3*r*(r - 2)*(2*r - 1)/2
Determine w so that 148/19*w - 90/19*w**2 + 96/19 - 4/19*w**3 = 0.
-24, -1/2, 2
Suppose r + 5*u = 0, 2*u = -4*r + 3*u. Let k be (-1)/(9/(-3)) + r. Factor 1/3*w**4 + w**2 - w**3 - k*w + 0.
w*(w - 1)**3/3
Solve 80/3*f + 32/3 + 24*f**2 + 4/3*f**4 + 28/3*f**3 = 0 for f.
-2, -1
Let s(y) = 3*y**2 + 6*y + 5. Let i be s(-1). Suppose -8/3*b**i + 2*b**3 - 8/3*b + 0 = 0. Calculate b.
-2/3, 0, 2
Let o(v) = 15*v**2 + 283*v + 19044. Let x(f) = 13*f**2 + 282*f + 19044. Let m(p) = -6*o(p) + 7*x(p). Find u, given that m(u) = 0.
-138
Let -3*s**3 - 35*s**2 + s - 21*s**2 + 107*s**2 - 49*s = 0. What is s?
0, 1, 16
Let r(m) be the second derivative of m**5/630 + m**4/252 - 2*m**3/63 - 2*m**2 - 15*m. Let s(c) be the first derivative of r(c). Let s(b) = 0. What is b?
-2, 1
Factor -8/17*g - 26/17*g**3 - 12/17*g**4 - 24/17*g**2 + 0 - 2/17*g**5.
-2*g*(g + 1)**2*(g + 2)**2/17
Let b(k) be the third derivative of 1/24*k**6 + 0*k + 0 - 5/168*k**8 + 5/3*k**3 + 5/42*k**7 - 15*k**2 - 7/12*k**5 + 5/24*k**4. Solve b(w) = 0.
-1, -1/2, 1, 2
Let f(w) = 2*w**2 - 4. Let y be f(2). Factor 3*u**5 - u**3 - 3*u**5 + u**2 - 4*u**2 + 3*u**y + u**5.
u**2*(u - 1)*(u + 1)*(u + 3)
Let w = 1006/21 + -142/3. Let c(i) be the first derivative of -w*i - 3/7*i**2 - 2/21*i**3 + 3. Factor c(o).
-2*(o + 1)*(o + 2)/7
Let j(u) be the third derivative of 0*u + 4/3*u**3 - 1/84*u**7 + 1/672*u**8 - 1/48*u**6 - 4*u**2 + 5/24*u**5 + 0 + 5/6*u**4. Factor j(d).
(d - 4)**2*(d + 1)**3/2
Suppose 3*v + 24 = 4*l, 2*l + 18 - 20 = -v. Suppose -1/6*s**4 - 2/3*s**l + 0 - 1/3*s - 5/6*s**2 = 0. Calculate s.
-2, -1, 0
Let o = 3/12406 - -18603/24812. Factor 0*r + 0*r**3 - o + 3/2*r**2 - 3/4*r**4.
-3*(r - 1)**2*(r + 1)**2/4
Suppose 3*j - 3 = -4*z, z - 3*j - 967 = -955. Factor 432/5*v + 1728/5 + 1/5*v**z + 36/5*v**2.
(v + 12)**3/5
Let 125 - 125 - 20*w - 8*w - 4*w**2 = 0. Calculate w.
-7, 0
Let c(b) be the second derivative of 5*b**4/12 + 35*b**3/3 - 667*b. Factor c(y).
5*y*(y + 14)
Let u(r) be the third derivative of -r**8/5880 - r**7/2940 + r**6/630 + 7*r**3/6 + 4*r**2. Let j(g) be the first derivative of u(g). Factor j(d).
-2*d**2*(d - 1)*(d + 2)/7
Let v(y) be the second derivative of 10*y**2 + 0 + 24*y + 4*y**3 + 1/3*y**4. Factor v(l).
4*(l + 1)*(l + 5)
Let z(k) = 2*k. Let q(p) = 5*p**2 - 10*p - 20. Let j(b) = q(b) + 5*z(b). Let j(w) = 0. What is w?
-2, 2
Let q = -13526 + 13529. Determine x so that 0 - 12/5*x**2 + 18/5*x - 2/5*x**5 - 16/5*x**q + 12/5*x**4 = 0.
-1, 0, 1, 3
Suppose 9 - 51 = -14*u. Factor 0*q + 4/5*q**2 + 2/5*q**5 + 8/5*q**4 + 2*q**u + 0.
2*q**2*(q + 1)**2*(q + 2)/5
Let w = 198 + -158. Suppose 0 = 38*r - w*r. Determine t, given that -1/2*t - 9/4*t**2 + r - 7/4*t**3 = 0.
-1, -2/7, 0
Suppose -558*h + 324 + 238 = -554. Factor -3/2*t**h - 1/2 - 3/2*t - 1/2*t**3.
-(t + 1)**3/2
Let -1401*z + 129 - 355*z - 262 - 307 - 220*z - 1522*z**2 + 14*z**3 = 0. What is z?
-1, -2/7, 110
Let m(q) be the first derivative of 3*q**3 - 169*q**2/2 - 38*q + 729. Factor m(f).
(f - 19)*(9*f + 2)
Let v be (270/(-50) - -5)/((-7)/15). Find a, given that 0 + v*a + 8/7*a**3 - 2*a**2 = 0.
0, 3/4, 1
Suppose 0 = -5*s + j - 33, 2*s + 6*j - 5*j = -9. Let f be 384/800*(-20)/s. Find l such that 18/5 + 2/5*l**4 - 4/5*l**2 - 24/5*l + f*l**3 = 0.
-3, 1
Let b(q) be the first derivative of -2*q**6/15 + q**5 - 3*q**4 + 14*q**3/3 - 4*q**2 + 31*q - 5. Let l(d) be the first derivative of b(d). Factor l(u).
-4*(u - 2)*(u - 1)**3
Let k be 26/65 - 4/10. Suppose k*o = -o - 4*q, o - 5*q - 9 = 0. Factor -12*n - 6 - 10 + 24*n + o*n**2.
4*(n - 1)*(n + 4)
Let o = -1767 - -1774. Let c(r) be the third derivative of 10*r**2 + 0*r**6 + 0*r + 0*r**4 + 0 - 1/1260*r**o + 0*r**3 + 1/360*r**5. Factor c(m).
-m**2*(m - 1)*(m + 1)/6
Suppose 0 + 1/6*d**5 + 25/6*d**3 + 5/3*d + 3/2*d**4