27. Let h(b) be the first derivative of 6 + k*b**2 + 0*b + 0*b**3 + 1/15*b**5 - 1/12*b**4. What is x in h(x) = 0?
0, 1
Factor -31*p**2 + p**3 - 23*p**2 - 11*p + 6 - 25*p**2 + 83*p**2.
(p - 1)**2*(p + 6)
Let d(z) be the second derivative of -z**6/3060 - z**5/1020 + z**4/102 - 17*z**3/6 + 10*z. Let a(v) be the second derivative of d(v). Factor a(u).
-2*(u - 1)*(u + 2)/17
Let p be (5/10)/((-1)/(-114)*1). Let j = 59 - p. Find y such that 0*y**j + 0*y + 0*y**4 - 2/7*y**3 + 2/7*y**5 + 0 = 0.
-1, 0, 1
Let x = 38 + -35. Solve 5*n**3 - 25*n**x - 48*n - 28*n**2 - 7*n**3 - 44*n**2 = 0 for n.
-4/3, 0
Let n = 5293/1452 - -38/363. Find u, given that 3/4*u**2 - n + 3*u = 0.
-5, 1
Let b = 2/207 + 611/1035. Suppose 85*v - 70 = 50*v. Factor 0*u - b*u**v + 0.
-3*u**2/5
Suppose p = -4*p + 25. Suppose -3*t = 4*m - 9 - 35, 3*m - 4 = p*t. Find z such that 92*z**2 - 20*z**2 + 218*z**3 + 98*z**5 + m*z + 0 + 0 + 252*z**4 = 0.
-1, -2/7, 0
Let i be 96/7*66/99. Let -i*a + 16/7 + 4*a**2 = 0. Calculate a.
2/7, 2
Let k(v) be the first derivative of -v**5/30 + v**4/4 - 2*v**3/3 - 3*v**2/2 - 15. Let g(d) be the second derivative of k(d). Factor g(b).
-2*(b - 2)*(b - 1)
Let y(k) be the third derivative of 0*k + 1/102*k**4 - 1/510*k**6 + 1/51*k**3 + 0*k**5 - 16*k**2 - 1/1785*k**7 + 0. Factor y(w).
-2*(w - 1)*(w + 1)**3/17
Let o(q) = 124 - 61 - 100*q - 56*q**3 - 51 - 66*q**2. Let i(p) = -5*p**3 - 6*p**2 - 9*p + 1. Let v(x) = 68*i(x) - 6*o(x). Factor v(j).
-4*(j + 1)**3
Suppose 5*t = 4*x - 1280, -1272 = -6*x + 2*x + 3*t. Determine v, given that -311*v**2 + 0 - 8 - 4*v + x*v**2 = 0.
-1, 2
Let y(c) be the first derivative of 2/7*c**3 + 1/14*c**4 + 51 + 0*c + 0*c**2. Factor y(g).
2*g**2*(g + 3)/7
Let v = 2160/1841 - 8/263. Factor -4/7*o**2 - v - 12/7*o.
-4*(o + 1)*(o + 2)/7
Suppose 3*l + 5*j = -10, -l - 3*j + 0 = 6. Factor l*h - 30 + 3*h - 2 + 13*h - 2*h**2.
-2*(h - 4)**2
Let j(y) = y**2. Let i be j(2). Suppose -2*g - 2*b = -5*g + 13, -i*b - 11 = -g. Factor t**5 + 2*t + t**2 - g*t**3 - t**4 + 5*t**3 - 2*t**3 - 3*t**3.
t*(t - 2)*(t - 1)*(t + 1)**2
Let o(s) = -2*s**2 - 8*s + 3. Let v be 0 + -4 + 4 + -4. Let r be o(v). Solve -39*z**r + 3 + 7 + 44*z**3 + 20*z**2 + 25*z = 0.
-2, -1
Let o(j) = -4*j**2 - 4*j. Let c(h) = -90*h**2 - 40*h - 288. Let t(a) = 2*c(a) - 44*o(a). Let t(y) = 0. What is y?
12
Let k(t) be the first derivative of -7*t**6/180 - t**5/5 + t**4/3 + 2*t**3 + 10. Let f(y) be the third derivative of k(y). Factor f(h).
-2*(h + 2)*(7*h - 2)
Let o = 971/319 + -25/29. Factor 14/11*x**2 + o*x - 8/11.
2*(x + 2)*(7*x - 2)/11
Let q = -21 - -25. What is x in -x**q - 3*x - 14*x**3 + 0*x**2 - 7*x**2 + 9*x**3 = 0?
-3, -1, 0
Let c = -1691 + 1696. Let f(t) be the first derivative of c - 7/9*t**4 + 4/9*t + 5/27*t**6 + 4/15*t**5 - 16/27*t**3 + t**2. Solve f(p) = 0.
-2, -1, -1/5, 1
Suppose 3*a + 3*b = -6, 5*a + 3*b + 9 - 1 = 0. Let p be 0/((-3 - a)/(-2)). Let 2/3*f**5 + 0 + p*f + 2/3*f**2 - 2/3*f**4 - 2/3*f**3 = 0. What is f?
-1, 0, 1
Let z be (-22)/11*(-10)/4. Suppose 27*c**2 - z*c**4 + c**4 + 7*c**4 + 10*c**3 - 28*c**3 = 0. What is c?
0, 3
Let t be (-103)/3*(14 - 11). Let o = t + 105. Let 0*h**o - 1/2*h**3 + 0 + 0*h = 0. Calculate h.
0
Let n(m) be the third derivative of -m**7/5880 - m**6/420 + m**5/56 - m**4/21 + 13*m**3/6 + 15*m**2. Let u(b) be the first derivative of n(b). Factor u(c).
-(c - 1)**2*(c + 8)/7
Let u be (-3)/(-6)*2/(-1). Let i be u/(-3) + 48/18. Let 3*z**4 - 2*z**3 - 2*z**i + 3*z**4 = 0. What is z?
0, 2/3
Let c be ((-2)/27)/(4/(-9)). Let p(u) be the second derivative of -1/24*u**4 + c*u**3 + 0 + 3*u + 0*u**2. Factor p(w).
-w*(w - 2)/2
Let d be (-6)/7 - (-266)/133. Factor -20/7*a**2 - 16/7*a**3 + 0 - 4/7*a**4 - d*a.
-4*a*(a + 1)**2*(a + 2)/7
Let m be 9 - -9*12/(-72). Factor -75/4*i**2 + m*i - 3/4.
-3*(5*i - 1)**2/4
Let t be (32/6)/(58/2871). Let j = t + -262. Factor -1/2*h**2 + 0*h + j.
-(h - 2)*(h + 2)/2
Suppose -12*h = -17*h - 160. Let x(z) = -20*z**3 + 136*z**2 - 32*z. Let g(b) = 3*b**3 - 21*b**2 + 5*b. Let u(k) = h*g(k) - 5*x(k). Find v, given that u(v) = 0.
0, 2
Factor -243*o - 18*o**5 - 108*o**2 + 42*o**5 - 78*o**4 + 35 + 127 + 210*o**3 - 15*o**5.
3*(o - 3)**3*(o + 1)*(3*o - 2)
Let n(i) = -6*i**3 - 96*i**2 - 1524*i - 8188. Let f(u) = 5*u**3 + 96*u**2 + 1527*u + 8189. Let k(a) = 4*f(a) + 3*n(a). Solve k(o) = 0.
-16
Find w, given that -1/6*w**4 + 1/6*w**2 + 0 - 5/2*w + 5/2*w**3 = 0.
-1, 0, 1, 15
Let z(y) = 20*y**3 - 31*y. Let o = 1 - -1. Let s(m) = 12*m - 73. Let i be s(7). Let c(g) = -4*g**3 + 6*g. Let l(r) = i*c(r) + o*z(r). Factor l(u).
-4*u*(u - 1)*(u + 1)
Let i(f) = f**2 + 7*f + 10. Let z be i(-6). What is u in z*u**3 - 17*u**4 + 9*u**4 + 13*u**4 + u**5 = 0?
-4, -1, 0
Let u(m) = -9*m**2 + 72*m - 319. Let q(j) = 8*j**2 - 72*j + 320. Suppose -16*s + 15 = -13*s. Let k(d) = s*q(d) + 4*u(d). Factor k(b).
4*(b - 9)**2
Factor -3/4*u**3 - 249/4*u - 81/2 - 45/2*u**2.
-3*(u + 1)*(u + 2)*(u + 27)/4
Suppose 2*a = -2*g + 12, g + 1 + 1 = a. Find d, given that -4*d**3 + a*d**5 + 0*d**3 + 4*d**2 - 4*d**4 + 0*d**5 = 0.
-1, 0, 1
Let i = -923179/52 - -17754. Let t = i - 4/13. Suppose 0 + 0*m - t*m**3 + 1/2*m**2 - 1/4*m**4 = 0. What is m?
-2, 0, 1
Suppose 1225/2 + 481/4*h**3 + 7/4*h**4 + 7947/4*h**2 - 10885/4*h = 0. Calculate h.
-35, 2/7, 1
Let l(t) = -11*t**2 + 37*t - 31. Let i(k) = -16*k**2 + 56*k - 47. Let q(g) = 5*i(g) - 7*l(g). Factor q(x).
-3*(x - 6)*(x - 1)
Solve -3/2*m - 3/4*m**2 + 6 = 0.
-4, 2
Let t = -69838/3 - -23280. Factor 2/3*h**3 - 2/3*h - 2/3*h**2 + t.
2*(h - 1)**2*(h + 1)/3
Find l, given that -30*l**3 + 7*l + 88*l + 126*l**2 - 150 + 95*l**2 - 6*l**2 = 0.
-1, 2/3, 15/2
Let p be (2 + (-21)/9)/(-28). Let i(j) be the third derivative of 0*j**3 + 0*j**4 - 1/35*j**7 + p*j**8 + 7*j**2 + 1/60*j**6 + 0*j + 0*j**5 + 0. Factor i(c).
2*c**3*(c - 1)*(2*c - 1)
Let g = -3802 - -3805. Solve 1/2*a**2 + 9/2 + g*a = 0 for a.
-3
Suppose g + h = -4*h + 10, -g + 2 = -3*h. Determine x so that 0*x + 0 - 2/7*x**g + 0*x**4 + 2/7*x**3 + 0*x**2 = 0.
-1, 0, 1
Suppose -5*t = 5, -11*t + 20*t + 7 = -y. Suppose -4/17 - 2/17*n**3 + 2/17*n**4 - 6/17*n**y + 10/17*n = 0. What is n?
-2, 1
Let a be 99/(-60) + 55/33. Let u(t) be the third derivative of 0*t + 1/8*t**4 - 1/3*t**3 - a*t**5 + 3*t**2 + 0. What is o in u(o) = 0?
1, 2
Let z(f) = -f + 14. Let y be z(-9). Solve 22*d + 5*d**3 + y*d - 50*d = 0 for d.
-1, 0, 1
Let s(v) be the second derivative of 23*v - 5/12*v**4 - 1/4*v**5 + 5/6*v**3 + 0 + 5/2*v**2. Factor s(c).
-5*(c - 1)*(c + 1)**2
Let t be (0/2)/(-12 - -11). Suppose -3*f + 5*k + 10 = 0, t*f + k + 2 = -4*f. Suppose f - 2/5*m**2 + 0*m + 2/5*m**3 = 0. Calculate m.
0, 1
Determine o, given that 1/2*o**5 + 14*o**2 - 31/2*o**3 + 0*o + o**4 + 0 = 0.
-7, 0, 1, 4
Suppose -19*v + 50 = -83. Let b(y) be the first derivative of 0*y + 7 + 9/2*y**2 + 3/5*y**5 + v*y**3 + 15/4*y**4. Factor b(u).
3*u*(u + 1)**2*(u + 3)
Let x(j) be the first derivative of -2*j**3/9 + 7*j**2/3 + 12*j - 86. Factor x(k).
-2*(k - 9)*(k + 2)/3
Factor -3*s**3 - 5*s**3 - 2*s**3 - 72*s**2 - 648*s + 8*s**3.
-2*s*(s + 18)**2
Determine q so that -531*q**3 + 266*q**3 + 24*q**2 + 263*q**3 - 512 = 0.
-4, 8
Let x = 307/65 - 51/13. Let f(z) be the first derivative of -8/15*z**3 - z**2 - 1/10*z**4 - x*z - 5. Factor f(l).
-2*(l + 1)**2*(l + 2)/5
Solve 45 - 57/4*g + 3/4*g**2 = 0 for g.
4, 15
Let n(v) be the first derivative of -v**4/4 - 2*v**3/3 - v**2/2 + 6*v - 9. Let f(y) be the first derivative of n(y). Find o such that f(o) = 0.
-1, -1/3
Let i be (-1078)/(-231)*(-20)/(-7). Let b(g) be the first derivative of i*g**3 - 1 - 32*g + 3*g**4 + 8*g**2. Find v, given that b(v) = 0.
-2, 2/3
Let r be (17*(-13)/(-442))/((-6)/(-8)). Determine d, given that -2/9*d**2 + 14/9*d + r*d**4 - 4/9 - 14/9*d**3 = 0.
-1, 1/3, 1, 2
Let w(u) be the second derivative of -u**4/8 - 47*u**3/4 + 31*u + 4. Factor w(n).
-3*n*(n + 47)/2
Let l(b) = -b**2 - 5*b - 4. Let x be l(-4). Suppose 12 = -52*r + 54*r. Let 4*p**5 + 3*p + x - 5*p - 2*p**3 + 0 + r*p**4 - 6*p**2 = 0. What is p?
-1, -1/2, 0, 1
Let h(f) be the third derivative of f**5/30 + 2*f**4/3 + 16*f**3/3 + 5*f**2 + 20*f. Factor h(x).
2*(x + 4)**2
Let y(r) be the third derivative of r**6/660 - 5*r**5/66 + 2*r**4/3 - 28*r**3/11 - 4*r**2 - 13*r. Factor y(s).
2*(s - 21)*(s - 2)**2/11
Determine a, given that 3/5*a**2 - 3/5 + 4/5*a