20. Suppose -k - t = s - 4, -4*s = -4. Factor -k*h**4 + 6*h**4 + 0*h**2 + 4*h**2 + 6*h**3 + 2*h**3.
4*h**2*(h + 1)**2
Let t(s) = -11*s**2 - 53*s - 17. Let j(v) = 39*v**2 + 186*v + 57. Let m(n) = -5*j(n) - 18*t(n). What is h in m(h) = 0?
-7, -1
Let r = 7969 - 7967. Factor -2*p**r - 19/2*p + 5/2.
-(p + 5)*(4*p - 1)/2
Let u(j) = -14*j**2 + 19*j - 27. Let k(i) = -32*i**2 + 39*i - 53. Let v(y) = 6*k(y) - 14*u(y). Suppose v(z) = 0. What is z?
3, 5
Let z be 3 - 2*(-2 - -1). Let b be (-2)/5 + 36/15. Let 6*h**3 - h - 4*h**z - b*h + h**5 = 0. What is h?
-1, 0, 1
Suppose -4*p - 7 = -7. Suppose 10 = 5*v - p*v. Solve -1/2*d**2 - 2*d - v = 0.
-2
Suppose 96*o - 8*o = 176. Factor 4/11*h + 0 - 2/11*h**o.
-2*h*(h - 2)/11
Let n(h) be the third derivative of h**6/360 - h**5/5 + 6*h**4 - 2*h**3 + 41*h**2. Let c(p) be the first derivative of n(p). Factor c(l).
(l - 12)**2
Let t = 19303 + -19299. Let 2/15*d**2 + 2/15*d**t + 4/15*d**3 + 0*d + 0 = 0. Calculate d.
-1, 0
Let j(p) = -11*p**3 - 61*p**2 + 26*p + 4. Let w(k) = -31*k**3 - 184*k**2 + 77*k + 11. Let l(f) = 11*j(f) - 4*w(f). Factor l(z).
z*(z + 22)*(3*z - 1)
Let g be (-3)/(4*9/24). Let z be (g - 0) + 20/10. Find k, given that 1/5*k + z + 0*k**2 - 1/5*k**3 = 0.
-1, 0, 1
Let b(q) be the first derivative of q**7/147 + q**6/105 - q**5/35 + 7*q - 2. Let g(i) be the first derivative of b(i). Suppose g(m) = 0. Calculate m.
-2, 0, 1
Suppose -2 = 11*k - 9*k. Let p be ((-8)/(-20))/(k/(-3 + 2)). Find c such that 0 + p*c**2 - 6/5*c = 0.
0, 3
Let g(d) be the third derivative of -2*d**7/105 - 3*d**6/5 - 32*d**5/15 - 66*d**2. Factor g(w).
-4*w**2*(w + 2)*(w + 16)
Let s(o) be the first derivative of 5*o**7/168 - o**6/6 + o**5/4 + 12*o + 12. Let k(m) be the first derivative of s(m). Factor k(q).
5*q**3*(q - 2)**2/4
Suppose 0*u**3 - 7*u**2 - 2*u**3 - 16 + 1286*u + 23*u**2 - 1284*u = 0. What is u?
-1, 1, 8
Let j be -9*3/9 - 49/(-11). Let v be ((-3)/33)/(20/(-560)). Find w such that 24/11*w + j - 30/11*w**3 - v*w**2 + 18/11*w**4 = 0.
-2/3, 1, 2
Let 167*g**3 - 136*g**3 + 50*g + 2*g**5 + 24*g**4 + 120*g**2 + 61*g**3 = 0. What is g?
-5, -1, 0
Let y = -24 + 30. Determine k so that -6*k**2 + 4*k - y + 7*k**2 + 4 - 3*k**2 = 0.
1
Let n(x) be the third derivative of -5*x**8/672 + x**7/84 + x**6/16 - 5*x**5/24 + 5*x**4/24 + 16*x**2. Factor n(u).
-5*u*(u - 1)**3*(u + 2)/2
Find h such that -5961 - h**3 + 2*h**3 + h**3 + 1061 - 144*h**2 + 0*h**3 + 2730*h = 0.
2, 35
Let l = -1/385 + 397/4620. Let q(b) be the first derivative of 0*b - 3 - l*b**2 + 1/18*b**3. Factor q(o).
o*(o - 1)/6
Let w be 2052/48 - (-3)/4*-1. Let f = w - 42. Let 0*g**2 + 3/5*g**3 + 0 + 0*g + f*g**4 - 3/5*g**5 = 0. Calculate g.
-1, 0, 1
Let r(x) be the third derivative of -x**6/180 + x**5/3 - 7*x**4 + 392*x**3/9 - 91*x**2. Suppose r(u) = 0. What is u?
2, 14
Factor -5/3*v**3 + 7/3*v**2 - 1 + 1/3*v.
-(v - 1)**2*(5*v + 3)/3
What is y in 3*y**4 + 53057*y**2 - 53102*y**2 - 35*y + 131*y - 6*y**3 - 48 = 0?
-4, 1, 4
What is g in -162/5*g**2 + 6/5*g**4 - 51/5*g**3 - 39/5*g + 66/5 = 0?
-2, -1, 1/2, 11
Determine n, given that 10*n**5 - 16 - 376/5*n + 68*n**4 - 332/5*n**2 + 398/5*n**3 = 0.
-5, -2, -2/5, 1
Determine c, given that 14*c + 37*c + 80 + c**3 + 19*c + 28*c**2 + c**3 + 18*c = 0.
-10, -2
Suppose -42 = -14*h - 532. Let b be (-4)/(20/h) - 2. Let 2/11*d**b + 2/11*d**4 + 0*d - 2/11*d**2 + 0 - 2/11*d**3 = 0. What is d?
-1, 0, 1
Let g = -91 - -112. Factor -339*m**2 - 121*m**3 - 48 + g*m**3 - 41*m**2 - 256*m.
-4*(m + 3)*(5*m + 2)**2
Let n(q) be the second derivative of 1/4*q**4 + 13*q + 3*q**2 + 0 - 3/2*q**3. Factor n(v).
3*(v - 2)*(v - 1)
Suppose -432 = -2*z - 424. Let t(n) be the first derivative of 8 - 8/3*n - 4*n**2 + 2*n**z + 22/9*n**3 - 14/15*n**5. Let t(u) = 0. What is u?
-1, -2/7, 1, 2
Let t(q) be the first derivative of -q**6/2 + 9*q**5/5 + 15*q**4/4 - 3*q**3 - 6*q**2 + 47. Let t(o) = 0. What is o?
-1, 0, 1, 4
Let i(u) be the second derivative of -u**5/120 + u**4/24 - u**2/3 - 69*u. Factor i(o).
-(o - 2)**2*(o + 1)/6
Let a be (12/(-16))/(165/(-40)). Factor 1/11 + 1/11*o**2 - a*o.
(o - 1)**2/11
Let s(q) be the first derivative of 4*q**3/3 + 10*q**2 + 24*q + 53. Suppose s(w) = 0. What is w?
-3, -2
Let f(t) = 25*t**2 + 376*t + 104. Let h(q) = -q**2 + 2*q + 1. Let a(v) = f(v) + 4*h(v). Factor a(l).
3*(l + 18)*(7*l + 2)
Let b(y) be the first derivative of 8*y**5/15 - 11*y**4/2 + 16*y**3 - 16*y**2/3 + 43. Factor b(h).
2*h*(h - 4)**2*(4*h - 1)/3
Let w(v) = -v**2 + 7*v + 3. Let i be w(7). Let a be (-2)/15 - (-22)/165 - -3. Factor -d**i + 32*d - 4*d**3 + 16 - 4*d**4 + d**a - 4*d**3 + 12*d**2.
-4*(d - 2)*(d + 1)**2*(d + 2)
Let p(u) = -16*u**3 + u**2 - u - 2. Let z be p(-1). Suppose -z*l**3 + 15*l**3 - 3*l**3 = 0. Calculate l.
0
Suppose -29*n = -28*n - 5. Factor 3*p**2 - 3*p**3 - 3*p**4 - 4*p**n + 0*p**4 + 7*p**5.
3*p**2*(p - 1)**2*(p + 1)
Let k(l) be the third derivative of l**5/140 + 19*l**4/14 + 722*l**3/7 - 87*l**2 - l. Factor k(r).
3*(r + 38)**2/7
Let w(m) = m**3 - 8*m**2 - 5*m - 9. Let y be w(9). Suppose 7 = -5*k + y. Find d such that 17*d**4 + 15*d**4 - 18*d**3 - 8*d**k + d - 9*d**5 + 2*d = 0.
-1/3, 0, 1
Let u(z) be the second derivative of -10*z**7/63 - 59*z**6/18 - 59*z**5/4 + 380*z**4/9 - 160*z**3/9 - 461*z. What is w in u(w) = 0?
-8, 0, 1/4, 1
Let w = -44 + 44. Let q(b) be the second derivative of -27/2*b**2 + w + 6*b - 1/4*b**4 - 3*b**3. What is j in q(j) = 0?
-3
Let n(h) be the third derivative of h**9/3024 + h**8/420 + h**7/210 + 7*h**3/6 + 19*h**2. Let q(v) be the first derivative of n(v). What is j in q(j) = 0?
-2, 0
Suppose 6*x - 4*x = 20. Suppose 3*d - x = 2. Factor -8*w**2 - 4*w**d - 2*w**3 - w + w - 10*w**3.
-4*w**2*(w + 1)*(w + 2)
Suppose -g = -1, 2*v = -2*v - 4*g + 244. Let s be v/35 + (-2)/(-7). Factor 0*x - 3*x - 8 + 2*x**s + 0*x**2 - 3*x.
2*(x - 4)*(x + 1)
Let v(t) be the third derivative of -t**6/20 - 29*t**5/30 + 5*t**4/6 + 26*t**2 + 7. Find f, given that v(f) = 0.
-10, 0, 1/3
Factor -32*j**3 + 4*j + 2/7 + 66/7*j**2 + 128/7*j**4.
2*(j - 1)**2*(8*j + 1)**2/7
Let o be 3*(1 + (-110)/132). What is m in -1/2 + 5/4*m - 5/4*m**3 + o*m**2 = 0?
-1, 2/5, 1
Let c = -9238 - -9241. Solve c - 15/4*o**3 - 39/4*o**2 - 3*o = 0.
-2, -1, 2/5
Let g be (6 + 2)*(-5)/(-10). Determine s so that -3/5*s**3 + 3/5*s**g + 3/5*s + 0 - 3/5*s**2 = 0.
-1, 0, 1
Factor 4/3*m**3 - 4/3 + 19/3*m**2 + 11/3*m.
(m + 1)*(m + 4)*(4*m - 1)/3
Factor -56 - 26*u**2 + 4*u**3 + 36*u**2 + 5*u - 24*u**3 + 2*u**4 + 32*u**2 + 3*u.
2*(u - 7)*(u - 2)**2*(u + 1)
Suppose 5*v = -13*p + 14*p + 4, -16 = 5*v + 4*p. Let w(y) be the first derivative of v*y**2 + 6/5*y**5 + 0*y - 3/4*y**4 + 4 - 1/2*y**6 + 0*y**3. Factor w(f).
-3*f**3*(f - 1)**2
Suppose 3 = -r, -6*r + r = -5*z + 35. Suppose 36 = -0*l + 4*l + z*k, 5 = k. Factor 0*g + 1/2*g**5 + g**2 - 1/2*g**3 + 0 - g**l.
g**2*(g - 2)*(g - 1)*(g + 1)/2
Let g be (0 - -1 - 2) + 1482/(-2565). Let w = g - -9/5. Determine b so that 2/9*b + 4/9 - w*b**2 = 0.
-1, 2
Let p be (-18)/(-10) + ((-21)/49)/((-15)/7). Let 0*u - 5/4*u**p + 5/4*u**3 + 0 = 0. Calculate u.
0, 1
Let m(d) be the first derivative of 10*d**5 + 55*d**4/4 - 23*d**3/3 - 52*d**2/5 + 36*d/5 - 249. Find n, given that m(n) = 0.
-1, -9/10, 2/5
Let r = 7/418 - -383/2090. Factor -2/5*b**3 + 2/5*b + 0 + r*b**4 - 1/5*b**2.
b*(b - 2)*(b - 1)*(b + 1)/5
Let b(n) be the third derivative of 0 + 0*n**6 + 0*n + 0*n**3 - 16*n**2 + 0*n**5 + 0*n**4 - 1/735*n**7. Suppose b(g) = 0. Calculate g.
0
Let p = 25924/13 - 1994. Factor -2/13*c**2 + 4/13 - p*c.
-2*(c - 1)*(c + 2)/13
Let z(v) be the first derivative of -v**4/14 + 32*v**3/21 + 17*v**2/7 - 198. Determine o, given that z(o) = 0.
-1, 0, 17
Let p = 7715 - 30851/4. Let 3*h - p*h**2 - 3*h**3 + 3 - 3/4*h**4 = 0. Calculate h.
-2, -1, 1
Let k(d) be the first derivative of -5*d**6/6 + 5*d**5 + 155*d**4/4 + 215*d**3/3 + 45*d**2 - 582. Determine r, given that k(r) = 0.
-2, -1, 0, 9
Let c(u) = -u**4 - u**3 + 5*u**2 + 2*u. Let r(h) = 8*h**4 + 144*h**3 + 2418*h**2 + 2300*h. Let s(b) = 12*c(b) + 2*r(b). Factor s(l).
4*l*(l + 1)*(l + 34)**2
Let y(x) = -x**2 + 5*x + 39. Let b be y(11). Let j be b/(-3) + 42/(-7). Find r such that 0 + 6/5*r + 12/5*r**3 + 3/5*r**4 + j*r**2 = 0.
-2, -1, 0
Let x(k) be the third derivative of k**6/40 + 53*k**5/20 + 4*k**2 - 14*k. Solve x(f) = 0 for f.
-53, 0
Let y be (-9