51/3. Factor -v*a**2 + 4/3*a + 0.
-2*a*(a - 2)/3
Suppose -2*t - 28*g = -33*g, 0 = -t + 11*g. Solve 0 + t*y**2 + 3/7*y**3 + 0*y = 0 for y.
0
Let q(b) be the first derivative of -b**6/24 + 17*b**5/20 - 31*b**4/16 + 5*b**3/4 + 10. Factor q(l).
-l**2*(l - 15)*(l - 1)**2/4
Let q(z) be the third derivative of z**6/8 - 5*z**5/12 - 5*z**4/4 + 20*z**3/3 - 3*z**2 - 7. Factor q(j).
5*(j - 2)*(j - 1)*(3*j + 4)
Let t be 16/3 - 5 - -2*(-2)/(-4). Let 5/3*l**2 + 1/3 - 2/3*l**3 - t*l = 0. Calculate l.
1/2, 1
Let x be 24*(11/(-4) + 2). Let n = 23 + x. Find i, given that -1 - 11*i + 7*i**2 + 5 - n*i = 0.
2/7, 2
Solve -4*y**4 - 41562 - 24*y + 41562 - 44*y**2 - 24*y**3 = 0 for y.
-3, -2, -1, 0
Let m be 4573/2152 + 1*1/(-8). Let j(r) = -r**2 - 4*r. Let i be j(-3). Suppose -h + 1/2*h**m + 1/2*h**i + 0 = 0. Calculate h.
-2, 0, 1
Suppose -6*u**3 + 900*u**2 - 31*u**3 - 250 - 9*u**3 - 615*u + 11*u**3 = 0. Calculate u.
-2/7, 1, 25
Let h(b) be the third derivative of -16/1365*b**7 - 2/39*b**4 + 0 + 2/195*b**6 - 8*b**2 + 1/26*b**5 + 1/39*b**3 + 0*b. Suppose h(m) = 0. Calculate m.
-1, 1/4, 1
Let g(u) be the third derivative of u**9/15120 + u**8/6720 - 7*u**4/8 + 22*u**2. Let i(n) be the second derivative of g(n). Factor i(k).
k**3*(k + 1)
Factor 2*x**3 - 1400 + 271*x**2 - 532*x**2 - 80*x + 287*x**2.
2*(x - 7)*(x + 10)**2
Suppose -1/4*l**3 + 33/4*l - 17/4 - 15/4*l**2 = 0. Calculate l.
-17, 1
Let c(i) be the third derivative of 0 - 35/24*i**4 + 5/6*i**3 - 5*i**2 + 5/12*i**5 + 0*i + 7/24*i**6 - 1/7*i**7. Find k, given that c(k) = 0.
-1, 1/6, 1
Let m(k) be the third derivative of -16*k**2 + 8/15*k**5 - 11/12*k**4 + 2/3*k**3 + 0 - 7/60*k**6 + 0*k. Solve m(g) = 0.
2/7, 1
Let b = 1187 - 1183. Factor m + 7/2*m**b - m**3 - 7/2*m**2 + 0.
m*(m - 1)*(m + 1)*(7*m - 2)/2
Let s = 519/25 - 913/50. Let 1 + 9/2*w**2 + 7/2*w + s*w**3 + 1/2*w**4 = 0. What is w?
-2, -1
Let w(d) be the third derivative of 8/45*d**5 - 9*d**2 - 8/9*d**4 - 1/63*d**7 + 1/504*d**8 + 1/45*d**6 + 0 + 0*d + 16/9*d**3. Factor w(n).
2*(n - 2)**3*(n - 1)*(n + 2)/3
Let w(y) be the third derivative of -5*y**8/4032 - y**7/84 - y**6/36 - 2*y**5/3 - y**2. Let u(q) be the third derivative of w(q). Factor u(b).
-5*(b + 2)*(5*b + 2)
Factor -4*q**2 + 3*q + q**5 - 4*q**4 - q**5 + q - 6*q**3 - q**5 - 5*q.
-q*(q + 1)**4
Let v(i) be the first derivative of 1/2*i**2 - 1/4*i + 9 - 1/3*i**3. Factor v(o).
-(2*o - 1)**2/4
Let j(k) be the first derivative of -k**4 + 24*k**3 - 192*k**2 + 512*k - 67. Factor j(u).
-4*(u - 8)**2*(u - 2)
Suppose -l**2 - 8/5*l - 1/5*l**3 - 4/5 = 0. What is l?
-2, -1
Let l be (-4 + 5)/(0 - 1). Let q be -12*(l/4 + 0). Factor -9*p**q - p + p + 0*p + 6*p**2 - 6*p**4.
-3*p**2*(p + 2)*(2*p - 1)
Determine s, given that 10/21*s**2 + 2/21*s**3 + 4/7*s + 0 = 0.
-3, -2, 0
Factor 299*g + 20*g**2 + 4*g**2 - 144*g - 4*g**3 - 47*g.
-4*g*(g - 9)*(g + 3)
Let q(v) be the second derivative of -v**4/60 - 23*v**3/15 - 529*v**2/10 + 170*v. Factor q(s).
-(s + 23)**2/5
Let t(a) be the third derivative of -1/32*a**6 - 3/4*a**3 + 3/20*a**5 - 23*a**2 + 0 + 11/32*a**4 + 0*a. Factor t(z).
-3*(z - 3)*(z + 1)*(5*z - 2)/4
Let r(f) be the third derivative of 10*f**2 + 0*f**4 + 0*f**5 + 0*f + 1/72*f**6 + 0 + 2/63*f**7 + 0*f**3. Determine c so that r(c) = 0.
-1/4, 0
Suppose 0 = -5*b + 3*j + 25, 3*b - 3*j = -j + 16. Suppose 74*k = 104*k - 60. Determine d, given that -b*d + 2/3 - 2/3*d**3 + k*d**2 = 0.
1
Let l(n) = n**2 - 1. Let q(x) = 121*x - 121*x + 7 - 7*x**2. Let w(a) = 6*l(a) + q(a). Factor w(p).
-(p - 1)*(p + 1)
Find d, given that 2/3*d**4 - 7/3*d**3 + 5/6*d + 0 - 2/3*d**2 + 3/2*d**5 = 0.
-1, 0, 5/9, 1
Let w be (-9)/21 - (8 - (-125)/(-14)). Let 0 + w*h**3 + h**2 - 3/4*h - h**4 + 1/4*h**5 = 0. What is h?
-1, 0, 1, 3
Let a(n) = 20*n**4 + 5*n**3 + 925*n**2 - 25*n - 50. Let j(c) = -3*c**4 - c**3 - 154*c**2 + 4*c + 8. Let x(u) = -4*a(u) - 25*j(u). Factor x(v).
-5*v**2*(v - 6)*(v + 5)
Let m(v) = -v - 1. Let s(b) = -10 - 2*b**2 + b**2 - 5*b - 3*b**2 + 3*b**2. Let y(x) = -24*m(x) + 3*s(x). Factor y(l).
-3*(l - 2)*(l - 1)
Let l(s) = 13*s - 74. Let f be l(6). Let k(w) be the first derivative of 0*w + f - 3/2*w**2 + w**3 + 3/4*w**4 - 3/5*w**5. Factor k(q).
-3*q*(q - 1)**2*(q + 1)
Let c = -2467 + 2469. Find k, given that 0*k - 8/5 + 2/5*k**c = 0.
-2, 2
Let a be (-7 - (-405)/55)*121/66. Let r - 1/3*r**3 + 0 + a*r**2 = 0. Calculate r.
-1, 0, 3
Suppose 2*z = -438 + 436. Let b be (z + 1)*(1 + 0) - 0. Suppose b*q**3 - 2/3*q**2 + 2/9*q**4 + 4/9*q + 0 = 0. What is q?
-2, 0, 1
Let g be ((-54)/42 + -1)*(5/(-4))/5. Let -g*z**4 + 4/7*z**2 - 4/7*z**5 + 0*z + 0 + 4/7*z**3 = 0. What is z?
-1, 0, 1
Suppose 58*j + 11 - 98 = 29. Factor 12/7*l + 2/7*l**j + 10/7.
2*(l + 1)*(l + 5)/7
Let x be (-496)/372*(28/16 + -3 + 1). Factor x*n + 0 - 1/3*n**2.
-n*(n - 1)/3
What is z in -3*z**5 - 10*z**3 + 35*z + 18*z**4 + 6*z**3 - 29*z**3 + 1 - 25 + z + 6*z**2 = 0?
-1, 1, 2
Let v(s) be the first derivative of s**5/60 - 5*s**4/12 + 25*s**3/6 + 13*s**2 - 4. Let i(u) be the second derivative of v(u). Determine f so that i(f) = 0.
5
Let i be 8/18*27/6. Determine s, given that 68*s - 20 - s - 5*s**i - 42*s = 0.
1, 4
Let v = -80/3 + 27. Let j(s) be the third derivative of 1/15*s**5 + 0*s + 2/3*s**3 - v*s**4 + 0 + s**2. Suppose j(p) = 0. What is p?
1
Factor -5*c**3 - 30*c - 15*c**3 - 6*c - 8*c**2 + 80*c**2.
-4*c*(c - 3)*(5*c - 3)
Let y(k) = 3*k**3 - 4*k**2 - 6*k + 7. Let g(f) = f**3 - 2*f**2 - 2*f + 3. Let w(b) = -14*g(b) + 6*y(b). Let w(r) = 0. Calculate r.
-2, 0, 1
Determine h, given that -9/2*h**4 - 1/6*h**5 + 151/6*h**3 + 37*h - 32/3 - 281/6*h**2 = 0.
-32, 1, 2
Let i be (-3)/(75/(-10))*5*2. Factor i*g - 51*g**3 + 27*g**3 + 23*g**3 - 3*g**2.
-g*(g - 1)*(g + 4)
Factor f + 4*f - 3*f + f**2 + f + 2*f**2.
3*f*(f + 1)
Let w(r) = r + 14. Let c be w(-11). Factor 19*b - 3*b**c - 8 - 15*b + 2*b**5 - 2*b**2 + 2*b**4 + 12*b - 7*b**3.
2*(b - 1)**3*(b + 2)**2
Let p(j) be the second derivative of 5/4*j**4 - 5/24*j**7 + 0 + 0*j**2 + 11/16*j**5 - 5/6*j**3 + 17*j - 1/2*j**6. Let p(x) = 0. What is x?
-2, -1, 0, 2/7, 1
Let i(o) = 26*o**2 + 352*o - 114. Let n(w) = w**3 - 26*w**2 - 352*w + 115. Let y(q) = 5*i(q) + 6*n(q). What is r in y(r) = 0?
-6, 1/3, 10
Let m(g) be the third derivative of 2*g**7/315 + 13*g**6/144 + 22*g**5/45 + 55*g**4/48 + g**3/2 + 465*g**2. Factor m(y).
(y + 2)*(y + 3)**2*(8*y + 1)/6
Let l be (-9)/((-18)/8) + -1. Factor 6*k**2 - 9*k**2 - l*k**3 + 9*k**2.
-3*k**2*(k - 2)
Suppose -131/2*k**2 + 8*k**5 - 165/2*k - 25/2 - 84*k**4 + 473/2*k**3 = 0. What is k?
-1/4, 1, 5
Let f(l) be the second derivative of -l**4/4 - 2*l**3 - 15*l + 1. Find h such that f(h) = 0.
-4, 0
Let t(z) be the second derivative of z**5/5 + 10*z**4/3 + 14*z**3/3 - 36*z**2 - 194*z. Solve t(g) = 0.
-9, -2, 1
Suppose 4*r = -0*a - a + 553, 3*a = -2*r + 1619. Let i = -5893/11 + a. Let 6/11*v**2 + 4/11*v**4 - 16/11*v + i*v**3 - 8/11 = 0. What is v?
-2, -1/2, 1
Let g(h) be the first derivative of -h**3/3 + 13*h**2 + 27*h + 78. Factor g(s).
-(s - 27)*(s + 1)
Let o(k) be the first derivative of 27*k**5/20 + 39*k**4/16 - k**3/12 - 11*k**2/8 + k/2 - 146. Suppose o(r) = 0. Calculate r.
-1, 2/9, 1/3
Let k = -25 - -40. Suppose 0 = 2*c + 5*n + 1, -4*c - n - 4*n = -3. Factor -3 - 6*i**c + 3 - 2 - 4 - k*i.
-3*(i + 2)*(2*i + 1)
Let s(l) be the third derivative of l**5/180 - 11*l**4/72 - 45*l**2 + 2. Factor s(d).
d*(d - 11)/3
Suppose -4*g + 8 = -x - 11, 3*g + 3*x = 3. Suppose 0*s + 2*s = g. Factor 4/3*v**2 - 2*v**4 - s*v + 4/3*v**3 + 2/3 + 2/3*v**5.
2*(v - 1)**4*(v + 1)/3
Let i be 1*7/((-21)/(-6)). Let o(h) be the second derivative of 2*h**3 + 0 + 0*h**i - 1/3*h**4 + 12*h. Factor o(b).
-4*b*(b - 3)
Let c(u) = -5*u**2 - 9*u. Let t(o) = -o**2 - o. Let g(r) = -c(r) + 6*t(r). Factor g(q).
-q*(q - 3)
Suppose -2*o - 148 = -148. Let t(j) be the second derivative of 2/3*j**3 - 1/2*j**4 - 5*j + o + 1/10*j**5 + 0*j**2. Solve t(b) = 0 for b.
0, 1, 2
Let z(r) be the first derivative of 1/3*r**6 + 0*r**2 - 1/6*r**3 + 1/10*r**5 - 1/2*r**4 + 0*r + 4. What is g in z(g) = 0?
-1, -1/4, 0, 1
Let d(u) = 15*u**3 - 2595*u**2 + 79980*u + 23067. Let c(b) = 17*b**3 - 2596*b**2 + 79980*b + 23066. Let t(w) = 3*c(w) - 2*d(w). Let t(x) = 0. What is x?
-2/7, 62
Let g be 26/7 + (-2)/(-7). Let b = 5394 + -5394. Find a such that b - 4/3*a - 2/3*a**g + 2/3*a**2 + 4/3*a**3 