6464. Factor 1/4*g + a + 3/4*g**2 + 1/4*g**4 + 3/4*g**3.
g*(g + 1)**3/4
Let m(v) be the second derivative of -v**4/8 - 11*v**3/4 - 15*v**2/2 + 3*v. Find u, given that m(u) = 0.
-10, -1
Let i(x) be the first derivative of 8*x**6/9 + 52*x**5/15 - 145*x**4/3 + 380*x**3/9 + 214*x**2 + 96*x - 101. Solve i(g) = 0.
-8, -1, -1/4, 3
Let j(g) be the first derivative of -g**4/4 + 8*g**3/3 - 19*g**2/2 + 12*g + 149. Suppose j(u) = 0. What is u?
1, 3, 4
Suppose 3*g = 32 - 11. Let l be (-6)/(-10) + g/5. Find p such that -3*p + 6*p**l - 2*p**4 - 4*p**2 + 7*p - 4*p**3 = 0.
-2, -1, 0, 1
Let n(g) be the first derivative of 10*g + 7*g**2 + 22/15*g**3 + 31 + 1/10*g**4. Determine f so that n(f) = 0.
-5, -1
Factor 1979*j**2 + 35 - 20 + 940*j**2 + 217*j**2 - 672*j + 21.
4*(28*j - 3)**2
Let t be 3/((-4)/(-2) - 1). Factor 4*w**t + w**3 - w**5 - 3*w + w**3 - 2*w**5.
-3*w*(w - 1)**2*(w + 1)**2
Let o = -397 - -397. Let d(b) be the second derivative of 0*b**2 + o*b**3 + 0*b**4 - 2/3*b**6 - 5*b - 2/5*b**5 + 0. Determine z, given that d(z) = 0.
-2/5, 0
Let a(x) be the second derivative of -x**6/6 + 3*x**5 + 5*x**4/12 - 10*x**3 - 359*x. Determine k, given that a(k) = 0.
-1, 0, 1, 12
Determine m, given that 81/5*m**2 + 0 - 3/5*m = 0.
0, 1/27
Let t be 25/(-75) - (0 - 22/48). Let f(u) be the second derivative of 0 - t*u**4 - 4*u - 1/2*u**3 - 3/4*u**2. Factor f(i).
-3*(i + 1)**2/2
Let y(g) be the second derivative of -g**6/90 + g**4/4 + 2*g**3/9 - 2*g**2 + 60*g. What is h in y(h) = 0?
-2, 1, 3
Suppose -5*t - 81 = -14*t. Suppose 2*k - 9 + 3 = -5*c, 3*c + 3*k = t. Let 3/7*o + c + 0*o**2 - 3/7*o**3 = 0. Calculate o.
-1, 0, 1
Let l(y) be the second derivative of -y**5/80 - y**4/16 + y**3/4 + y**2 - 7*y - 3. Find j, given that l(j) = 0.
-4, -1, 2
Factor 27 - 70*b**2 - 576*b - 55*b**2 - 255 + 110*b**2.
-3*(b + 38)*(5*b + 2)
Factor 31*o - 5*o + 56*o**2 - 35*o**2 + 3*o**3 + 10*o.
3*o*(o + 3)*(o + 4)
Let x(o) be the second derivative of -1/36*o**4 + 1/3*o**2 - 1/18*o**3 + 0 + 31*o. Determine k so that x(k) = 0.
-2, 1
Let u(q) be the third derivative of q**5/12 - 5*q**4/3 + 25*q**3/2 - 84*q**2. Factor u(x).
5*(x - 5)*(x - 3)
Let y(o) be the first derivative of o**4/54 + 4*o**3/27 + 4*o**2/9 - 26*o - 4. Let p(m) be the first derivative of y(m). Let p(z) = 0. Calculate z.
-2
Let d(r) = 4*r**4 - 144*r**3 + 74*r**2. Let c(y) = -y**4 + 48*y**3 - 24*y**2. Let b(p) = 17*c(p) + 6*d(p). What is a in b(a) = 0?
0, 6/7, 6
Let y(j) = -11*j**4 + 16*j**3 - 13*j**2 - 29*j - 24. Let q(r) = -3*r**4 + 5*r**3 - 4*r**2 - 10*r - 8. Let k(u) = -21*q(u) + 6*y(u). Factor k(t).
-3*(t - 2)*(t + 1)*(t + 2)**2
Solve 0 + 75/4*i - 5/4*i**3 + 5/2*i**2 = 0.
-3, 0, 5
Factor t + 4*t**4 - 24*t**2 + 17*t**2 - 3*t + 5*t**3.
t*(t - 1)*(t + 2)*(4*t + 1)
Let k(s) be the first derivative of -s**4/2 - 4*s**3/3 + s**2 + 4*s - 34. Factor k(b).
-2*(b - 1)*(b + 1)*(b + 2)
Let r = 146288/7 - 20898. Factor 6/7*v - r*v**2 + 0.
-2*v*(v - 3)/7
Let i(x) be the first derivative of -2/9*x**3 + 1/12*x**4 + 1/6*x**2 + 0*x - 1. Suppose i(o) = 0. What is o?
0, 1
Let u(l) be the third derivative of l**6/30 - 49*l**5/15 + 70*l**4/3 - 184*l**3/3 + 700*l**2 - 2. Factor u(y).
4*(y - 46)*(y - 2)*(y - 1)
Let m(b) be the second derivative of 0 - 18*b + 1/6*b**2 - 1/20*b**5 - 1/18*b**3 - 5/36*b**4. Factor m(u).
-(u + 1)**2*(3*u - 1)/3
Let p(h) = 10*h + 21. Let m be p(-3). Let u be (m/6)/(-3)*4. Factor -2/5*s**3 - 54/5 - 18/5*s**u - 54/5*s.
-2*(s + 3)**3/5
Let t be (3 + -2 + 1)*6/4. Suppose -3/7*b**2 + 2/7*b + 1/7*b**t + 0 = 0. What is b?
0, 1, 2
Suppose -36646 + 36700 = 18*x. Let 0 + 64/9*j + 2/9*j**4 - 4/3*j**x + 0*j**2 = 0. Calculate j.
-2, 0, 4
Let q(g) be the first derivative of g**4/2 + 4*g**3/3 - 4*g**2 - 16*g - 128. Let q(w) = 0. What is w?
-2, 2
Let x be ((2/4)/(-1))/((-14)/140). Let m be 1 + -1*4*x/20. Factor m - 3/4*z - 1/4*z**2.
-z*(z + 3)/4
Let w(d) be the third derivative of -d**6/30 - 11*d**5/3 - 364*d**4/3 + 1568*d**3/3 - 111*d**2 + 3. Factor w(o).
-4*(o - 1)*(o + 28)**2
Factor -7442/13 + 974/13*h**2 + 29524/13*h + 8/13*h**3.
2*(h + 61)**2*(4*h - 1)/13
Let y = -7/177 - -81/59. Factor -y*l**2 + 4*l**3 + 0 + 7/3*l**4 + 0*l.
l**2*(l + 2)*(7*l - 2)/3
Suppose -2*j - 8 = -0*u + 4*u, -3*j - 3*u = 3. Let n(z) be the second derivative of 0*z**4 + 3/20*z**5 + 4*z + 0 - 3*z**j - 3/2*z**3. Factor n(y).
3*(y - 2)*(y + 1)**2
Let f(u) be the first derivative of -2/9*u**2 - 1/27*u**3 + 5 + 0*u. Let f(d) = 0. What is d?
-4, 0
Let f(z) = -z**3 - 6*z**2 - 18*z - 12. Let l be f(-7). Find t such that 183*t**3 + l - 139 - 70*t**5 - 5*t**5 - 108*t - 90*t**4 + 66*t**2 = 0.
-2, -1, 2/5, 1
Suppose -7*p = 2*p. Let b(w) be the third derivative of 0*w**6 + 0*w**4 - 1/420*w**7 + 0 + 1/120*w**5 + p*w + 0*w**3 - 5*w**2. Solve b(q) = 0.
-1, 0, 1
Let p(k) be the third derivative of 0*k - 1/30*k**6 - 1/105*k**7 + 8*k**2 + 0*k**3 + 0 - 1/30*k**5 + 0*k**4. Factor p(q).
-2*q**2*(q + 1)**2
Let c(s) = s**3 + 3*s**2 - 5*s - 4. Let k be c(-3). Suppose -21 + k = -5*j. Let -5*z**3 + j*z**3 + 5*z**3 - 2*z**5 = 0. Calculate z.
-1, 0, 1
Let i(r) be the first derivative of r**7/840 + r**6/360 - r**5/120 - r**4/24 + 11*r**3/3 + 4. Let j(q) be the third derivative of i(q). Factor j(f).
(f - 1)*(f + 1)**2
Let 0 - 1/2*b**4 - 3*b + 3*b**3 + 1/2*b**2 = 0. What is b?
-1, 0, 1, 6
Let f(x) be the second derivative of -x**4/102 + 16*x**3/51 - 64*x**2/17 - 2*x - 6. Factor f(t).
-2*(t - 8)**2/17
Let f = -12614 + 164002/13. Factor -32/13 - 2/13*b**4 + 80/13*b + f*b**3 - 66/13*b**2.
-2*(b - 4)**2*(b - 1)**2/13
Let m(p) = p**3 + 3*p**2 - 5*p + 3. Let q be m(1). Let b(k) be the first derivative of -5 + 8/3*k**3 + 1/2*k**4 - k**q - 8/5*k**5 + 0*k. Factor b(g).
-2*g*(g - 1)*(g + 1)*(4*g - 1)
Let n(q) = 13*q**2 + 31*q - 6. Let c(f) = f**2 + f. Let y(s) = -3*c(s) + n(s). Factor y(z).
2*(z + 3)*(5*z - 1)
Let a(l) be the third derivative of -l + 1/12*l**4 + 17*l**2 + 0*l**3 + 0 - 1/270*l**5. Factor a(u).
-2*u*(u - 9)/9
Let r(s) = 2*s**3 + 4*s**2 + 4*s - 7. Let v(i) = 9*i**3 + 17*i**2 + 16*i - 29. Let x(j) = 26*r(j) - 6*v(j). Factor x(n).
-2*(n - 2)*(n - 1)*(n + 2)
Let z be (-66)/(-180)*15/110. Let m(v) be the third derivative of 1/20*v**6 + 0*v - 1/70*v**7 - 1/4*v**4 + z*v**5 + 0*v**3 + 0 + 2*v**2. Solve m(i) = 0.
-1, 0, 1, 2
Let f - 7*f**2 + 0 - 137/4*f**3 - 105/4*f**4 = 0. What is f?
-1, -2/5, 0, 2/21
Let z(l) be the second derivative of l**7/273 - 2*l**6/39 + 4*l**5/13 - 40*l**4/39 + 80*l**3/39 - 32*l**2/13 + 85*l. What is r in z(r) = 0?
2
Let b(g) be the first derivative of -g**4/6 - 16*g**3/9 - 17*g**2/3 - 20*g/3 - 117. Factor b(o).
-2*(o + 1)*(o + 2)*(o + 5)/3
Let t(y) = y + 8. Let v be t(-6). Factor 4*r**4 - 17*r**v + 17*r**2.
4*r**4
Suppose -398 = -293*c + 318 + 749. Factor 4/5*v**2 + 4/5*v**c + 12/5*v**4 + 0 + 12/5*v**3 + 0*v.
4*v**2*(v + 1)**3/5
Let f(g) = 3*g**2 - 106*g + 105. Let d be f(1). Determine l so that -3/2*l**5 + 45/2*l - 27/2 + 3*l**d - 21*l**3 + 21/2*l**4 = 0.
-1, 1, 3
Let t = 3103 + -6205/2. Let c(v) be the third derivative of 1/20*v**5 + 0 - t*v**3 + 0*v - 2*v**2 + 0*v**4. Factor c(z).
3*(z - 1)*(z + 1)
Suppose 43*i - 6 = 38*i - 3*a, 4*a = 8. Let f(j) be the third derivative of i*j + 1/5*j**3 + 0 - 1/150*j**5 - 1/30*j**4 + j**2. Let f(m) = 0. What is m?
-3, 1
Let n = -1016 + 1018. Let d(m) be the first derivative of -3/4*m**4 + 3/2*m**n + m**3 - 3*m - 1. Suppose d(q) = 0. Calculate q.
-1, 1
Let v = 77/996 + 1/166. Let h(g) be the second derivative of 0*g**3 + 0*g**2 - v*g**4 - 2*g - 1/30*g**6 + 1/10*g**5 + 0. Factor h(s).
-s**2*(s - 1)**2
Factor 50 - 48*w + 3*w**4 + 92*w**2 - 13*w + w - w**4 - 60*w - 24*w**3.
2*(w - 5)**2*(w - 1)**2
Let g(o) = 2*o**2 - 26*o + 21. Let a be g(12). Let z be 3/a*0/22. Solve -16/5*n**4 + 4/5*n**3 + z*n + 2/5*n**2 + 0 = 0.
-1/4, 0, 1/2
Factor -135/2*y**2 - 3/4*y**3 - 6075/4*y + 0.
-3*y*(y + 45)**2/4
Factor -2/9*v**5 + 10/9*v**4 + 0 + 0*v + 2/3*v**2 - 14/9*v**3.
-2*v**2*(v - 3)*(v - 1)**2/9
Factor -47*k + 91*k + 25 - 99*k**2 + 2*k**4 - 52*k + 279*k**2 - 265 + 66*k**3.
2*(k - 1)*(k + 2)**2*(k + 30)
Suppose 0 = 20*a - 18*a - 4. Factor -19*o**3 - 21*o**5 + 6*o**5 - 32*o**4 - 3*o**2 - 2*o**a + 3*o**2.
-o**2*(o + 1)**2*(15*o + 2)
Let k(m) be the third derivative of -1/160*m**6 - 1/96*m**4 + 0 + 0*m**3 + 1/840*m**7 + 0*m + 1/80*m**5 - 23*m**2. Let k(b) = 0. Ca