- 95*g**3/12 + 47*g**2/2 + 5*g - 8. Factor n(b).
(b - 94)*(b - 1)/2
Suppose -65 = -19*k - 8. Let p(t) be the first derivative of 4*t**4 - 8*t - 6*t**2 + 8/3*t**k + 0*t**5 + 13 - 2/3*t**6. Let p(l) = 0. Calculate l.
-1, 1, 2
Let 8/11*x + 2/11*x**2 - 24/11 = 0. What is x?
-6, 2
Let f(a) be the third derivative of 0*a**3 - 1/24*a**6 - 1/12*a**5 - 12*a**2 + 0 + 5/24*a**4 + 1/42*a**7 + 0*a. Factor f(j).
5*j*(j - 1)**2*(j + 1)
Let j(o) be the third derivative of o**6/480 + o**5/40 + o**4/12 + 159*o**2. Factor j(y).
y*(y + 2)*(y + 4)/4
Let o(c) be the third derivative of c**6/40 - 9*c**5/20 + 9*c**4/4 + 78*c**2. Factor o(d).
3*d*(d - 6)*(d - 3)
Let j = 29 + -29. Let h be 1*12/4 - j. Determine v so that -4/3*v**2 + 2/3*v**4 + 2/3 + 0*v + 0*v**h = 0.
-1, 1
Let a = 93 + -39. Let g = a - -69. Factor -12*b - g*b**3 - 96*b**2 - 203*b**4 - 50*b**3 - 58*b**3 + 56*b**4.
-3*b*(b + 1)*(7*b + 2)**2
Suppose 0 = 11*v + 1410 - 6162. Factor -6*k + 9*k - 3*k + 216*k**3 - 36*k**4 + 2*k**5 - v*k**2.
2*k**2*(k - 6)**3
Let c(k) be the third derivative of k**8/784 + 8*k**7/245 + 41*k**6/280 + 13*k**5/70 + 39*k**2. Solve c(o) = 0 for o.
-13, -2, -1, 0
Let l(m) = m**3 - 18*m**2 + 15*m + 40. Let r be l(17). Let u = 8 + 0. Suppose 3*z**3 + 19*z**3 + 2*z + r*z**4 + u*z**2 + 14*z**2 - 4 = 0. Calculate z.
-2, -1, 1/3
Factor -2*o**2 + 2/3*o**3 + 4/3*o + 0.
2*o*(o - 2)*(o - 1)/3
Let h(u) be the second derivative of -u**5/100 + 2*u**4/15 - 7*u**3/10 + 9*u**2/5 + 14*u. Factor h(b).
-(b - 3)**2*(b - 2)/5
Let q(d) = -3*d - 16. Let w be q(-7). Determine t so that 8*t + 2*t**2 - 2*t**2 - t**3 - w*t - 2 = 0.
-2, 1
Suppose 0 = -o + 5*x + 40, 0*x - 80 = -2*o - 3*x. Suppose 9*a + 13 = o. Factor 4/3*h**2 + 2/3*h - 4/3 - 2/3*h**a.
-2*(h - 2)*(h - 1)*(h + 1)/3
Suppose 0 = 3*v + 5*t + 7 - 2, 16 = 4*v + t. Suppose 3*d - 76 = v*o - 15, 2*o = 2. Factor -2*m + m**2 + d*m - 50 - 3*m**2.
-2*(m - 5)**2
Let w(u) = 2*u**3 - 5*u**2 - u + 10. Let i be w(3). Let d = i - 40/3. Factor 4/3*q**2 + 2/3*q**4 - 2 + 8/3*q - d*q**3.
2*(q - 3)*(q - 1)**2*(q + 1)/3
Find n, given that 4/5*n + 0 - 1/5*n**3 - 3/5*n**2 = 0.
-4, 0, 1
Let s = 5046 - 5043. Determine m, given that -3/2*m**5 + 3/2*m**4 + 0*m - 3/2*m**2 + 0 + 3/2*m**s = 0.
-1, 0, 1
Suppose -21 = 2*h - 5*w, -2*h + 4*w - 14 = h. Let j(r) be the first derivative of -h*r - 2*r + r + 2*r**3 - 10 - r**3. Let j(z) = 0. Calculate z.
-1, 1
Let f(k) be the first derivative of 0*k**2 + 0*k + 1/6*k**3 - 5. Factor f(o).
o**2/2
Suppose -1058 - 922 = -495*r. Let -27/4*z**2 - 5/4*z + 25/4*z**r + 1/2 + 5/4*z**3 = 0. What is z?
-1, -2/5, 1/5, 1
Let r(a) = -a + 17. Let h be r(-12). Suppose 10 = h*d - 77. Solve 2/3*i**d + 4/9 - 14/9*i**2 - 2/3*i + 10/9*i**4 = 0.
-1, 2/5, 1
Let f(m) be the third derivative of -m**5/60 + m**4/4 - 3*m**3/2 + 223*m**2 + m. Factor f(t).
-(t - 3)**2
Let w = 74 - 58. Factor 35*h**3 - h - 15*h - 31*h**3 - 4*h**2 + w.
4*(h - 2)*(h - 1)*(h + 2)
Suppose -q + 3*q = -20. Let n be (2 - 1)/((-5)/q). Find y, given that -2*y**4 + 5*y**4 + 2*y**n - 2*y**2 = 0.
0
Suppose -x - 3*d = -7 - 0, 0 = 4*x + 5*d - 28. Suppose -5*i + r = -10*i + x, 7 = -i - 3*r. Factor -2/5 + 3/5*w**i - 1/5*w.
(w - 1)*(3*w + 2)/5
Let b(z) be the third derivative of z**6/228 + 11*z**5/285 - 13*z**4/57 - 8*z**3/19 - 3*z**2 - 3. Factor b(p).
2*(p - 2)*(p + 6)*(5*p + 2)/19
Let v(y) be the third derivative of -y**5/510 + 5*y**4/51 + 7*y**3/17 - 233*y**2. Factor v(d).
-2*(d - 21)*(d + 1)/17
Let t = -84/731 - -18443/1462. Factor -1/2*h + 5*h**2 + 0 - t*h**3.
-h*(5*h - 1)**2/2
Let i = -1717 - -1720. Factor 0 - 6/13*c**2 - 2/13*c**i + 0*c.
-2*c**2*(c + 3)/13
Suppose -c + 0*c = -2. Let i(q) = q**3 - q**2 + q + 3. Let m be i(0). Factor -2*w**3 - 14 + 9*w**2 + c - w**m.
-3*(w - 2)**2*(w + 1)
Suppose 123*z - 625 + 93 = -10*z. Factor 30/7*c - 30/7*c**3 + 36/7 - 6*c**2 + 6/7*c**z.
6*(c - 6)*(c - 1)*(c + 1)**2/7
Let h(s) = -8*s + 6*s**2 - 5*s**2 + 0*s**2 + 3. Let l(m) = 8*m - 2. Suppose 0 = 3*p - 5 - 1. Let k(a) = p*h(a) + 3*l(a). Find f such that k(f) = 0.
-4, 0
Let c(h) = -2*h - 3. Let v be c(-6). Let b = v + -7. Factor 0*j - 2 - 6*j**b + 4*j**2 - 4*j.
-2*(j + 1)**2
Solve 8 + 5*k**2 - 27*k - 28 + 27*k = 0 for k.
-2, 2
Let y(w) be the third derivative of 1/27*w**3 + 0 + 15*w**2 + 1/36*w**4 + 0*w + 1/90*w**5 + 1/540*w**6. Solve y(u) = 0 for u.
-1
Let o = -163627/9 + 18181. Let o*f**3 - 8/9*f + 8/9 - 2/9*f**2 = 0. What is f?
-2, 1, 2
Let -63*n**2 - 249*n + 15*n**3 - 251*n + 500*n = 0. What is n?
0, 21/5
Let t(p) be the second derivative of 19*p**6/90 + 37*p**5/30 + 29*p**4/12 + 14*p**3/9 - 2*p**2/3 + 566*p. Solve t(o) = 0 for o.
-2, -1, 2/19
Let h(x) be the second derivative of x**6/150 + x**5/100 - x**4/10 + 2*x + 5. Factor h(a).
a**2*(a - 2)*(a + 3)/5
Determine j, given that 15/2 - 3/4*j**2 + 27/4*j = 0.
-1, 10
Let q(w) be the third derivative of 25/4*w**3 + 0*w - 14*w**2 + 5/8*w**4 + 1/40*w**5 + 0. Suppose q(b) = 0. Calculate b.
-5
Let c be (2 - 6/5)/((-6)/(-60)). Let j = -31/4 + c. What is p in j*p**2 + 9/4 - 3/2*p = 0?
3
Let 100*d - 95*d**2 + 126*d**3 - 54*d**3 - 77*d**3 = 0. What is d?
-20, 0, 1
Let u be (-7 - -7)*(-2)/(-6). Let c(t) be the third derivative of 6*t**2 - 1/4*t**4 + 1/60*t**5 + 3/2*t**3 + 0 + u*t. What is k in c(k) = 0?
3
Let a(q) = -q - 3 - 36*q**2 + 37*q**2 + 4. Let d(f) = 7*f**2 - 10*f - 5. Let x(k) = 4*a(k) - d(k). Factor x(v).
-3*(v - 3)*(v + 1)
Suppose -5*t + 7*t - 4 = 3*v, 4*t - 30 = -5*v. Let 11*z**t + 14*z**5 - 29*z**5 = 0. Calculate z.
0
Let w = 4409 + -17611/4. Determine b, given that 35/4*b**2 + 0 + w*b**3 + 15/4*b + 5/4*b**4 = 0.
-3, -1, 0
Let f be (10/(-25))/(1/(-10)). Let t(h) be the first derivative of -h**3 - 3*h + 2 - 2*h**3 + f*h**3. Factor t(c).
3*(c - 1)*(c + 1)
Let 0*b + 7/2*b**5 - b**2 + 3/2*b**3 + 0 + 6*b**4 = 0. Calculate b.
-1, 0, 2/7
Let c = -17 + 25. Factor -41*h**2 + 5 + c*h + 20*h**2 + 20*h**2 - 20.
-(h - 5)*(h - 3)
Let b(i) = -2*i**4 + 26*i**3 - 774*i**2 + 3572*i - 5126. Let w(a) = -a**4 - a**3 - a**2 - 2*a - 1. Let x(h) = -b(h) + 6*w(h). Let x(d) = 0. What is d?
-20, 4
Factor 0*g - 22/5*g**3 - 2/5*g**4 + 0 - 36/5*g**2.
-2*g**2*(g + 2)*(g + 9)/5
Let j(k) be the third derivative of 1/120*k**6 + 0*k + 1/48*k**4 + 1/840*k**7 + 1/48*k**5 + 0 + 33*k**2 + 0*k**3. Factor j(z).
z*(z + 1)**2*(z + 2)/4
Let f(l) be the first derivative of -l**3 - 21/2*l**2 - 18*l + 18. Solve f(y) = 0.
-6, -1
Factor -364*m**2 + 4*m**3 + 0*m**3 + 852*m - 21632 + 10796*m - 89*m**2 + 29*m**2.
4*(m - 52)**2*(m - 2)
Let l(q) be the third derivative of -343*q**8/48 - 7301*q**7/30 - 65611*q**6/20 - 202293*q**5/10 - 217503*q**4/8 + 771147*q**3/2 + 2*q**2 - 152*q. Factor l(k).
-(k - 1)*(7*k + 39)**4
Let a(z) = -9*z**4 - 13*z**3 + z**2 - 9*z. Let j(p) = -6*p**4 - 3*p + p**4 - 2*p + p**2 - 7*p**3 + 0*p. Let m(h) = -4*a(h) + 7*j(h). Solve m(y) = 0 for y.
-1, 0
Let m(w) be the second derivative of -5*w**7/14 + 25*w**6/6 - 53*w**5/4 - 15*w**4/4 + 140*w**3/3 - 40*w**2 - 3*w - 17. Find u, given that m(u) = 0.
-1, 1/3, 1, 4
Let g(u) = -u**3 - 39*u**2 + 33*u. Let q(a) = -a**2 - 2*a. Let j be q(-3). Let c(r) = r**3 + 19*r**2 - 17*r. Let k(x) = j*g(x) - 7*c(x). Solve k(i) = 0.
-5, 0, 1
Let s(t) be the second derivative of t**6/180 + t**5/40 - 3*t**4/8 - 15*t**3/4 - 27*t**2/2 + 2*t - 207. Let s(y) = 0. Calculate y.
-3, 6
Suppose 6*u**2 - 6 + 0*u**2 + 63*u + 63*u**2 = 0. Calculate u.
-1, 2/23
Let g be 754/208 + 6/16. Let m(q) be the third derivative of -1/120*q**6 + 1/6*q**g + 0*q - 1/30*q**5 + 4/3*q**3 + 3*q**2 + 0. Suppose m(y) = 0. Calculate y.
-2, 2
Let z(y) be the third derivative of 0*y - 1/20*y**5 + 9*y**2 - y**4 - 7/2*y**3 + 0. Suppose z(n) = 0. What is n?
-7, -1
Factor 0 - 6/7*t**3 + 16/7*t - 2/7*t**4 + 12/7*t**2.
-2*t*(t - 2)*(t + 1)*(t + 4)/7
Let q(a) be the second derivative of a**5/4 + 5*a**4/2 + 15*a**3/2 - 11*a + 1. Factor q(g).
5*g*(g + 3)**2
Factor 31 + 40 - 23 - 12*v**4 - 336*v - 63*v**4 + 18*v**5 + 12*v**3 + 288*v**2.
3*(v - 2)**3*(v + 2)*(6*v - 1)
Suppose -2/9*u**3 + 0 - 10/9*u**2 - 4/3*u = 0. Calculate u.
-3, -2, 0
Let h be -4 + 5/6 + (-1)/(-2). Let q = 10/3 + h. Factor -q*x**2 + 0 + 2/3*x.
-2*x*(x - 1)/3
Determine r, given that 140789 + 1064*r + 25*r**2 + 58*r + 17*r**2 - 35882 - 39*r**2 = 0.
-187
Let x(r) be the first derivative of -r**6/6 - 3*r**5/5 - 3*r**4/4 - r**3/3 - 158. Fac