derivative of -y**7/5040 - 8*y**3/3 + 3. Let l(b) be the third derivative of z(b). Factor l(p).
-p**3/6
Let i(k) be the first derivative of 5/8*k**2 - 1/4*k**3 - 7 - 1/2*k. Solve i(v) = 0.
2/3, 1
Solve 3/4*z**5 + 9/2*z**2 - 7/2*z**4 + z**3 - 7/4*z - 1 = 0 for z.
-1, -1/3, 1, 4
Let t(w) be the second derivative of 1/10*w**3 - 9/5*w**4 + 0 + 54*w + 9/5*w**2 - 3/70*w**7 + 63/50*w**5 - 1/5*w**6. Let t(l) = 0. Calculate l.
-6, -1/3, 1
Let y(x) be the third derivative of 121*x**5/270 - 11*x**4/54 + x**3/27 - 2*x**2 - 8. Factor y(s).
2*(11*s - 1)**2/9
Let r = 7 - 4. Suppose y - r*l = 3, -y + 2*y - 5 = l. Suppose 0*s - 6 + y + s - s**2 = 0. What is s?
0, 1
Let z be 19/5 + ((-231)/(-55) - 5). Factor -1100/3*a**z + 480*a**2 + 36 - 222*a - 500/9*a**4 + 1250/9*a**5.
2*(a + 2)*(5*a - 3)**4/9
Suppose 4*c + 2*p - 3 = 5*c, -5*c = p - 18. Factor 0*f - 3*f**2 - 5*f**2 + 4*f**4 - 4*f**c + 4*f**2 + 4*f.
4*f*(f - 1)**2*(f + 1)
Let r(y) = 16*y**2 - 4*y - 9. Let x(v) = -15*v**2 + 5*v + 10. Let k(i) = 5*r(i) + 4*x(i). Factor k(h).
5*(2*h - 1)*(2*h + 1)
Let p = -72 - -74. Suppose 0 = p*x + 143 - 153. Let 11/6*y - 8/3*y**4 + 1/3 + 7/3*y**2 - 7/6*y**x - 2/3*y**3 = 0. Calculate y.
-1, -2/7, 1
Let m(u) = u**3 - u**2 - 5*u + 5. Let v be m(2). Let o = -1 - v. What is w in 0 + o*w + 1/5*w**2 = 0?
0
Let c(j) be the third derivative of -j**7/840 + j**6/240 - j**5/240 - 2*j**2 + 10. Suppose c(t) = 0. What is t?
0, 1
Factor -10/3 + 0*w + 5/6*w**3 + 5/2*w**2.
5*(w - 1)*(w + 2)**2/6
Let q(y) = -y**4 + 3*y**3 - 3*y**2 - 7*y + 6. Let w(k) = -k**4 + 4*k**3 - 3*k**2 - 8*k + 7. Let o(s) = 7*q(s) - 6*w(s). Determine u so that o(u) = 0.
-1, 0
Factor 50*g + 38*g**2 - 17*g**2 - 17*g**2 + 43 + 23.
2*(g + 11)*(2*g + 3)
Factor -16*p**2 + 3921 - 3901 + 5*p**3 + p**2.
5*(p - 2)**2*(p + 1)
Let s(b) = -12*b - 9. Let a(c) be the first derivative of c**3/3 - 13*c**2/2 - 10*c + 8. Let p(n) = 3*a(n) - 4*s(n). Factor p(k).
3*(k + 1)*(k + 2)
Let l = -134 + 157. Let t be (-2)/(-7)*(l - 16). Factor 0 - 3*r + 3/2*r**t.
3*r*(r - 2)/2
Let p(d) be the second derivative of -d**4/30 - 4*d**3/5 - 32*d**2/5 + 100*d. Determine w so that p(w) = 0.
-8, -4
Let j(r) be the third derivative of -r**8/10920 - r**7/910 - r**6/260 - 19*r**3/6 + 16*r**2. Let f(z) be the first derivative of j(z). Solve f(i) = 0.
-3, 0
Let i be ((-27)/45 - (-145)/(-50)) + 4. Let s(f) be the third derivative of 1/80*f**6 + 0 + 0*f + i*f**4 + 1/8*f**5 + f**3 - 9*f**2. Factor s(t).
3*(t + 1)*(t + 2)**2/2
Let l be 0/(4*(-1)/(-4)). Let r = 1 - l. Determine m, given that -m + 0 + m**3 - 1 + r = 0.
-1, 0, 1
Let z(l) = 6*l**2 + 69*l + 600. Let v(h) = h**2 + 11*h + 100. Let i(g) = 34*v(g) - 6*z(g). Factor i(d).
-2*(d + 10)**2
Let d(i) be the second derivative of -i**9/432 + i**8/105 - i**7/210 - 7*i**3/6 - 8*i. Let a(o) be the second derivative of d(o). Solve a(m) = 0.
0, 2/7, 2
Let i(j) = -8*j**2 - 98*j - 192. Let t(x) = 4*x**2 + 48*x + 96. Let y(z) = 4*i(z) + 7*t(z). Factor y(u).
-4*(u + 2)*(u + 12)
Let 43/2*s**2 + 76*s + 24 + 4*s**4 - 53/2*s**3 = 0. What is s?
-1, -3/8, 4
Let y = -4843/3 + 1617. Factor 2/3*a**3 + y + 4/3*a**2 - 14/3*a.
2*(a - 1)**2*(a + 4)/3
Let y be (-5 - -6)/((-3)/(-12)). Let 32*g + y*g**2 + 7 - 16*g + 10 - 1 = 0. What is g?
-2
Suppose -b = -c + 43, 217 = 4*c - 2*b + 49. Let d = c - 39. Factor -1/4*j**3 - 1/4*j**4 + 0 + 1/4*j**d + 1/4*j.
-j*(j - 1)*(j + 1)**2/4
Let g(c) = -4*c + 2. Let o be g(-4). Suppose -r - o = -3*r. Factor 4*i**3 + 3*i**3 - r*i**3 - 3*i**3 + 5*i**5.
5*i**3*(i - 1)*(i + 1)
Let j(r) be the third derivative of -r**8/1176 - 2*r**7/735 + r**5/105 + r**4/84 - 43*r**2. Find s, given that j(s) = 0.
-1, 0, 1
Let s(v) be the second derivative of -v**4/102 + 320*v**3/51 - 25600*v**2/17 - v - 115. Suppose s(c) = 0. What is c?
160
Let n(v) = 9*v - 20. Let f be n(3). Factor 19*b**2 + 28*b - 8*b**3 + 16*b - f*b**2 + 16 - 4*b**4 - 12*b.
-4*(b - 2)*(b + 1)**2*(b + 2)
Let z(s) be the first derivative of -s**9/18144 - s**8/5040 + s**7/5040 + s**6/1080 + 3*s**3 - 11. Let o(w) be the third derivative of z(w). Solve o(v) = 0.
-2, -1, 0, 1
Let y(o) be the first derivative of o**4/42 + 4*o**3/21 - o**2/21 - 4*o/7 + 101. Solve y(f) = 0.
-6, -1, 1
Let x = 2308 + -2305. Suppose 0*i**2 - 2/7*i**5 + 0*i + 2/7*i**4 + 0*i**x + 0 = 0. What is i?
0, 1
Determine f so that 12/5 + 8*f + 21/5*f**3 + 47/5*f**2 + 1/5*f**4 - 1/5*f**5 = 0.
-2, -1, 6
Let n(p) be the second derivative of -2/15*p**3 + 2/15*p**4 - 38*p + 2/105*p**7 + 0*p**2 + 0*p**5 - 4/75*p**6 + 0. Factor n(y).
4*y*(y - 1)**3*(y + 1)/5
Suppose 688*q = -f + 693*q - 12, 5*f + 2*q = 21. Factor 64/7*t**2 + 2/7*t**4 + 20/7*t**f + 0 + 64/7*t.
2*t*(t + 2)*(t + 4)**2/7
Let q(p) be the first derivative of -p**4/14 + 2*p**3/3 - 8*p**2/7 - 32*p/7 + 5. Determine k so that q(k) = 0.
-1, 4
Factor 1/3*c**2 + 7/3*c + 4.
(c + 3)*(c + 4)/3
Suppose 61 + 67 = 10*l + 108. Solve 4/7*i + 0 - 4/7*i**3 + 0*i**l = 0.
-1, 0, 1
Let y(h) = 4*h**3 + 2*h**2 - 5*h + 60. Let b(o) = -o**3 - 2*o**2 - 2. Let i(q) = -5*b(q) - y(q). Factor i(p).
(p - 2)*(p + 5)**2
Suppose 7*p + 7835 = 7849. Factor 0*k + 0 + 2/3*k**5 + 0*k**p + 4/3*k**3 - 2*k**4.
2*k**3*(k - 2)*(k - 1)/3
Let h be 2/10*-3*25*4/(-20). Find x, given that 5/2*x**h - 3/2*x**2 + x**4 + 2 - 4*x = 0.
-2, 1/2, 1
Factor -2/9*j**4 + 2/3*j**3 - 4/9*j**2 + 0*j + 0.
-2*j**2*(j - 2)*(j - 1)/9
Let v(b) be the third derivative of 2*b**7/315 + 2*b**6/45 + 2*b**5/15 + 2*b**4/9 + 2*b**3/9 + 85*b**2. Suppose v(d) = 0. What is d?
-1
Let g(z) be the first derivative of -z**7/1050 + z**6/600 + z**5/100 - z**4/24 + z**3/15 - 7*z**2/2 + 8. Let o(x) be the second derivative of g(x). Factor o(j).
-(j - 1)**3*(j + 2)/5
Let n(w) be the first derivative of 3*w**5 + 25*w**4 - 55*w**3 - 15*w**2 + 80*w + 100. Factor n(x).
5*(x - 1)**2*(x + 8)*(3*x + 2)
Let r(q) = -4*q**2 + 24*q + 28. Suppose -5*t - 45 + 30 = 0. Let j(o) = 20*o**2 - 120*o - 140. Let i(p) = t*j(p) - 16*r(p). Determine h so that i(h) = 0.
-1, 7
Let q(w) be the third derivative of 0 + 0*w - 1/25*w**5 - 3/40*w**4 + 13*w**2 + 7/200*w**6 + 0*w**3. Factor q(s).
3*s*(s - 1)*(7*s + 3)/5
Let q(b) be the second derivative of b**4/9 - 88*b**3/9 + 968*b**2/3 - 405*b. Suppose q(u) = 0. What is u?
22
What is c in -40*c + 12*c**2 - 215*c - 14*c**2 - 10658 - 37*c = 0?
-73
Determine i, given that -2*i + 13/3*i**2 + 0 + 1/3*i**4 - 8/3*i**3 = 0.
0, 1, 6
Determine t, given that -13/4*t + 1/4*t**3 + 5/4*t**2 + 7/4 = 0.
-7, 1
Suppose 0 = 2*u - 0*u. Suppose m - 4*z = -2*z - 8, 3*m + 2*z - 8 = u. Factor -4 + 6*w + m*w - 3*w**3 + 3*w**2 + 4.
-3*w*(w - 2)*(w + 1)
Let q(o) = -2*o**3 - 2*o**2 + 7*o - 1. Let p be q(-3). Let f be 9/(-36) + p/8. Let f*r**3 + 0*r + 0 - 3/2*r**2 = 0. Calculate r.
0, 1
Let l = 15 + -13. Factor 3*x**2 - 15 - 6*x**l + 33*x - 18*x**2 + 3*x**3.
3*(x - 5)*(x - 1)**2
Factor 6*h**2 - 11/2 + 5*h**3 - 5*h - 1/2*h**4.
-(h - 11)*(h - 1)*(h + 1)**2/2
Let z(j) be the second derivative of -j**5/110 + 2*j**4/33 + 19*j**3/33 + 14*j**2/11 + j + 10. Suppose z(g) = 0. What is g?
-2, -1, 7
Suppose 5*a + 0*a + 4*r - 23 = 0, -4*r = -2*a - 2. Suppose -20 = a*b - 8*b. Solve -b*s**2 - 8 - 26*s + 2*s + 12*s = 0.
-2, -1
Let l(d) be the second derivative of d**4/66 - 52*d**3/33 + 676*d**2/11 + 90*d. Suppose l(a) = 0. Calculate a.
26
Suppose -4*j - 2 = 2*m, -14*j + 35 = -9*j - 5*m. Suppose 5*r + 0*r = 4*f + 5, 0 = -2*f - 3*r + 3. Factor f*g + 2/5 - 2/5*g**j.
-2*(g - 1)*(g + 1)/5
Suppose 5160 - 21*k**3 - 5160 + 48*k + 3*k**4 - 30*k**2 = 0. Calculate k.
-2, 0, 1, 8
Let i be (-182)/1872 - (-4)/18. Suppose 4 = 61*w - 59*w. Factor 1/4 + i*h - 1/8*h**w.
-(h - 2)*(h + 1)/8
Let y = -1417/8610 - -22/123. Let l(b) be the second derivative of 0 - 1/7*b**2 + 4*b - 1/21*b**3 + y*b**5 + 1/42*b**4. Factor l(a).
2*(a - 1)*(a + 1)**2/7
Let y(k) be the third derivative of -k**5/120 - 23*k**4/24 + 47*k**3/12 + 54*k**2. Factor y(s).
-(s - 1)*(s + 47)/2
Let j(s) = -6*s**4 - 173*s**3 - 1112*s**2 - 67*s + 6106. Let a(l) = -2*l**4 - 58*l**3 - 370*l**2 - 22*l + 2036. Let o(y) = -11*a(y) + 4*j(y). Factor o(d).
-2*(d - 2)*(d + 3)*(d + 13)**2
Let n(g) be the second derivative of -2/3*g**3 - 7*g + 0*g**2 + 0 - 1/6*g**4. Suppose n(y) = 0. What is y?
-2, 0
Let z(s) = 15*s**2 + 264*s - 17432. Let v(r) = -2*r**2 + 1. Let y(d) = 24*v(d) + 3*z(d). Find f such that y(f) = 0.
132
Fact