3. Factor x(m).
-(m - 1)**2*(m + 1)/2
Suppose 2*f + z = 24, 3*f + 5*z - 32 = 11. Let a(p) be the second derivative of 2/3*p**3 + 0 - 3/5*p**5 - 2/3*p**4 + 0*p**2 - f*p. Let a(r) = 0. What is r?
-1, 0, 1/3
Let o be -35*(-28)/60 - 13. Let o*s**4 - 80/3*s + 32/3 - 40/3*s**3 - 1/3*s**5 + 80/3*s**2 = 0. What is s?
2
Factor 24/5 + 8/5*v - 2/5*v**3 - 6/5*v**2.
-2*(v - 2)*(v + 2)*(v + 3)/5
Factor 216 + 669*i - 2*i**3 + 615*i + 30*i**2 - 1428*i.
-2*(i - 6)**2*(i - 3)
Let t(u) be the second derivative of u**5/70 - u**4/21 + 67*u + 2. Determine b so that t(b) = 0.
0, 2
Let s(q) be the second derivative of -q**5/60 - q**4/36 + 28*q**3/9 + 572*q. Suppose s(h) = 0. What is h?
-8, 0, 7
Factor 18/5 - 2/5*m**2 + 0*m.
-2*(m - 3)*(m + 3)/5
Let -5/2*l + 3/2*l**2 + 1/2*l**4 - 2 + 5/2*l**3 = 0. What is l?
-4, -1, 1
Let f(d) be the third derivative of -d**6/1980 - d**5/165 + 5*d**3/3 - 10*d**2. Let a(p) be the first derivative of f(p). Factor a(c).
-2*c*(c + 4)/11
Let q(b) be the first derivative of -b**6/10 + 8*b**5/15 - 2*b**4/3 - 9*b**2/2 + 6. Let i(d) be the second derivative of q(d). What is x in i(x) = 0?
0, 2/3, 2
Let l(f) be the second derivative of -3*f**5/40 - f**4/4 + f**3/4 + 3*f**2/2 + 361*f. Factor l(r).
-3*(r - 1)*(r + 1)*(r + 2)/2
Suppose -48 = -12*k + 24. Let v(u) be the first derivative of 0*u**2 - 1 - 1/5*u**5 - 1/4*u**4 + 0*u - 1/18*u**k - 1/9*u**3. Factor v(n).
-n**2*(n + 1)**3/3
Suppose -5*m + 5*c = 0, 3*m - 4*c - 3 = -5. Suppose -m*k = -3*k - h - 3, -2*h = 5*k. What is w in 81 - 81 + k*w**2 = 0?
0
Let y be (-24)/(-3) + -14 + (-180)/(-27). Let v be (-21)/9 - (-2 + -1). Factor -2/3*p**5 + 0*p + 0 + y*p**3 + v*p**2 - 2/3*p**4.
-2*p**2*(p - 1)*(p + 1)**2/3
Let h = -952/45 - -194/9. Determine v, given that -h - 1/5*v**2 + 3/5*v = 0.
1, 2
Let n(g) be the second derivative of 1/15*g**4 - g**2 + 8*g + 0 + 3/5*g**3. Factor n(p).
2*(p + 5)*(2*p - 1)/5
Let l(g) be the second derivative of -7*g**4/90 + 4*g**3/15 + 4*g**2/15 - 53*g + 4. Factor l(m).
-2*(m - 2)*(7*m + 2)/15
Factor 3*i + 3*i**2 - i**2 - 81*i + 0*i**2.
2*i*(i - 39)
Let g(y) = 3*y**3 + y**2 - 3*y + 1. Let k be g(1). Suppose 0 = k*s - 7*s. What is f in s - 1/2*f**4 + 0*f - f**3 - 1/2*f**2 = 0?
-1, 0
Factor -4/5*t**3 + 2/5*t**4 + 0 - 2/5*t**2 + 4/5*t.
2*t*(t - 2)*(t - 1)*(t + 1)/5
Let s(l) be the second derivative of 29*l**6/30 + 263*l**5/60 + 89*l**4/12 + 31*l**3/6 + l**2/3 - 12*l + 8. Solve s(a) = 0 for a.
-1, -2/87
Let l = 19 - 7. Let c = -9 + l. Find x such that -3*x**2 - 4*x**5 + 3*x**5 - 2*x**c + 3*x**4 - x + x**2 + 4*x - 1 = 0.
-1, 1
Let m = 1/1821 + 7279/9105. Find s such that 0 - 6/5*s**3 - m*s**2 + 2/5*s = 0.
-1, 0, 1/3
Let s(d) be the second derivative of 2*d**6/15 - 7*d**5/5 + 5*d**4/3 + 14*d**3/3 - 12*d**2 - 278*d. Factor s(f).
4*(f - 6)*(f - 1)**2*(f + 1)
Let w be (56/(-175))/(6/(-5))*2. Factor 2/3*n**2 + w + 8/5*n.
2*(n + 2)*(5*n + 2)/15
Determine v, given that -4*v + 30/11 + 2/11*v**4 + 0*v**2 + 12/11*v**3 = 0.
-5, -3, 1
Let r(y) be the third derivative of y**9/40320 + y**8/40320 - y**7/1260 + y**6/360 - y**5/60 + y**2. Let m(t) be the third derivative of r(t). Factor m(k).
(k - 1)*(k + 2)*(3*k - 2)/2
Suppose -2/3*t**5 - 20/3*t + 22/3*t**3 + 2*t**4 - 2*t**2 + 0 = 0. Calculate t.
-2, -1, 0, 1, 5
Let x = -14 + 28. Let m = -8 + x. Factor -6*k**3 + 9*k**4 + 0*k - 6*k**5 - 3 + 9*k + 3*k**5 - m*k**2.
-3*(k - 1)**4*(k + 1)
Suppose 33*q + 72 = 39*q. Let c(t) = t**3 - 9*t**2 - 35*t - 9. Let j be c(q). Solve 1/7*s**4 + 6/7*s**j + 8/7*s + 12/7*s**2 + 0 = 0.
-2, 0
Let z be 6 + (-297)/55 - (-12)/(-20). Suppose -v**3 + 0 + 1/2*v**4 + z*v**2 + 0*v + 1/2*v**5 = 0. Calculate v.
-2, 0, 1
Suppose -5 + 2 = -3*f. Let t = 56 + -54. Suppose f - y**t + y**3 + y + 0 - 2*y = 0. What is y?
-1, 1
Suppose -4*c + a = -2*c - 9, -c = -3*a - 2. Let h be -2*6/4 + c. Factor 4/5*n + 2/5 + 2/5*n**h.
2*(n + 1)**2/5
Suppose -3*b = 2*b - 15. Suppose -g = -8*g + b*g. Factor g*i**2 - 1/3*i**5 + 0*i - 1/3*i**3 + 0 + 2/3*i**4.
-i**3*(i - 1)**2/3
Suppose 96*i**2 - 2*i**4 + 272*i - 16*i - 73*i**3 + 73*i**3 = 0. Calculate i.
-4, 0, 8
Let f be (-46)/2*(2 + -1). Let k = 47/2 + f. What is r in -1/4*r**2 + 0 - 1/4*r**3 + k*r = 0?
-2, 0, 1
Factor 22/15*z**2 - 4/5*z**3 - 4/5*z + 0 + 2/15*z**4.
2*z*(z - 3)*(z - 2)*(z - 1)/15
Let i(v) be the first derivative of v**7/840 + v**6/120 - v**4/6 - 22*v**3/3 - 20. Let o(a) be the third derivative of i(a). Factor o(f).
(f - 1)*(f + 2)**2
Suppose -i**5 - 4*i**5 + 175*i**2 + 173*i + 31*i**4 + 165*i**3 - 113*i + 14*i**4 = 0. Calculate i.
-1, 0, 12
Let r(i) = i**3. Let q(o) = 3*o**3 + 144*o - 384. Let a(y) = -q(y) + 6*r(y). Factor a(s).
3*(s - 4)**2*(s + 8)
Let b(m) = -20*m**2 + 39*m**2 - 1 - 5 + 11*m - 21*m**2. Let h be b(4). Factor 3/2*z**4 - h*z**3 - 6 + 6*z + 9/2*z**2.
3*(z - 2)**2*(z - 1)*(z + 1)/2
Determine u so that -2/17*u**5 + 2/17*u**4 + 10/17*u**3 - 10/17*u**2 + 8/17 - 8/17*u = 0.
-2, -1, 1, 2
Suppose 20*z - 140 = -15*z. Suppose 4*u = 3*s - 2, u - 2 = -5*s + 9. Let 2/3 + l**s - 1/3*l**z - 5/3*l + 1/3*l**3 = 0. Calculate l.
-2, 1
Let s(c) be the third derivative of -c**6/720 + c**5/90 - 5*c**4/144 + c**3/18 + 2*c**2 - 240. Suppose s(r) = 0. What is r?
1, 2
Let v(s) = -s. Suppose 6 = 4*a + 2. Let f(o) = -3*o**5 + 9*o**4 - 6*o**3 - 3*o. Let z(p) = a*f(p) - 3*v(p). Factor z(n).
-3*n**3*(n - 2)*(n - 1)
Let q = 84 + -82. Let f be 0 + ((-9)/(-5))/((-12)/(-15)). Suppose 3/4*v**q - f + 3/2*v = 0. Calculate v.
-3, 1
Let d(p) be the third derivative of -1/1848*p**8 - 1/330*p**5 + 0*p**3 + 0*p**4 + 0*p - 1/385*p**7 + 0 + 31*p**2 - 1/220*p**6. Let d(v) = 0. What is v?
-1, 0
Let h(v) be the third derivative of -v**8/10080 + v**7/2520 - v**5/30 - 16*v**2. Let z(k) be the third derivative of h(k). Factor z(s).
-2*s*(s - 1)
Let y be (-48)/627 + 10/55. What is u in 8/19 + y*u**2 - 8/19*u = 0?
2
Let w(r) be the second derivative of -r**6/900 - r**5/100 + r**4/15 - 7*r**3/3 + 6*r. Let h(g) be the second derivative of w(g). Let h(i) = 0. Calculate i.
-4, 1
Suppose 4*o - 21 = o. Suppose -12*w**4 - 4*w**2 + 5*w**3 + 32*w + 4*w**5 + o*w**3 - 32*w = 0. What is w?
0, 1
Solve -4*q**4 - 24*q**3 - 192 + 4*q**4 + 97*q**2 + 3*q**4 + 87*q + 9*q - 61*q**2 = 0.
-2, 2, 4
Let w be -4*15/(-84)*(-12)/(-60). Suppose -1/7*f**4 + 0*f**2 + 2/7*f**3 + w - 2/7*f = 0. Calculate f.
-1, 1
Let c be (-13 + -1)/(2 + -3). Suppose 3*a - 9 = d, -4*a = 5*d + 21 - c. Factor 0*m**a + 1/3 + 1/2*m - 1/6*m**3.
-(m - 2)*(m + 1)**2/6
Let o = 270/53 + -121/159. Factor -o*h**3 - 1/3*h**5 - 2*h**4 - 4/3*h - 4*h**2 + 0.
-h*(h + 1)**2*(h + 2)**2/3
Suppose 325*f = 340*f. Let p(x) be the second derivative of 3*x - 1/15*x**3 - 1/30*x**4 + f + 0*x**2. Suppose p(z) = 0. Calculate z.
-1, 0
Let v be 11/(33/9)*5*10/825. Factor 24/11*h**2 + 12/11*h**3 + 20/11*h + v*h**4 + 6/11.
2*(h + 1)**3*(h + 3)/11
Let l = -2038447 - -3088247332/1515. Let c = l + 5/101. Solve 2/5*k - 4/15 - c*k**3 + 0*k**2 = 0 for k.
-2, 1
Let x = -126 - -138. Let q be x/(-15)*35/(-14). Suppose 1/2*y**3 - 3/2*y - 1 + 0*y**q = 0. What is y?
-1, 2
Let a(z) be the first derivative of -z**3 + 8 + 0*z**2 + 3/4*z**4 + 0*z. Factor a(y).
3*y**2*(y - 1)
Find a such that 12*a**2 - 70697*a - 12 - 3*a**3 + 70699*a + a**3 = 0.
-1, 1, 6
Factor 0*x**2 + 31/9*x**3 + 1/9*x**4 + 0*x + 0.
x**3*(x + 31)/9
Let d = -10334 + 41341/4. Solve d*r + 1/2 + 1/2*r**2 = 0.
-2, -1/2
Let b(h) = -9*h**4 + 22*h**3 + 83*h**2 + 27*h. Let t(j) = 17*j**4 - 44*j**3 - 165*j**2 - 53*j. Let u(w) = 5*b(w) + 3*t(w). Factor u(q).
2*q*(q - 6)*(q + 2)*(3*q + 1)
Let n = -14260/343 - -50/343. Let b = 42 + n. Factor b*v + 4/7 + 1/7*v**2.
(v + 2)**2/7
Let w be 15 + -11 + -9 + 7. Let s(d) be the third derivative of 0*d + 3*d**w - 1/168*d**8 - 1/15*d**6 + 0*d**4 + 0 + 4/105*d**7 + 0*d**5 + 0*d**3. Factor s(t).
-2*t**3*(t - 2)**2
Let k(y) be the second derivative of -7/12*y**3 + 3/2*y**2 + y + 1/60*y**6 + 3/40*y**5 + 5 - 1/8*y**4. Suppose k(t) = 0. Calculate t.
-3, -2, 1
Let b(i) be the first derivative of 3*i**4/4 + 71*i**3 + 1836*i**2 - 3888*i + 101. Let b(g) = 0. Calculate g.
-36, 1
Suppose -4*n = -11 - 1. Let u = 2709 - 2705. Factor 12/5*c**n + 0 - 16/5*c - 4/5*c**u + 0*c**2.
-4*c*(c - 2)**2*(c + 1)/5
Let g(f) be the first derivative of 0*f**2 + 4*f + 1/18*f**5 + 4/27*f**3 + 4/27*f**4 + 1/135*f**6 + 4. Let w(s) be the first derivativ