- 5 = -5*b + 2*b, -d + 1 = -h*b. Solve 2/7*y + b - 2/7*y**2 = 0 for y.
0, 1
Let p(h) be the first derivative of -h**4 - 1892*h**3/3 + 1900*h**2 - 321. Factor p(w).
-4*w*(w - 2)*(w + 475)
Let k = 20/619 - -149059/3714. Let u = k - 1097/30. Find i, given that 168/5*i + 144/5 + 36/5*i**2 - 6/5*i**4 - u*i**3 = 0.
-2, 3
Let x = -563 - -646. Suppose 20 = -x*j + 93*j. Let 4/11*a - 26/11*a**j + 0 = 0. Calculate a.
0, 2/13
Let b(o) be the third derivative of o**7/70 - 89*o**6/40 + 129*o**5/10 + o**4/2 - 172*o**3 - 1634*o**2 - o. Factor b(i).
3*(i - 86)*(i - 2)**2*(i + 1)
Let a(c) be the second derivative of c**4/24 - 11*c**3/2 - 9518*c. Solve a(g) = 0 for g.
0, 66
Suppose -121658*a + 56 - 5*a**2 + 121638*a + 169 = 0. Calculate a.
-9, 5
Let x(w) = -6*w**3 + w**2 - w + 1. Let z(r) = -17*r**3 - 25*r**2 - 83*r + 4803. Let a(s) = 6*x(s) - 2*z(s). Determine j so that a(j) = 0.
-12, 20
Let f(v) be the third derivative of v**5/150 - 109*v**4/30 - 73*v**3/5 - 7*v**2 + 3*v - 1. Suppose f(m) = 0. Calculate m.
-1, 219
Let p(m) = m**2 + 3*m - 3. Let s(t) = -30*t**2 - 4585*t + 1170. Let c(b) = 10*p(b) + s(b). Let c(q) = 0. Calculate q.
-228, 1/4
Let h(u) be the third derivative of u**7/735 + 59*u**6/420 + 73*u**5/14 + 2175*u**4/28 - 37*u**2 - 32*u. Find l, given that h(l) = 0.
-29, -15, 0
Suppose 3*h - 3*y = -6, -3*y + 15 = 3. Let o = 1 + h. Solve 4*q + 3*q**3 + q + 2*q**2 - 2*q**o - 4*q = 0 for q.
-1, 0
Factor -9*v**2 + 2*v**3 - 3672 - v**3 + 59*v**2 - 3701 + 7557 + 188*v.
(v + 2)**2*(v + 46)
Let f(a) = 4*a**3 - 4*a**2 - 3. Let k be f(2). Suppose -4*r = -3*n - 21, 0 = -4*r - n - 4 + k. Factor 0 + 2/3*l**4 - 10/3*l**2 - 2*l**r + 2/3*l**5 - 4/3*l.
2*l*(l - 2)*(l + 1)**3/3
Suppose -37*d + 120 = -32*d. Factor 6*q**2 - 3*q**5 + 0*q**5 + 9*q**3 + 12*q**4 - d*q**3.
-3*q**2*(q - 2)*(q - 1)**2
Let o(x) be the second derivative of x**5/40 - 9*x**4/8 + 65*x**3/4 - 169*x**2/4 + 2*x + 56. Factor o(n).
(n - 13)**2*(n - 1)/2
Let n be ((-84)/(-1050))/(-2 + 181/90). Suppose 2*s + 4*l - 4 = 14, 6 = s + l. Solve 27/5*g - n*g**2 - 6/5 + 3*g**s = 0.
2/5, 1
Let -385*g - 45*g**2 + 0 - 5/4*g**3 = 0. What is g?
-22, -14, 0
Suppose 58*c + 19 = 65*c - 16. Let k(t) be the first derivative of 3/4*t**4 - 8/15*t**3 - 8/5*t**2 + 1/30*t**6 + 0*t + 8/25*t**c - 38. Factor k(j).
j*(j - 1)*(j + 1)*(j + 4)**2/5
Find i, given that 0*i + 4/5*i**4 - 6/5*i**2 + 23/5*i**3 + 0 = 0.
-6, 0, 1/4
Let f(l) be the second derivative of -l**10/6048 + l**9/1512 - l**8/1344 - l**4/4 + l**3/6 + 24*l. Let b(s) be the third derivative of f(s). Solve b(d) = 0.
0, 1
Let 0 + 6/5*s + 3/5*s**2 = 0. Calculate s.
-2, 0
Let b be -26*2/(-20) - 4/(-10). What is m in 7*m**3 - 6*m - 12*m**b - 10*m**3 - 33*m**2 = 0?
-2, -1/5, 0
Let z(q) be the third derivative of 0*q - 8/3*q**3 - 1/3*q**5 - 1/30*q**6 - 4/3*q**4 + 0 - 60*q**2. Determine r so that z(r) = 0.
-2, -1
Let z(a) be the first derivative of -a**3/18 - 61*a**2/12 + 1370. Factor z(q).
-q*(q + 61)/6
Let a = 7915/87636 + -1/1308. Let j = 164/335 - a. Factor 7/5*k**3 - k**2 + 0 - j*k.
k*(k - 1)*(7*k + 2)/5
Suppose -2311 - 937 = 29*p. Let y be 6*(1/2)/(p/(-48)). Let y*f**2 + 0 + 6/7*f**3 + 0*f - 3/7*f**4 = 0. What is f?
-1, 0, 3
Let q = 4144637/11 - 376785. Solve 0*l**2 - q*l**3 + 2/11*l**4 + 0*l + 0 = 0 for l.
0, 1
Let h(r) be the second derivative of r**5/150 - r**4/6 - 9*r**2/2 + 3*r + 9. Let q(l) be the first derivative of h(l). Let q(n) = 0. Calculate n.
0, 10
Let m be (3/2)/(594/(-2448)). Let o = m - -564/77. Find z, given that -o*z**2 + 8/7*z**4 + 0 + 0*z + 4/7*z**3 - 4/7*z**5 = 0.
-1, 0, 1, 2
Let w(z) = 8*z**2 + 730*z + 1468. Let o(n) = -22*n**2 - 2190*n - 4404. Let y(g) = -5*o(g) - 14*w(g). Factor y(r).
-2*(r - 367)*(r + 2)
Let h(z) be the first derivative of -2*z**6/3 + 32*z**5/5 - 5*z**4 - 56*z**3/3 - 2782. Find j, given that h(j) = 0.
-1, 0, 2, 7
Find n, given that 5*n**2 + 18/11*n + 1/11*n**4 - 18/11*n**3 - 56/11 = 0.
-1, 1, 4, 14
Suppose 102 = 4*k + 15*s, 2*k - 5*s + s + 18 = 0. Factor -9/2*m + 0 - 3/2*m**k - 9/2*m**2 - 1/6*m**4.
-m*(m + 3)**3/6
Let f(r) be the second derivative of r**4/12 - 2309*r**3/3 + 5331481*r**2/2 - 28*r - 72. Solve f(q) = 0 for q.
2309
Let q be 8/(-12)*((-848)/1792 + (-4)/(-14)). Let v(c) be the first derivative of q*c**4 - 3 - 27/2*c + 27/4*c**2 - 3/2*c**3. Factor v(a).
(a - 3)**3/2
Let y be ((-8)/(-12))/((-62)/(-60) - 1). Factor 1373*u**2 - 2 - y*u + 2 - 2737*u**2 + 1366*u**2.
2*u*(u - 10)
Let r(q) = 11*q**2 + 34*q - 73. Let y be r(2). Let x(i) be the third derivative of -1/24*i**4 - 1/12*i**3 + 0*i - 1/120*i**5 + 0 - y*i**2. Factor x(f).
-(f + 1)**2/2
Suppose 8*x - 24 = 288. Determine m so that x - 4*m**4 + m**4 - 5*m**3 + 9 - 7*m**3 + 48*m = 0.
-2, 2
Let n be (-240130)/(-5698) - (40 + 0). Factor -n*x**2 + 9/7*x + 3/7*x**4 + 12/7 - 9/7*x**3.
3*(x - 4)*(x - 1)*(x + 1)**2/7
Factor -18*r + r**2 + r**3 - r**4 + 57*r - 16*r - 9*r - 15*r.
-r*(r - 1)**2*(r + 1)
Let b(g) be the third derivative of -g**8/756 - 2*g**7/105 - g**6/18 + 5*g**5/27 + 16*g**2 - 11. Factor b(d).
-4*d**2*(d - 1)*(d + 5)**2/9
Let o(l) = -l**3 + l**2 + l. Let r(g) = 19*g**3 - 95*g**2 - 45*g. Let p = 54 - 52. Let j(d) = p*r(d) + 18*o(d). Factor j(x).
4*x*(x - 9)*(5*x + 2)
Let b(c) be the first derivative of -2*c**3/15 - 109*c**2 + 4811. Factor b(p).
-2*p*(p + 545)/5
Let a = 837219 - 266235289/318. Let t = -50/53 + a. Factor t*k**2 + 5/6 - k.
(k - 5)*(k - 1)/6
Let o be 170/6 - (-4 - -6)/6. Suppose o = h + h. Suppose 3*u + 10 + 10*u**2 - u**3 - h*u**2 + 8 = 0. Calculate u.
-3, 2
Let z = 798 + -439. Factor 5*c**3 + z*c**2 - 347*c**2 - 3*c**3.
2*c**2*(c + 6)
Let w = 316 - 299. Let y be 15/3 + w + -22. Let 0*v**3 + y - 3/4*v**5 + 0*v**2 + 0*v**4 + 0*v = 0. What is v?
0
Suppose -2*l = -3*o + 125, -4*o + 166 = -6*l + 3*l. Let v be (-7)/3 + (46 - o). Suppose 6*s**3 + 0 - 2*s**5 - 2*s**2 - v*s**4 - 4/3*s = 0. What is s?
-2, -1/3, 0, 1
Find u such that 368/9 + 2/9*u**2 + 100/9*u = 0.
-46, -4
Solve -15*m**4 - 549*m - 324 + 699*m**5 - 11980*m**2 + 59*m**3 + 12211*m**2 - 701*m**5 = 0 for m.
-9, -4, -1/2, 3
Factor 75/2*v**2 - 9 - 79/6*v**3 + 3/2*v**4 - 63/2*v.
(v - 3)**3*(9*v + 2)/6
Let p(r) = 30*r**3 + 314*r**2 + 340*r + 66. Let g(y) be the second derivative of y**5/20 + y**4/12 + y**2/2 + 15*y + 1. Let m(z) = 10*g(z) - p(z). Factor m(a).
-4*(a + 1)*(a + 14)*(5*a + 1)
Let b(c) = 29*c**2 - 40*c - 109. Let w(s) = 7*s**2 - s + 2. Let p(q) = b(q) - 4*w(q). Factor p(l).
(l - 39)*(l + 3)
Let h be (-2)/6*(-271 + 271). Let l(d) be the second derivative of 0*d**2 - 3*d - d**4 + h + 1/2*d**3. Factor l(b).
-3*b*(4*b - 1)
Let j(n) be the third derivative of -2*n**3 - 2/135*n**5 + 0*n + 0*n**4 - 36*n**2 - 1/810*n**6 + 0. Let s(i) be the first derivative of j(i). Factor s(z).
-4*z*(z + 4)/9
Let c(a) be the first derivative of -9*a**3 + 2*a**4 + 4*a**3 + 3*a**4 + 2*a**5 - 3*a**5 - 91. What is d in c(d) = 0?
0, 1, 3
Suppose 12 = 3*o + 3*d - 15, 3*o - 2*d - 17 = 0. Factor 19*q**4 - 4*q**2 + 8*q**3 + o*q**5 + 61 - 61.
q**2*(q + 1)*(q + 2)*(7*q - 2)
Let p(f) = -15*f**3 + 9*f**2 + 13*f - 11. Let x = 242 + -244. Let t(n) = -75*n**3 + 45*n**2 + 64*n - 56. Let z(w) = x*t(w) + 11*p(w). Factor z(j).
-3*(j - 1)*(j + 1)*(5*j - 3)
Suppose -888 - 2/3*n**2 + 298*n = 0. What is n?
3, 444
Let x(q) be the third derivative of -q**5/360 - 59*q**4/144 + 943*q**3/18 - 5376*q**2. Factor x(h).
-(h - 23)*(h + 82)/6
Let c be (-117)/(-42)*20 - (-4)/14. Suppose 51*x + 300 = c*x. Suppose 3 + 10*z**2 + 30*z**4 + 5*z**5 + 3 + 55*z**3 - x*z - 46 = 0. What is z?
-2, -1, 1
Let g(m) be the second derivative of 0 + 47*m - 9/40*m**5 + 3/8*m**2 - m**3 + 13/16*m**4. Suppose g(t) = 0. What is t?
1/6, 1
Let b(r) be the second derivative of -r**6/30 - 21*r**5/20 + 23*r**4/6 - 77*r + 8. Factor b(k).
-k**2*(k - 2)*(k + 23)
Let h(j) be the first derivative of -j**6/360 + j**5/60 + 5*j**4/8 + 9*j**3/2 + j**2/2 - 14*j + 106. Let r(i) be the second derivative of h(i). Factor r(t).
-(t - 9)*(t + 3)**2/3
Let h = -34 + 52. Let b = 20 - h. Factor 15*y**b - 9 + 0 - 6*y**2 + 24*y.
3*(y + 3)*(3*y - 1)
Let l(m) be the second derivative of -m**6/15 - 2*m**5 - m**4/2 + 284*m**3/3 - 380*m**2 - 4648*m. Factor l(i).
-2*(i - 2)**2*(i + 5)*(i + 19)
Let g be (5 + (-5 - -1))/(128 + -122)*24. Factor 0 - 6/5*j**3 - 2*j - 18/5*j**2 + 2/5*j**g.
2*j*(j - 5)*(j + 1)**2/5
