679/2. Suppose 5/6*y**2 - 1/6*y**4 + 1/6*y**5 - q*y**3 + 0 - 1/3*y = 0. Calculate y.
-2, 0, 1
Let d(n) be the third derivative of n**6/8 + 73*n**5/30 - 11*n**4/6 - 20*n**3/3 + 667*n**2 - n. Solve d(l) = 0 for l.
-10, -2/5, 2/3
Let v = 53 + -48. Suppose v*s = 4*k - 4, 1 = 3*s + k - 0. Factor 0*y**3 + s - 1/5*y + 2/5*y**2 + 1/5*y**5 - 2/5*y**4.
y*(y - 1)**3*(y + 1)/5
Let a(c) be the first derivative of 4*c**3/3 - 612*c**2 + 93636*c + 569. Let a(d) = 0. Calculate d.
153
Let u be (-440)/408*(-1)/6. Let w = u - -9/34. Factor w*f + 2*f**2 - 22/9*f**3 + 0.
-2*f*(f - 1)*(11*f + 2)/9
Solve 21*p**4 - 38*p**2 - 10*p - 74*p**3 - 60*p**3 + 87*p + 9*p**5 - 15 - 16*p**2 = 0 for p.
-5, -1, 1/3, 3
Let m(c) = c**3 - 20*c**2 + 29*c - 13. Let u be -3 + (2 + -2)/(-2). Let o(j) = 20*j**2 - 28*j + 12. Let z(a) = u*o(a) - 4*m(a). Suppose z(s) = 0. What is s?
1, 2
Suppose 0 = -8*h + 3*h + 10. Let k be (-4)/12*0 + h. Find o such that o + 14*o**3 + o**2 - 2 + 18*o**2 - k*o**2 = 0.
-1, -1/2, 2/7
Let m(q) = 32*q**2 - 86*q + 26. Let f(g) = -21*g**2 + 57*g - 17. Suppose 5*s = -2*x + 31, 4*x - 3*x = -4*s + 23. Let d(u) = s*m(u) + 8*f(u). Factor d(o).
-2*(o - 3)*(4*o - 1)
Let l be ((8 - -1) + -10)/(1 - 10). Factor -2/9*a + 1/3*a**2 + 0 + 1/9*a**5 - 1/3*a**4 + l*a**3.
a*(a - 2)*(a - 1)**2*(a + 1)/9
Let v(b) be the second derivative of -b**4/12 + b**3/3 - b**2/2 - 7*b + 7. Factor v(y).
-(y - 1)**2
Let k(u) = -u**4 - u**3 + u + 1. Let d(n) = 10*n - n**3 - 43*n**5 - 2*n**4 + 10 - 9*n**3 + 47*n**5. Let x(h) = -d(h) + 10*k(h). Factor x(b).
-4*b**4*(b + 2)
Let o(y) = 116*y**3 - 52*y**2 - 80*y + 12. Let z(g) = -117*g**3 + 54*g**2 + 80*g - 12. Let v(k) = -5*o(k) - 4*z(k). Factor v(l).
-4*(l - 1)*(4*l + 3)*(7*l - 1)
Let m(j) be the third derivative of -j**7/1680 + j**6/160 + 17*j**5/480 - j**4/32 - j**3/3 - 2*j**2 + 151*j. Solve m(y) = 0.
-2, -1, 1, 8
What is f in 2/19*f**2 - 176/19*f + 0 = 0?
0, 88
Let a = -37 + 37. Let p(j) be the first derivative of -1/16*j**4 + a*j - 1/12*j**3 + 0*j**2 - 7. Let p(z) = 0. What is z?
-1, 0
Factor 1/2*b**5 + 0 + 0*b + 17/2*b**3 + 5*b**4 + 4*b**2.
b**2*(b + 1)**2*(b + 8)/2
Let p(f) be the second derivative of -3/2*f**2 + 3*f + 11/12*f**4 + 7/60*f**6 + 0 - 8/15*f**5 - 2/3*f**3. Let w(q) be the first derivative of p(q). Factor w(m).
2*(m - 1)**2*(7*m - 2)
Factor 3/2*l**4 + 0 + 11*l - 53/2*l**2 + 14*l**3.
l*(l - 1)*(l + 11)*(3*l - 2)/2
Let r be ((-22)/(-308))/((-1)/(-7)). Factor 1/4 + r*z + 1/4*z**2.
(z + 1)**2/4
Let w be ((8/(-14))/2)/(2691/91 + -30). Factor 2*u + w*u**4 - 4/3 - 2*u**3 + 2/3*u**2.
2*(u - 2)*(u - 1)**2*(u + 1)/3
Factor 14/9*q**3 + 0*q + 2/3*q**2 + 0 + 2/9*q**5 + 10/9*q**4.
2*q**2*(q + 1)**2*(q + 3)/9
Let d(o) be the second derivative of o**5/270 - 5*o**4/108 - 12*o**2 + 17*o. Let p(h) be the first derivative of d(h). What is q in p(q) = 0?
0, 5
Let j = 79809/31045 - -3/4435. Suppose j*u - 2*u**2 - 4/7 = 0. Calculate u.
2/7, 1
Let j be 35 + 5 - (-3)/(-3). Factor 44*t**2 - t**3 - 5*t - j*t**2 + 6*t**3 - 5.
5*(t - 1)*(t + 1)**2
Let o be 1/(34/6)*(-82)/(-123). Factor -2/17*c**2 + o + 0*c.
-2*(c - 1)*(c + 1)/17
Let i(x) be the first derivative of x**6/51 + 2*x**5/17 + 7*x**4/34 - 2*x**3/51 - 8*x**2/17 - 8*x/17 + 37. Solve i(o) = 0.
-2, -1, 1
Suppose -2*l**2 + 2/11*l**4 - 12/11*l - 8/11*l**3 + 0 = 0. What is l?
-1, 0, 6
Let r(o) be the first derivative of o**3/18 - 139*o**2/12 + 23*o - 67. Solve r(i) = 0.
1, 138
Let o(n) = -n**2 - 6*n - 3. Let l(k) = -k**2 - 12*k - 5. Let x = -18 + 23. Suppose 3*q = -2*q - 15. Let t(j) = q*l(j) + x*o(j). Factor t(r).
-2*r*(r - 3)
Determine x, given that -1/7*x**2 + 5/7*x - 4/7 = 0.
1, 4
Let g(k) be the second derivative of k**3/6 - 11*k**2/2 - 16*k. Let d be g(14). Factor 0 + 2/9*c**4 + 0*c + 2/9*c**d + 0*c**2.
2*c**3*(c + 1)/9
Let k = 136/605 + -3/121. Let m(d) be the second derivative of 0 - k*d**5 + 1/3*d**3 + 1/21*d**7 + d**2 - d - 1/3*d**4 + 1/15*d**6. Find w such that m(w) = 0.
-1, 1
Let s(j) = 36*j**3 + 94*j**2 + 144*j - 10. Let n(d) = -11*d**3 - 31*d**2 - 48*d + 3. Let k(v) = -20*n(v) - 6*s(v). Determine z, given that k(z) = 0.
-12, -2, 0
Let x(y) be the second derivative of y**8/2240 + y**7/280 - y**6/240 - 3*y**5/40 - 3*y**4/4 + 22*y. Let p(c) be the third derivative of x(c). Factor p(w).
3*(w - 1)*(w + 1)*(w + 3)
Let i(s) = s**3 - 6*s**2 + 7*s - 6. Let q be i(5). Suppose -3*g - 4*v = 0, 3 - 31 = -4*g + q*v. Solve 2*r**4 + r**4 + r**g = 0 for r.
0
Let l(s) = -11*s**3 - 2*s**2 + s. Let p(r) = 30*r**3 + 6*r**2 - r + 1. Let k(t) = -11*l(t) - 4*p(t). Let k(f) = 0. What is f?
-1, 4
Suppose -7*w + 166 = -2. Factor 27*b**2 + 9*b**2 + w*b - 6*b**3 + 24*b**3 + 3*b**4.
3*b*(b + 2)**3
Let q(h) = 5 - 4 + 2*h + h**2 + 0. Let n(s) = s + 1. Let l(o) = 4*n(o) - 2*q(o). Factor l(f).
-2*(f - 1)*(f + 1)
Suppose 2*m + 406 = 3*c, -4*m = 3*c - 0*c - 394. Let a = c - 132. Let -4/11 + 6/11*t + 18/11*t**4 + 50/11*t**3 + 42/11*t**a = 0. Calculate t.
-1, 2/9
Let c be 12/(-40)*65/(-13). Factor c*z + 1/4*z**2 + 5/4.
(z + 1)*(z + 5)/4
Let d = -97 - -489/5. Let x be -1 - (12/(-10))/(8/20). Factor -4/5*i - 1/5*i**3 - d*i**x + 0.
-i*(i + 2)**2/5
Let j(m) = 884*m - 5304. Let h be j(6). Suppose -3/4*k**2 + h*k + 0*k**4 + 9/8*k**3 - 3/8*k**5 + 0 = 0. What is k?
-2, 0, 1
Let z(l) = -14*l**4 - 126*l**3 - 1792*l**2 + 126*l + 1794. Let t(h) = 26*h**4 + 251*h**3 + 3585*h**2 - 251*h - 3589. Let x(b) = 6*t(b) + 11*z(b). Factor x(s).
2*(s - 1)*(s + 1)*(s + 30)**2
Let s be -1 + 2 + 3/(-3). Let s - 13 + 0 - 116*b**2 - 11 - 100*b - 40*b**3 = 0. What is b?
-3/2, -1, -2/5
Let l = 2028 - 2028. Let g = 2 + 0. Factor 3*b**g + l + b + 5/4*b**3.
b*(b + 2)*(5*b + 2)/4
Let z(b) be the second derivative of 2*b**7/189 - 4*b**6/135 + 2*b**4/27 - 2*b**3/27 - 10*b + 2. Solve z(h) = 0 for h.
-1, 0, 1
Let j(z) be the first derivative of -3*z**4/16 - 2*z**3 - 57*z**2/8 - 9*z - 71. Factor j(p).
-3*(p + 1)*(p + 3)*(p + 4)/4
Let u = 31826 + -31826. Factor 0*n**2 - 3*n**4 + u*n - 3/2*n**5 + 0 - 3/2*n**3.
-3*n**3*(n + 1)**2/2
Let k(u) be the second derivative of u**5/10 - 2*u**4/3 + 5*u**3/3 - 2*u**2 - 95*u. What is r in k(r) = 0?
1, 2
Suppose -4*z + 16 = -0*z. Find b such that -7*b**2 + 5*b**5 + 7 + 5*b - 3*b**2 - 2 + 5*b**z - 10*b**3 = 0.
-1, 1
Let s = -330 + 6284/19. Factor -10/19*f**3 - 2/19*f**4 - s*f - 4/19 - 18/19*f**2.
-2*(f + 1)**3*(f + 2)/19
Factor 0 - 20/3*o**2 + 1/3*o**3 + 19/3*o.
o*(o - 19)*(o - 1)/3
Let d(i) = 18*i - 447. Let h be d(25). Let z = 1 - 1. Factor 0*c + z*c**2 - 1/2*c**h + 0.
-c**3/2
Let r(b) = b**3 - 10*b**2 + 14*b + 18. Let p be r(8). Let g be (9/6)/(5/p). Factor -3/5*a**3 - g*a**2 + 0 + 0*a.
-3*a**2*(a + 1)/5
Let t be 2*(21*(-32)/(-132) + -5). Factor 0 - 2/11*m**5 - 2/11*m**4 + 2/11*m**2 + 0*m + t*m**3.
-2*m**2*(m - 1)*(m + 1)**2/11
Let z(x) be the third derivative of 0 + 1/18*x**4 + 1/180*x**5 + 8*x**2 + 1/6*x**3 + 0*x. Factor z(c).
(c + 1)*(c + 3)/3
Factor 30/11 - 2/11*v**3 - 62/11*v + 34/11*v**2.
-2*(v - 15)*(v - 1)**2/11
Find a, given that 0 + 26/7*a**2 + 60/7*a - 2/7*a**3 = 0.
-2, 0, 15
Suppose -6*u + 14 = u. Let t(z) be the second derivative of 0*z**u + 0 + 5*z + 1/45*z**3 + 1/90*z**4. Factor t(n).
2*n*(n + 1)/15
Let 0 + 15/2*c - 5/6*c**2 = 0. Calculate c.
0, 9
Let w be (-4)/8*3*(-42)/9. Suppose x = 2*x - w*x. Factor -2/19*a**4 + 0*a**2 + x*a + 0 + 0*a**3.
-2*a**4/19
Let l(a) be the third derivative of a**6/30 - a**5 + 8*a**4 + 128*a**3/3 - 232*a**2. Find i, given that l(i) = 0.
-1, 8
Let v(j) be the third derivative of 13*j**2 + 0 + 1/30*j**5 + 0*j + 0*j**3 - 1/6*j**4. Factor v(h).
2*h*(h - 2)
Let j = 1/24112 - 37301269/120560. Let p = -307 - j. Determine k so that -p + 9/5*k**2 + 3/5*k**4 - 12/5*k**3 + 12/5*k = 0.
-1, 1, 2
Let m be 2/105*-3 - 81/(-405). Factor -16/7 - m*p**2 - 8/7*p.
-(p + 4)**2/7
Let o(s) be the first derivative of -3*s**4/4 - 11*s**3 - 21*s**2/2 + 441*s + 218. Let o(r) = 0. Calculate r.
-7, 3
Let w(g) = 2*g**2 - 10*g + 4. Let q be w(5). Suppose 8*l - q*l - 8 = 0. Factor 12/5 - 12/5*c + 3/5*c**l.
3*(c - 2)**2/5
Let x(d) = -2*d + 46. Let m be x(18). Suppose -m = -34*v + 29*v. Determine o so that -1/6*o**v + 0 - 2/3*o = 0.
-4, 0
Let u(d) = 5*d**5 + 60*d**4 + 70*d**3 - 10*d**2 - 100*d + 25. Let o(q) = -q**5 + q**4 + q**3 - 3*q**2 + q - 1. Let y(i) = -25*o(i) - u(i). Solve y(m) = 0.
-1, -3/4, 0, 1, 5
Let h(b) be t