*3/(-14). Let l = 31021/7 + -4431. Factor -l*f + 2/7*f**2 + k.
2*(f - 1)**2/7
Suppose 0 = -4*f - 3*y + 4, f + 0*f + 3*y = -8. Find h, given that -4*h**2 + 9*h**2 + 10*h + 30*h**f - 35*h**3 - 6*h**2 - 4*h**2 = 0.
-1/2, 0, 2/3, 1
Let i(x) be the third derivative of -x**8/40320 - x**7/2160 - x**6/540 + x**5/45 + 5*x**4/12 - 24*x**2. Let v(j) be the second derivative of i(j). Factor v(s).
-(s - 1)*(s + 4)**2/6
Let a be -1 + 32 + 60/(-15). Suppose 10*z = z + a. Factor -2/3*w**2 + 0*w + 0 - 4/3*w**z - 2/3*w**4.
-2*w**2*(w + 1)**2/3
Let f(p) = -281*p - 279. Let z be f(-1). Determine h, given that 5/4 - 11/4*h + 7/4*h**z - 1/4*h**3 = 0.
1, 5
Let v(q) be the second derivative of q**9/3780 + q**8/420 + 2*q**7/315 + 11*q**4/12 + 9*q. Let t(r) be the third derivative of v(r). Factor t(x).
4*x**2*(x + 2)**2
Let p be (-8)/(-14) + 996/21. Let -p*b + 32 - 2*b**3 + 8*b**2 + 10*b**2 + b**3 - b**3 = 0. What is b?
1, 4
Let r = 6815 - 4579679/672. Let v(o) be the third derivative of -1/140*o**7 + 3*o**2 + r*o**8 - 1/120*o**5 + 0 + 0*o + 0*o**4 + 1/80*o**6 + 0*o**3. Factor v(x).
x**2*(x - 1)**3/2
Suppose 5*x + 7 = -3*l + 1, -3 = 3*l + 4*x. Let w be (-90)/(-150) + 3*-1 + 64/10. Factor -2/19*o**w + 0 + 0*o - 2/19*o**l + 4/19*o**2.
-2*o**2*(o - 1)*(o + 2)/19
Suppose 2/9*p**2 + 2 - 20/9*p = 0. Calculate p.
1, 9
Let d(y) be the third derivative of y**6/90 - 2*y**5/45 - y**4/18 + 4*y**3/9 + 54*y**2. What is l in d(l) = 0?
-1, 1, 2
Let j be (-2)/8 + (-184)/32 + 6. Let w(a) be the third derivative of 0 - 1/40*a**6 + 0*a + j*a**3 + 0*a**4 + 2/35*a**7 - 5*a**2 + 0*a**5. Factor w(t).
3*t**3*(4*t - 1)
Let s = -2/3299 - -3343/72578. Let r(d) be the first derivative of 0*d - s*d**4 - 4/33*d**3 + 9 - 1/11*d**2. Factor r(v).
-2*v*(v + 1)**2/11
Let u be (-14)/(-91) - 3828/(-468). Solve 10/3*w - u*w**5 + 5*w**3 + 35/3*w**2 + 0 - 35/3*w**4 = 0.
-1, -2/5, 0, 1
Let m(z) be the second derivative of -z**5/24 + 5*z**4/48 + 5*z**3/6 + 12*z**2 + 4*z. Let c(o) be the first derivative of m(o). What is y in c(y) = 0?
-1, 2
Let b(s) = -s**2 + 1. Let o(z) = z**3 + 4*z**2 - z - 4. Let t = 31 + -26. Let c(q) = t*o(q) + 20*b(q). Solve c(p) = 0.
-1, 0, 1
What is p in 2/7*p**2 + 108/7 + 30/7*p = 0?
-9, -6
Let c(q) be the third derivative of 3*q**7/56 - 19*q**6/120 + 23*q**5/120 - q**4/8 - q**3/6 + 3*q**2. Let g(l) be the first derivative of c(l). Factor g(n).
(3*n - 1)**2*(5*n - 3)
Let g be (1/(-4))/(3*10/(-360)). Let l(p) be the third derivative of 0 + 11*p**2 - 3/20*p**5 + 1/40*p**6 + 0*p + 1/4*p**4 + 0*p**g. What is z in l(z) = 0?
0, 1, 2
Let p = 5731 + -17191/3. Suppose p - 17/6*b**2 + 2/3*b**4 + 2*b - 1/2*b**3 = 0. Calculate b.
-2, -1/4, 1, 2
Let f be -3 + -2 + 2 + 3. Let r be ((-5)/10 + 0)*f. Solve r - 1/2*z**2 + 13/4*z**3 + 0*z = 0 for z.
0, 2/13
Let z(y) be the second derivative of -y**6/20 - 3*y**5/10 - 3*y**4/8 - 550*y. Find t such that z(t) = 0.
-3, -1, 0
Let q(y) = 5*y**2 - 3410*y + 194930. Let s(l) = 2*l**2 - 1137*l + 64977. Let t(p) = -3*q(p) + 10*s(p). Let t(a) = 0. What is a?
114
Let n(d) be the third derivative of -d**7/42 - 28*d**6/3 - 4181*d**5/4 + 140*d**4/3 + 31360*d**3/3 + 591*d**2. Let n(p) = 0. What is p?
-112, -1, 1
Let n(b) = 15*b**3 + 86*b**2 + 120*b + 49. Let p(a) = -5*a**3 - 29*a**2 - 40*a - 16. Let k(w) = -4*n(w) - 11*p(w). Solve k(u) = 0.
-2, -1
Let b(u) = 10*u**5 - 10*u**4 + 26*u**3 + 10*u**2 + 34*u + 28. Let s(j) = 2*j**5 - 2*j**4 + 6*j**3 + 2*j**2 + 7*j + 6. Let z(p) = 6*b(p) - 28*s(p). Factor z(k).
4*k*(k - 2)*(k - 1)*(k + 1)**2
Let -2/3*p**4 - 2/3*p**3 + 10/3*p + 4/3 + 2*p**2 = 0. What is p?
-1, 2
Suppose 6 = -5*g + 3*a, -2*g - g - 3*a + 6 = 0. Find y such that -3/2*y + g - 3/2*y**2 = 0.
-1, 0
Let l(f) be the first derivative of -f**8/336 - f**7/168 + f**6/18 + f**5/6 + 17*f**3/3 + 28. Let n(q) be the third derivative of l(q). Let n(h) = 0. What is h?
-2, -1, 0, 2
Let y be 2/14 + (-138)/(-3542). Factor 0 - 4/11*b**2 + 4/11*b**4 + y*b**5 + 0*b**3 - 2/11*b.
2*b*(b - 1)*(b + 1)**3/11
Find d such that -7*d**2 + 36*d - 2*d**2 - 354*d**3 - 3*d**2 + 3*d**4 + 345*d**3 = 0.
-2, 0, 2, 3
Suppose 2 - 3*d**3 + 7*d**2 + 43*d**2 - 115*d + 58*d**3 + 8 = 0. What is d?
-2, 1/11, 1
Let q be 2 + (3/(-60))/((-9)/(-306)). Let a(s) be the second derivative of 0*s**2 + q*s**5 + 1/5*s**6 - 7*s + 0*s**3 + 0 + 1/21*s**7 + 1/6*s**4. Factor a(z).
2*z**2*(z + 1)**3
Let f(w) be the first derivative of w**6/300 + w**5/100 + w**4/120 + 4*w**2 + 5. Let t(l) be the second derivative of f(l). Determine b, given that t(b) = 0.
-1, -1/2, 0
Let s(m) be the first derivative of -1/5*m**5 + 0*m + 1/4*m**4 + 5/3*m**3 + 3/2*m**2 + 3. Solve s(h) = 0 for h.
-1, 0, 3
Let g(m) = 289*m**2 - 3*m - 2. Let z be g(-1). Suppose 120*r + 16 + 2*r**5 + 120*r**4 + 5*r**5 + 11*r**5 + 300*r**2 + z*r**3 = 0. What is r?
-2, -1/3
Suppose 5*x = 0, 0 = -5*v - x + 6*x + 10. Let j(n) be the second derivative of 7/10*n**3 + 3/5*n**v + 1/4*n**4 + n + 0. Factor j(t).
3*(t + 1)*(5*t + 2)/5
Let c be 4 - (-2 + (-11097)/21). Let o = c + -533. Let 10/7*a + o*a**4 + 20/7*a**2 + 20/7*a**3 + 2/7 + 2/7*a**5 = 0. What is a?
-1
Factor 10*a**2 - 20*a**3 - 5*a**4 - 5*a**4 - 3*a**5 - 4*a**5 + 15*a + 3*a**5 + 9*a**5.
5*a*(a - 3)*(a - 1)*(a + 1)**2
Let o = 19 + -14. Suppose -3*n = -o - 4. Factor -72*d**2 + 2 - n - 1 - 24*d.
-2*(6*d + 1)**2
Suppose 5*z = -d - 8, 0 = -d - d - 4*z - 4. Let h be -3 + 3/d + (-5 - -8). Factor 6*w**2 - h*w - 9/2*w**3 + 0.
-3*w*(w - 1)*(3*w - 1)/2
Let 0 - 1/9*z**2 + 2/3*z = 0. What is z?
0, 6
Let k(o) be the second derivative of o**4/12 - o**2/2 - 45*o. Factor k(g).
(g - 1)*(g + 1)
Let 0 - 2/3*u**3 + 2/3*u + 0*u**2 = 0. What is u?
-1, 0, 1
Suppose -6/5*u + 0 - 27/5*u**3 + 3*u**4 - 3/5*u**5 + 21/5*u**2 = 0. Calculate u.
0, 1, 2
Let r be ((-8)/2)/(-1 + (-28)/4 + 6). Factor 9/2*q**3 + 0*q + 0 + 3/2*q**4 + 0*q**r.
3*q**3*(q + 3)/2
Let n(s) be the second derivative of 2*s + 1/3*s**3 + 0*s**2 + 1/12*s**4 + 0. Factor n(j).
j*(j + 2)
Let o = -63803/3828 - -1/1276. Let y = -97/6 - o. Find g, given that 5/4*g**4 - y*g**3 - 1 + 4*g - 15/4*g**2 = 0.
-2, 2/5, 1
Let j(h) be the second derivative of h**6/180 - h**5/30 + 4*h**3/9 - 4*h**2/3 + 645*h. Factor j(c).
(c - 2)**3*(c + 2)/6
Suppose -2 = 2*g + 18. Let x be (20/50)/((-2)/g). Factor -3*f**4 - 9*f**4 + 20*f**3 + 0*f**4 - 4*f + f**x - 5*f**2.
-4*f*(f - 1)**2*(3*f + 1)
Let h be 2/9*(-1 + 4). Let m = 10 - 7. Suppose -1/3*d**4 - h*d**m + 0*d**2 + 1/3*d**5 + 0 + 0*d = 0. What is d?
-1, 0, 2
Let j = -3725/3 - -1242. Find w such that 1/3*w**3 - 1/6*w + 1/3 - 2/3*w**2 - 1/6*w**5 + j*w**4 = 0.
-1, 1, 2
Solve 2/5*m**3 + 0 - 4/5*m - 2/5*m**2 = 0 for m.
-1, 0, 2
Let g(o) be the second derivative of -o**7/1050 + o**5/50 - o**4/15 - 7*o**3 + 3*o. Let u(k) be the second derivative of g(k). Determine r, given that u(r) = 0.
-2, 1
Let o = -15267/124 + 3840/31. Suppose 3/2*t - o*t**2 + 3/4*t**4 - 9/4*t**3 + 0 + 3/4*t**5 = 0. Calculate t.
-2, -1, 0, 1
Let q(r) be the second derivative of 8*r**6/45 - 61*r**5/60 - r**4/3 - 282*r. Factor q(w).
w**2*(w - 4)*(16*w + 3)/3
Let n(o) be the third derivative of -o**6/60 + o**5/10 + o**4/12 - o**3 - 323*o**2. Find p, given that n(p) = 0.
-1, 1, 3
Let q(x) be the second derivative of x**7/280 + x**6/80 + x**5/80 + 5*x**2/2 + 4*x. Let z(i) be the first derivative of q(i). Solve z(d) = 0 for d.
-1, 0
Let m(u) = -u**2 + 3*u - 6. Let i be m(0). Let o(k) = -10*k**2 - 18*k - 8. Let f(h) = 90*h**2 + 162*h + 72. Let p(t) = i*f(t) - 52*o(t). Factor p(a).
-4*(a + 1)*(5*a + 4)
Suppose 2*b - 7 = -b - 2*v, 2*v + 1 = 5*b. Let g be (b - 2)/(2/(-6)). Let 10/11*c + 4/11 + 6/11*c**2 - 2/11*c**g - 2/11*c**4 = 0. Calculate c.
-1, 2
Let a(v) = 12*v**3 - 16*v**2 + 8*v - 4. Suppose l - 8 = -5*u, -9 = u - 5*l + 5. Let x(i) = i**2 - i. Let k(h) = u*a(h) - 12*x(h). Factor k(z).
4*(z - 1)**2*(3*z - 1)
Let p(h) = h**3 - 4*h**2 + 4*h + 5. Let v(s) = -s**3 + 4*s**2 - 4*s - 4. Suppose 21 = 4*i + 5. Let r(l) = i*p(l) + 5*v(l). Determine a, given that r(a) = 0.
0, 2
Factor 34 + 134 + 153*b**2 + 30*b - 156*b**2.
-3*(b - 14)*(b + 4)
Let h(j) be the second derivative of 22*j - 3/10*j**5 - 1/15*j**6 - 1/3*j**3 + 0 - 1/2*j**4 + 0*j**2. Factor h(k).
-2*k*(k + 1)**3
Let l(a) be the first derivative of a**4/22 - 4*a**3/33 - a**2 + 24*a/11 + 37. Let l(v) = 0. What is v?
-3, 1, 4
What is o in -3/4*o**5