 1)**2
Let r(a) be the first derivative of -5*a**7/42 - 4*a**6/3 - 6*a**5 - 40*a**4/3 - 40*a**3/3 - 4*a - 9. Let j(i) be the first derivative of r(i). Factor j(u).
-5*u*(u + 2)**4
Suppose -2*a + 475 = 17*a. Suppose -4*h = -a*h. Solve 2/9*o**2 - 2/9*o + h = 0 for o.
0, 1
Solve 12*d - 2*d**4 + 612 + 16*d**3 - 66*d - 212 + 6*d**2 - 43*d - 163*d = 0 for d.
-4, 2, 5
Suppose 0 = -104*l + 108*l - 4. Let w be (l/2)/(1/(4/8)). Factor 0*s - w*s**3 + 1/4*s**5 + 0 + 1/2*s**4 - 1/2*s**2.
s**2*(s - 1)*(s + 1)*(s + 2)/4
Let b(k) be the second derivative of k**6/15 + 3*k**5/10 + k**4/2 + k**3/3 + 72*k. Suppose b(z) = 0. What is z?
-1, 0
Determine x so that 12/7*x - 80/7 + 2/7*x**2 = 0.
-10, 4
Let h = -134248/5 + 26855. Find c, given that -3/5*c**4 + 0 - h*c**2 - 18/5*c**3 + 0*c = 0.
-3, 0
Let k(s) be the first derivative of -5*s**3 - 51*s**2/2 - 18*s + 224. Factor k(n).
-3*(n + 3)*(5*n + 2)
Let b(q) be the third derivative of -q**5/360 - 17*q**4/144 + 591*q**2. Suppose b(p) = 0. What is p?
-17, 0
Let r(b) be the first derivative of -b**8/210 + b**7/42 - b**6/20 + 7*b**5/120 - b**4/24 + 6*b**3 - 17. Let f(y) be the third derivative of r(y). Factor f(x).
-(x - 1)*(2*x - 1)**3
Suppose 4*f - 311 = -295. Let -33/2*l**2 - 5/4*l**3 - 2 - 11*l + 25/4*l**f = 0. Calculate l.
-1, -2/5, 2
Suppose 5*p - 5*x + 2 = 22, 3*p - 2 = -2*x. Factor 0*t**2 + 3*t**3 + 15*t + 12*t**2 + 6 + 0 + 0*t**p.
3*(t + 1)**2*(t + 2)
Let t = 1530 + -1526. Factor 15/4*k - 21/4*k**t + k**5 - 37/4*k**2 + 41/4*k**3 - 1/2.
(k - 2)*(k - 1)**3*(4*k - 1)/4
Let k(z) be the first derivative of -z**6/240 - z**5/60 - z**4/48 + z**2 - 6. Let l(c) be the second derivative of k(c). Let l(s) = 0. What is s?
-1, 0
Suppose -8*s + 5*s = -9. Factor 13 - s - 8*g - 32*g - 90 - 5*g**2.
-5*(g + 4)**2
Factor 1/6*h**4 - 3 - 7/2*h + 1/6*h**2 + 5/6*h**3.
(h - 2)*(h + 1)*(h + 3)**2/6
Find k, given that -204/7*k**2 + 3*k**3 + 96/7 + 276/7*k = 0.
-2/7, 2, 8
Let y(d) be the second derivative of d**7/42 + d**6/5 + 9*d**5/20 + 52*d. Determine q, given that y(q) = 0.
-3, 0
Find o such that 25/4*o - 5/4 - 25/4*o**4 + 25/2*o**3 + 5/4*o**5 - 25/2*o**2 = 0.
1
Let y be 0/((-1)/(-6) + (-33)/(-18) + -7). Solve -o**2 + 3/2*o**3 + 0 + y*o - 1/2*o**4 = 0 for o.
0, 1, 2
Determine l so that -50/3 + 70/3*l + 2/3*l**3 - 22/3*l**2 = 0.
1, 5
Let d(v) be the second derivative of -v**7/70 + v**6/40 + 3*v**5/10 - v**4/2 - 4*v**3 - 7*v**2 + 2*v. Let f(x) be the first derivative of d(x). Factor f(k).
-3*(k - 2)**2*(k + 1)*(k + 2)
Suppose 9*f + 9 = 54. Let c(y) = -y**4 - y**3 - y**2 - y - 1. Let n(r) = 5*r**3 + 30*r**2 + 5*r - 15. Let x(b) = f*c(b) + n(b). What is v in x(v) = 0?
-2, -1, 1, 2
Let p = 1313 - 1310. Find t, given that 2/9*t**5 + 0*t + 4/9*t**4 - 4/9*t**2 + 0 - 2/9*t**p = 0.
-2, -1, 0, 1
Let a be 10/16 + 96/(-384). Factor a*j**2 + 9/8*j + 0.
3*j*(j + 3)/8
Let w(l) be the third derivative of l**8/1512 + 4*l**7/945 + l**6/135 - l**5/135 - 5*l**4/108 - 2*l**3/27 + 4*l**2 - 4*l. Factor w(z).
2*(z - 1)*(z + 1)**3*(z + 2)/9
Let i(j) be the third derivative of j**8/20160 - j**6/720 - j**5/12 + 4*j**2. Let t(n) be the third derivative of i(n). Let t(x) = 0. Calculate x.
-1, 1
Let m(t) be the second derivative of -t**5/10 - 5*t**4/6 - 7*t**3/3 - 3*t**2 + 95*t. Suppose m(w) = 0. Calculate w.
-3, -1
Let 0 + 33/2*o + 3/2*o**2 = 0. What is o?
-11, 0
Let p(w) be the first derivative of w**5/50 - w**4/60 - w**3/10 + 10*w + 51. Let m(b) be the first derivative of p(b). Factor m(z).
z*(z + 1)*(2*z - 3)/5
Let f(r) be the second derivative of -4/9*r**3 + 1/18*r**4 + 4/3*r**2 + 0 - 5*r. Find d, given that f(d) = 0.
2
Suppose -7/2*u**3 + 0 + 14*u + 48*u**2 = 0. What is u?
-2/7, 0, 14
Let u = 10 + -8. Let w be 26/u - (0 + 0). Suppose -12*h + 27*h - w*h - 2*h**2 = 0. Calculate h.
0, 1
Let u be (-2)/(-3) + 12/9. Let i(w) = -w + 4. Let m be i(u). Factor k**m + k + 2*k**2 + k + k.
3*k*(k + 1)
Let n(u) be the second derivative of -u**4/8 - 77*u**3/2 - 17787*u**2/4 + 159*u. Factor n(f).
-3*(f + 77)**2/2
Let f(l) = -3*l + 6. Let r be f(10). Let v be -1 - ((-3570)/r)/(-7). Determine d, given that -1/4*d**4 - 27/2*d**2 + 27*d + 3*d**3 - v = 0.
3
Let g(p) be the third derivative of 0 + 5/336*p**8 + 1/8*p**6 + 0*p**3 - 7*p**2 + 0*p - 1/12*p**5 + 0*p**4 - 1/14*p**7. Factor g(s).
5*s**2*(s - 1)**3
Let d = 20/21 + 5/7. Let n = -12 + 14. Factor -6*s**n + 2/3 + d*s.
-(2*s - 1)*(9*s + 2)/3
Let d(z) = -z**2 - 13*z - 5. Let n be d(-5). Factor -17*m**2 - 8 + n*m - 6*m**4 + m + 56*m**3 - 18*m**4 + 4*m**5 - 47*m**2.
4*(m - 2)*(m - 1)**4
Let -3*x**5 - 2*x - 41/3*x**2 - 73/3*x**3 + 0 - 47/3*x**4 = 0. What is x?
-3, -1, -2/9, 0
Let y = -27311/5 + 5463. Factor -y*q**2 + 0*q + 4/5.
-4*(q - 1)*(q + 1)/5
Let r(k) be the third derivative of 0 + 1/20*k**4 + 1/100*k**5 + 0*k - 1/100*k**6 + 4*k**2 - 1/350*k**7 + 0*k**3. Factor r(a).
-3*a*(a - 1)*(a + 1)*(a + 2)/5
What is z in -5/3*z**4 - 28/3*z - 13/3*z**2 + 4 + 22/3*z**3 = 0?
-1, 2/5, 2, 3
Factor 2/3*z**4 + 128/3*z**2 + 0 - 32/3*z**3 + 0*z.
2*z**2*(z - 8)**2/3
Let k(r) = -r**2 - 3*r - 2. Let d(u) be the third derivative of 0*u - 5*u**2 + 1/12*u**4 + 1/3*u**3 + 0. Let w(z) = -4*d(z) - 5*k(z). Factor w(o).
(o + 1)*(5*o + 2)
Suppose 234*l + 45 - 508 = 239. Solve 8/7 - 24/7*n - 6/7*n**2 + 16/7*n**l + 6/7*n**4 = 0.
-2, 1/3, 1
Let t be (2 - (-14)/(-10))*126/81. Let s(p) be the first derivative of -2/3*p**2 + p**4 + t*p**5 - 6 + 0*p - 14/9*p**3 - 4/9*p**6. Solve s(l) = 0 for l.
-1, -1/4, 0, 1, 2
Factor 135/2*t**3 + 0*t + 243*t**2 + 3/2*t**5 - 24*t**4 + 0.
3*t**2*(t - 9)**2*(t + 2)/2
Suppose h + 30 = 4*h. Suppose 0 - h = -5*m. Determine a so that a - 31*a**m + a + 1 + 32*a**2 = 0.
-1
Let q be (-15)/(-10)*(2/4 - (-6)/(-108)). Determine t so that q + 1/6*t**2 + 2/3*t = 0.
-2
Let q = 8581/99 - 951/11. Find o such that 4/9*o**2 + 0*o**4 - 4/9 + 8/9*o**3 - q*o**5 - 2/3*o = 0.
-1, 1, 2
Let g(d) be the first derivative of 4*d**5 + 715*d**4/4 - 60*d**3 + 224. Factor g(a).
5*a**2*(a + 36)*(4*a - 1)
Suppose 16/3*c - 32 - 2/9*c**2 = 0. What is c?
12
Let t be 6/(-21)*-2 + (-52)/(-56). Let c(s) be the third derivative of t*s**4 + 0*s + 7/15*s**5 - 3*s**2 + 4/3*s**3 + 0. Factor c(b).
4*(b + 1)*(7*b + 2)
Let x(s) be the first derivative of s**4/2 - 412*s**3/3 - 415*s**2 - 416*s - 484. Factor x(n).
2*(n - 208)*(n + 1)**2
Let v(z) be the second derivative of z**7/168 + z**6/24 - 5*z**4/6 - z**3/6 + 5*z. Let u(i) be the second derivative of v(i). Determine f so that u(f) = 0.
-2, 1
Suppose 0*u + 2*u - 8 = 0. Suppose 3*c - b = 3, -2*c - b - 15 = u*b. Solve c*k**2 + 3/4*k**3 - 3*k + 0 = 0.
-2, 0, 2
Suppose -2*z - 14 = -4*s - 0*s, 0 = -4*z - s + 17. Suppose -g + 5*y - 3 = 2, 3 = 2*g + z*y. Factor -2/9*p**2 + 2/9*p**3 + 0 + g*p + 2/9*p**4 - 2/9*p**5.
-2*p**2*(p - 1)**2*(p + 1)/9
Suppose 3*a - 66 = -9. Suppose -2*z - a = -23. Factor 0 + 3/4*l**3 + 0*l - 3/2*l**z + 3/4*l**4.
3*l**2*(l - 1)*(l + 2)/4
Suppose 7*q**3 + 14*q**4 - 10096*q**2 - q**3 + 10034*q**2 + 40*q + 2*q**5 = 0. Calculate q.
-5, -4, 0, 1
Let j(r) be the second derivative of 6*r - 3/4*r**3 + 0 + 1/16*r**4 + 15/8*r**2. Factor j(l).
3*(l - 5)*(l - 1)/4
Suppose -21*v = -20*v + 1. Let f(j) = j**2 + j - 1. Let n(x) = 18*x**2 + 12*x - 21. Let l(k) = v*n(k) + 15*f(k). Let l(y) = 0. What is y?
-1, 2
Let u = -32085 + 32085. Factor 1/2*d**2 - 2*d + u.
d*(d - 4)/2
Suppose -7*d - 20 = -12*d. Suppose 4*l - 3*v + d - 24 = 0, 4*l - 5*v - 28 = 0. Factor 0*o + 0 + 3/2*o**l.
3*o**2/2
Find s such that -22*s**4 - 272*s**2 - 43*s**3 - 13*s**3 - 520*s - 300 + 18*s**4 = 0.
-5, -3, -1
Let c(g) = -2*g. Let u be c(-2). Let y = 10946/4565 - -2/913. Factor -12/5*r - 9/5 + y*r**3 + 3/5*r**u + 6/5*r**2.
3*(r - 1)*(r + 1)**2*(r + 3)/5
Let b(m) be the second derivative of 1/5*m**6 + 0*m**3 + 1/6*m**4 + 0 - 1/21*m**7 - 3/10*m**5 - 11*m + 0*m**2. Factor b(z).
-2*z**2*(z - 1)**3
Let i(v) = -13*v**2 - 79*v - 101. Let u(b) = -63*b**2 - 396*b - 501. Let k(t) = 24*i(t) - 5*u(t). Factor k(n).
3*(n + 1)*(n + 27)
Factor -18/7*v**2 + 2/7*v**4 + 0*v**3 + 0 + 0*v.
2*v**2*(v - 3)*(v + 3)/7
Let v be (-11 + 14)*(-2 + 3). Factor -3*n - 3*n**5 + 3*n - 3*n**3 - 9*n**4 - v*n**2 - 6*n**3.
-3*n**2*(n + 1)**3
Let f(b) be the first derivative of -b**4/24 - b**3/9 - b**2/12 + 15. Determine a, given that f(a) = 0.
-1, 0
Let g = 71 - 61. Let z be 504/32 - (-3)/(-