 1)**4/3
Suppose 7*n - 8 = 3*n. Let 20*c + 9*c + n*c**2 - c + 98 = 0. Calculate c.
-7
Factor 129/5*l**2 + 3/5*l**3 + 0 - 132/5*l.
3*l*(l - 1)*(l + 44)/5
Suppose -28 + 337/3*v - 424/3*v**2 - 2/3*v**4 + 173/3*v**3 = 0. Calculate v.
1/2, 1, 84
Let x be ((3240/(-105))/24)/(1/(-7)). Factor -4*y**3 + x*y**2 + 0*y + 1/2*y**4 - 27/2.
(y - 3)**3*(y + 1)/2
Let a(l) be the first derivative of -2197*l**6/180 + 169*l**5/15 - 13*l**4/3 + 8*l**3/9 + 5*l**2/2 + 3. Let i(x) be the second derivative of a(x). Factor i(d).
-2*(13*d - 2)**3/3
Let b(f) be the first derivative of -f**4/26 + 40*f**3/39 + 67*f**2/13 + 92*f/13 + 183. Determine t so that b(t) = 0.
-2, -1, 23
Let q(g) be the third derivative of g**2 + 4/15*g**5 + 0 + 4/3*g**3 + 0*g + 5/6*g**4 + 1/30*g**6. Factor q(n).
4*(n + 1)**2*(n + 2)
Suppose 3*k = 3, 49*g = 44*g + 2*k + 13. Let z(y) = 3*y - 4. Let s be z(3). Suppose 30*i - 245/4*i**g - s - 105/4*i**2 = 0. What is i?
-1, 2/7
Let u(v) = -22 + 6*v**2 + 4*v**3 - 21*v - 5*v**3 + 14*v**2 + 3*v**2. Let p be u(22). Factor 0*f - 2/5*f**4 - 2/5*f**3 + 0*f**2 + p + 4/5*f**5.
2*f**3*(f - 1)*(2*f + 1)/5
Factor 12*d**3 - 95*d**4 + 116*d**4 - 1 + 1.
3*d**3*(7*d + 4)
Let 3*a**3 + 9770*a**4 + 52*a**2 - 50 - 9772*a**4 - 3*a**3 = 0. What is a?
-5, -1, 1, 5
Factor 36*x - 4*x**2 + x + 11*x - x**2 + 2*x.
-5*x*(x - 10)
Suppose -6*h - 78 = -3*h. Let a = h - -31. Let -9*f**3 + 0 - 12*f**4 + 0*f**2 + 3/2*f - 9/2*f**a = 0. Calculate f.
-1, 0, 1/3
Factor 1/2 + 1/6*w**2 + 2/3*w.
(w + 1)*(w + 3)/6
Suppose -144/13*d**5 + 10/13*d - 244/13*d**3 + 54/13*d**2 + 328/13*d**4 - 4/13 = 0. Calculate d.
-2/9, 1/2, 1
Let a(v) be the third derivative of v**5/60 - v**4/24 - v**3/2 + 6*v**2. Let s(k) = -k + 1. Let h(b) = 3*a(b) - 3*s(b). Factor h(i).
3*(i - 2)*(i + 2)
Suppose 64 = u - 12. Let o be (u/16 + -4)/(21/8). Factor -o*t + 0 - 2/7*t**2.
-2*t*(t + 1)/7
Let j be 2660/(-11) - (-6)/(-3). Let i = 244 + j. Factor 4/11 - i*s - 2/11*s**2.
-2*(s - 1)*(s + 2)/11
Let o(d) be the third derivative of d**5/480 + d**4/12 + 4*d**3/3 - 3*d**2 + 10. Solve o(b) = 0 for b.
-8
Suppose 0 + 2/7*z**3 - 20/7*z**2 + 18/7*z = 0. What is z?
0, 1, 9
Let v(a) be the first derivative of -17/9*a**3 + 1/12*a**4 + 27*a + 16 + 21/2*a**2. Factor v(h).
(h - 9)**2*(h + 1)/3
Factor 7/2*a**2 + 27/4*a**3 - 1/4*a**5 + 0 + 0*a + 3*a**4.
-a**2*(a - 14)*(a + 1)**2/4
Let z(y) be the third derivative of y**8/588 - 8*y**7/735 - y**6/70 + 2*y**5/15 - 4*y**4/21 + 14*y**2 + 2. Find m such that z(m) = 0.
-2, 0, 1, 4
Let a(i) be the second derivative of -i**5/90 + 5*i**4/54 + 22*i**3/27 + 16*i**2/9 - 321*i. Factor a(t).
-2*(t - 8)*(t + 1)*(t + 2)/9
Let x(a) be the second derivative of -a**8/26880 - a**7/10080 - 11*a**4/12 - 9*a. Let j(f) be the third derivative of x(f). Find d, given that j(d) = 0.
-1, 0
Let -4*z - 50/13*z**2 + 0 + 54/13*z**3 + 50/13*z**4 - 2/13*z**5 = 0. What is z?
-1, 0, 1, 26
Let p(r) = 5*r**3 + 2*r**2 - 2. Let u be p(1). Factor -s**3 + 0*s**3 + 0*s**5 - 2*s**5 + 3*s**u.
s**3*(s - 1)*(s + 1)
Factor 0 + 9/5*v**2 - 1/10*v**3 - 13/2*v.
-v*(v - 13)*(v - 5)/10
Let j(u) be the second derivative of -42*u - 9/2*u**5 + 160*u**2 + 485/12*u**4 + 1/6*u**6 + 0 - 120*u**3. Factor j(n).
5*(n - 8)**2*(n - 1)**2
Let a(i) be the third derivative of -i**9/12096 - i**8/1008 - 5*i**7/1008 - i**6/72 + i**5/12 + 6*i**2. Let s(z) be the third derivative of a(z). Factor s(o).
-5*(o + 1)**2*(o + 2)
Let r = -4 + 6. Factor 15*l - 7 - r*l**2 - 1 + 0 - 5*l.
-2*(l - 4)*(l - 1)
Let o be 9/(3 + -66) + 568/840. Solve 2/15 + 2/3*i**4 + 8/15*i - 4/5*i**2 - o*i**3 = 0 for i.
-1, -1/5, 1
Let s be (24/(-7) - -4)/(15/((-420)/(-8))). Solve 3*w**2 - 2*w + 1/2 - s*w**3 + 1/2*w**4 = 0.
1
Let 0 + 28*r - 2/3*r**2 = 0. Calculate r.
0, 42
Let n(j) be the second derivative of -j**6/150 - 3*j**5/100 + j**4/20 + 7*j**3/30 - 3*j**2/5 + j - 314. Factor n(b).
-(b - 1)**2*(b + 2)*(b + 3)/5
Let d = -1 - -9. Factor -10*p - d*p**2 + 2*p**4 - 4*p**4 + 4 + 2*p**3 + 17*p**2 - 3*p**2.
-2*(p - 1)**3*(p + 2)
Let a(o) be the third derivative of 3*o**7/140 - 7*o**6/80 + 3*o**5/40 + 3*o**4/16 - o**3/2 - 65*o**2. Determine i, given that a(i) = 0.
-2/3, 1
Let v(t) be the first derivative of -t**8/1008 + 2*t**7/315 - t**6/72 + t**5/90 - 17*t**2/2 - 10. Let s(b) be the second derivative of v(b). Factor s(f).
-f**2*(f - 2)*(f - 1)**2/3
Let z be (-77)/(-5) - 2/5. Let -3*b**4 + 22*b**4 + 8*b**3 - z*b**4 = 0. What is b?
-2, 0
Let w(u) = -u**2 + 149*u + 3380. Let d be w(-20). Suppose d - c - 1/4*c**2 = 0. Calculate c.
-4, 0
Let y(m) be the first derivative of m**4/24 + m**3/12 - m**2/2 + 11*m + 9. Let b(s) be the first derivative of y(s). Factor b(f).
(f - 1)*(f + 2)/2
Let c(s) = -17*s**3 - 396*s**2 + 54666*s - 2460384. Let m(q) = 2*q**3 - q**2 + q + 1. Let f(a) = -2*c(a) - 18*m(a). Factor f(h).
-2*(h - 135)**3
Let i(v) be the first derivative of 10*v - 5/3*v**3 + 5/2*v**2 - 3. Factor i(n).
-5*(n - 2)*(n + 1)
Suppose 12*k = -57 + 129. Let x(c) be the second derivative of 0 - 1/3*c**4 + 1/15*c**k + 0*c**3 + 0*c**5 + 2*c + c**2. Determine z so that x(z) = 0.
-1, 1
Let y(d) be the first derivative of -d**4/14 - 74*d**3/21 + 38*d**2/7 + 284. Factor y(t).
-2*t*(t - 1)*(t + 38)/7
Let x(d) = -15*d**4 + 38*d**3 - 26*d**2 - 40*d. Let b(c) = -2*c**3 - c**2. Let s(f) = 6*b(f) - x(f). Factor s(j).
5*j*(j - 2)**2*(3*j + 2)
Suppose -11*g - 18 = -4*f - 12*g, -2*g = 4. Let v be (f - 11/2)*-10. Let 8/11*n**4 + 2/11*n + 0 + 12/11*n**3 + 2/11*n**v + 8/11*n**2 = 0. Calculate n.
-1, 0
Let t(n) be the first derivative of n**6/30 - 7*n**5/60 + n**4/12 + 5*n**3/3 - 7. Let l(i) be the third derivative of t(i). Factor l(f).
2*(f - 1)*(6*f - 1)
Let l(a) = -14*a - 64. Let z be l(-8). Suppose 24 - z = -8*w. Determine j, given that 10/7*j**5 + 0 - 4/7*j**2 + 4/7*j**4 + 0*j - 10/7*j**w = 0.
-1, -2/5, 0, 1
Let f be 2*9/15 - (-22 + 12 + 10). Find n such that -2/5*n**2 + 0 + f*n = 0.
0, 3
Suppose -h = -4 - 4. Determine u so that 0*u - 8 - h*u**2 - 2*u**2 - 18*u = 0.
-1, -4/5
Determine o so that 35/6*o**3 + 10*o + 0 + 5/6*o**4 + 40/3*o**2 = 0.
-3, -2, 0
Let s(j) be the second derivative of j**4/30 + 16*j**3/15 + 48*j**2/5 - 45*j + 1. Factor s(y).
2*(y + 4)*(y + 12)/5
Solve -86*b**2 - 124*b**2 + 54*b**3 + 60*b + 53*b**3 + 25*b**2 - 92*b**3 = 0 for b.
0, 1/3, 12
Suppose -12 = -119*x + 27 + 437. Factor -1/2*b**2 - x*b - 8.
-(b + 4)**2/2
Let s(b) = -2*b**2 + 33*b - 43. Let i(r) = -3*r + 1. Let d(g) = 3*i(g) + s(g). Find k, given that d(k) = 0.
2, 10
Let j(b) = 2*b**5 - b**4 - b**2 - 1. Let r(w) = 9*w**5 - 6*w**4 + 3*w**3 + 2*w - 5. Let x(m) = -5*j(m) + r(m). Find n, given that x(n) = 0.
-1, 0, 2
Let i = 356 - 1057/3. Let y = -19/6 + i. Factor 0*a**2 - y*a**3 + 1/4*a**5 + 1/4*a**4 + 0*a + 0.
a**3*(a - 1)*(a + 2)/4
Let r(h) be the second derivative of 9*h**7/1540 - h**6/110 + h**5/165 + h**4/3 + 3*h. Let v(y) be the third derivative of r(y). Suppose v(u) = 0. Calculate u.
2/9
Let h(o) be the first derivative of 4/7*o - 1/7*o**3 - 4 + 0*o**2 + 1/28*o**4. Factor h(w).
(w - 2)**2*(w + 1)/7
Let r(x) = x**2 - 44*x + 147. Let v(n) = 12*n**2 - 573*n + 1911. Let h be ((-14)/4 + 2)*8/(-6). Let s(g) = h*v(g) - 27*r(g). Find a such that s(a) = 0.
7
Let g(i) be the third derivative of -i**8/756 + 8*i**7/315 - 7*i**6/90 + 2*i**5/27 + 21*i**2 - 9*i. Solve g(h) = 0.
0, 1, 10
Let o(y) be the second derivative of 9*y**5/10 + 47*y**4/6 + 46*y**3/3 + 8*y**2 + 59*y - 2. Factor o(j).
2*(j + 1)*(j + 4)*(9*j + 2)
Factor 16/9 + 4/3*m + 2/9*m**2.
2*(m + 2)*(m + 4)/9
Suppose 5*q - 35 = 5*n, -3*n = 7 + 8. Let x = 2 - q. Suppose -6*j**2 + x*j - 8*j**3 + 6*j**3 - 4*j = 0. Calculate j.
-2, -1, 0
Let g(b) = -b**3 - b**2 + b - 1. Let w(s) = 6*s**3 + 22*s**2 + 58*s - 76. Let h(m) = -15*g(m) - 3*w(m). Factor h(f).
-3*(f - 1)*(f + 9)**2
Let s be (-8)/(-2) + 4 + -3. Let w(o) be the first derivative of -4/11*o**3 + 3 - 2/11*o + 2/11*o**4 + 4/11*o**2 - 2/55*o**s. Factor w(p).
-2*(p - 1)**4/11
Let t = 186 + -2231/12. Let r(q) be the first derivative of -1/2*q**2 + t*q**3 - 1 + q. Factor r(f).
(f - 2)**2/4
Factor 78*u + 5*u**2 - 120 - 36*u**2 + 3*u**3 + 70*u**2.
3*(u - 1)*(u + 4)*(u + 10)
Let l(d) = 11 + d**4 + 3*d**4 - 12 - 3*d**4. Let s(w) = -50*w**4 - 80*w**3 - 90*w**2 - 40*w + 20. Let x(y) = -25*l(y) - s(y). Factor x(h).
5*(h + 1)**3*(5*h + 1)
Let z(h) be the fir