ine a so that -2 + 833*a + 4 + 2*a**3 - 826*a + n*a**2 = 0.
-2, -1, -1/2
Let r = -215 + 103. Let h be (-8)/(-10) + r/240. Factor h*j**4 - 1/3*j - 1/3*j**5 + 2/3*j**3 + 1/3 - 2/3*j**2.
-(j - 1)**3*(j + 1)**2/3
Let d be 11/44 + 11/4. Let s(n) = n - 1. Let v be s(5). Suppose -9*a**v - 56*a**2 - 35*a**d - 28*a**3 + 8*a**2 - 12*a - 18*a**4 = 0. Calculate a.
-1, -2/3, 0
Let a(b) be the second derivative of -b**7/10080 + b**6/2880 + b**5/80 - b**4/12 + 11*b. Let i(d) be the third derivative of a(d). Solve i(z) = 0 for z.
-2, 3
Let n be (-104)/(-12) - 4/6. Suppose -n = -4*f - 0. Determine l, given that 0*l**f + 7*l - 3*l + 4*l**2 + l**3 = 0.
-2, 0
Let z(p) be the first derivative of p**3/3 + 9*p**2 + 17*p + 6. Factor z(v).
(v + 1)*(v + 17)
Let x be 4/(-22) - (150306/(-19800))/41. Let z(y) be the third derivative of -1/120*y**4 - 2*y**2 - 1/15*y**3 + x*y**5 + 0*y + 0. Factor z(b).
(b - 2)*(b + 1)/5
Let m(r) be the second derivative of r**6/120 - r**5/4 - 23*r**4/48 + 7*r**3/4 + 40*r - 1. Factor m(j).
j*(j - 21)*(j - 1)*(j + 2)/4
Suppose 2*j = -2*w + 4, 4 = 3*w - 0*j + 4*j. Let t be (w - 1)*800/540. Factor -2/9*d**4 - 16/9 - 4*d**2 + 14/9*d**3 + t*d.
-2*(d - 2)**3*(d - 1)/9
Suppose -13*s + 2*s + 55 = 0. Suppose -s*k + 12 = 2*m, 0 = 3*k - 3*m - 3. Factor 2/7*i**k + 0*i + 0.
2*i**2/7
Suppose -4*l = -20 - 32. Let l*p**2 + 0*p + 20 - 8*p**2 + 20*p = 0. Calculate p.
-2
Let s(h) be the third derivative of -1/15*h**3 - 1/200*h**6 + 7*h**2 + 2/75*h**5 + 0 - 1/40*h**4 + 0*h. Factor s(m).
-(m - 2)*(m - 1)*(3*m + 1)/5
Let m be 2/(-64)*-14*41/(287/84). Factor -m*w**2 - 343/4 + 1/4*w**3 + 147/4*w.
(w - 7)**3/4
Let d(w) be the second derivative of -w**7/1400 - w**6/150 - 3*w**5/200 + 7*w**3/3 - 3*w. Let c(q) be the second derivative of d(q). Find p such that c(p) = 0.
-3, -1, 0
Find w, given that -6*w**2 - 26/5*w - 14/5*w**3 - 8/5 - 2/5*w**4 = 0.
-4, -1
Factor 22/7*b**2 + 8/7 + 2/7*b**5 - 24/7*b - 2/7*b**3 - 6/7*b**4.
2*(b - 2)*(b - 1)**3*(b + 2)/7
Suppose 3*h = -2*h - 10. Let o be (-2)/(1 + h) - (-5)/(-3). Solve 0*k + 1/3 - o*k**2 = 0 for k.
-1, 1
Let p(r) be the third derivative of 0 + 3/20*r**5 - 24*r**2 - 1/120*r**6 - 25/6*r**3 - 5/8*r**4 + 0*r. Solve p(s) = 0.
-1, 5
Factor -4*u**2 + 16 + 2124*u - 2124*u.
-4*(u - 2)*(u + 2)
Suppose 3*x - 4*r - 13 = 0, 4 = 3*r - 7*r. Factor 15*c - 8*c + 9*c**x + 15*c**2 - 20 + 21.
(c + 1)*(3*c + 1)**2
Let k(h) = 9*h**4 - 14*h**3 - 4*h**2 + 14*h + 1. Let x(f) = 28*f**4 - 43*f**3 - 13*f**2 + 43*f + 2. Let i(p) = -17*k(p) + 6*x(p). Factor i(n).
5*(n - 1)**2*(n + 1)*(3*n - 1)
Let m = 275 + -272. Let y(o) be the first derivative of -1/2*o - 2/3*o**m - o**2 - 3. Find k, given that y(k) = 0.
-1/2
Suppose -v + 24 = -0*y + 4*y, -4*y + 24 = -5*v. Suppose -10 = -3*q - 1. What is a in 0*a**3 - 2*a**q - 4*a**2 - 8*a + y*a**3 = 0?
-1, 0, 2
Suppose -2*n + 2 + 2 = 0. Let x be (13 - 14)/((-2)/(-1))*0. Factor x*a**2 - 56*a**3 - 18*a**n - 4*a - 3*a**2 - 9*a**2.
-2*a*(4*a + 1)*(7*a + 2)
Let v(m) be the first derivative of 16 - 2/7*m - 2/7*m**3 + 3/7*m**2 + 1/14*m**4. Suppose v(a) = 0. What is a?
1
Let w be 5/(-2)*3*(-4)/10. Determine u so that 0*u**2 + 5*u**2 + 31*u**3 - 6 - u + u**2 - 30*u**w = 0.
-6, -1, 1
Let r(u) be the second derivative of 2*u**7/21 + 14*u**6/15 + 8*u**5/5 - 16*u**4/3 - 2*u + 108. Factor r(n).
4*n**2*(n - 1)*(n + 4)**2
Find u, given that 3660*u + 2*u**2 + 73926 + 265682 + 3*u**2 - 1090*u - 9363 = 0.
-257
Suppose 165/2*m - 25/2*m**3 - 45*m**2 - 25 = 0. What is m?
-5, 2/5, 1
Let x be (-314)/(-18) - 8/18. Suppose 9 = 5*m + 4*j - x, -5*m - 5*j + 30 = 0. Factor -4/3*g + 0 + 8/3*g**3 + 2/3*g**2 - m*g**4.
-2*g*(g - 1)**2*(3*g + 2)/3
Let d(c) be the third derivative of -c**9/120960 - c**8/13440 + c**6/360 - 7*c**5/60 + 36*c**2. Let i(u) be the third derivative of d(u). Factor i(j).
-(j - 1)*(j + 2)**2/2
Suppose 0 = -4*s + 8, -o - 2*s = -0*o - 6. Suppose -3*t = -2*b + 1, o*t = -0*t + b + 1. Find a, given that -24*a**3 + 6*a + t*a**2 + 27*a**3 + 6*a**2 = 0.
-2, -1, 0
Let b(h) = -h**3 + 12*h**2 - 34*h - 4. Let s(t) = 5*t**3 - 60*t**2 + 169*t + 22. Let j(k) = 22*b(k) + 4*s(k). Suppose j(n) = 0. What is n?
0, 6
Factor 2/11*f**4 + 10092/11*f**2 - 232/11*f**3 - 195112/11*f + 1414562/11.
2*(f - 29)**4/11
Let z(g) be the third derivative of g**7/210 + 23*g**6/120 - 49*g**5/60 + 25*g**4/24 - 131*g**2. Factor z(j).
j*(j - 1)**2*(j + 25)
Let s = 54332/9783 - -2/1087. Solve -s - 2/9*t**3 - 10/3*t + 2*t**2 = 0.
-1, 5
Let u(f) be the first derivative of f**4/2 + 2*f**3 + 3*f**2 + 2*f - 74. Find b, given that u(b) = 0.
-1
Let o(p) be the first derivative of p**3 + 3*p**2 + 3*p - 76. Determine r so that o(r) = 0.
-1
Factor -1/3*l**5 - 3*l**4 - 14/3*l**3 + 0*l + 0 + 0*l**2.
-l**3*(l + 2)*(l + 7)/3
Let i(j) be the third derivative of j**8/112 - 3*j**7/35 + 3*j**6/10 - 2*j**5/5 + 172*j**2. Find t such that i(t) = 0.
0, 2
Let y(l) be the third derivative of l**6/40 - 17*l**5/20 + 11*l**4/8 + 605*l**3/2 + 2*l**2 + 85. What is w in y(w) = 0?
-5, 11
Let k be (-1)/(-4) - 14/(-8). Let r(p) = p**3 - 7*p**2 - p + 10. Let a be r(7). Factor k*u + 2*u**a - 4*u**3 + 2*u - 2*u.
-2*u*(u - 1)*(u + 1)
Let v(j) be the first derivative of j**4/14 - 82*j**3/21 - 6*j**2 - 688. Factor v(l).
2*l*(l - 42)*(l + 1)/7
Suppose -53*f - 2*w = -55*f - 6, 0 = 5*f + 3*w - 9. Let l(o) be the third derivative of 5*o**2 - 1/30*o**3 + 0*o**4 + 1/300*o**5 + 0*o + f. Solve l(z) = 0.
-1, 1
Let m = 14203/741 + -1/1482. Let v = 41/2 - m. Factor v - 2/3*t**2 + 2/3*t.
-2*(t - 2)*(t + 1)/3
Let r(c) be the first derivative of -c**7/3360 - c**6/144 - c**5/40 + 3*c**4/4 - 28*c**3/3 - 16. Let y(s) be the third derivative of r(s). Factor y(z).
-(z - 2)*(z + 6)**2/4
Suppose -5*w = -y - 70, 4*w + y = -0*y + 65. Factor 21*u - 2*u**4 + 0*u**4 + 27*u**2 + 5*u**4 + 6 + w*u**3.
3*(u + 1)**3*(u + 2)
Let d(c) be the first derivative of -30 - 3*c + 5/2*c**3 + 3/2*c**4 - 21/4*c**2. Solve d(w) = 0.
-2, -1/4, 1
Let m be (6/(-15))/(2/(-20)). Suppose -m*o = -0*o. Determine w, given that 5*w**3 - 8*w**3 + o*w**4 - 3*w**4 = 0.
-1, 0
Let z(r) be the first derivative of -r**5/20 + r**4/8 + 3*r**2 + 8. Let h(l) be the second derivative of z(l). Find q such that h(q) = 0.
0, 1
Let g(b) be the first derivative of 3*b**4/8 - 4*b**3 - 33*b**2/4 + 27*b + 498. Factor g(q).
3*(q - 9)*(q - 1)*(q + 2)/2
Let s(w) be the third derivative of 0*w**3 + 2/1155*w**7 - 1/132*w**4 + 3*w**2 + 0*w**6 - 1/165*w**5 + 1/1848*w**8 + 0 + 0*w. Factor s(u).
2*u*(u - 1)*(u + 1)**3/11
Suppose t + 5*u = 25, 5*u = -4*t + 6 + 19. Let d(i) be the first derivative of t*i + 0*i**2 - 1/9*i**3 + 2 - 1/12*i**4. Solve d(f) = 0.
-1, 0
Factor -6*s**3 + 10 + 16*s**2 + 7*s + 5*s**3 - 11*s**2 - 9*s**2.
-(s - 2)*(s + 1)*(s + 5)
Let p(x) be the first derivative of -6/7*x**2 - 1/14*x**4 + 10/21*x**3 - 16 + 0*x. Factor p(g).
-2*g*(g - 3)*(g - 2)/7
Let z = -18 - -16. Let o(x) = -x**3 - x**2 + x + 1. Let a(i) = -3*i**3 + 23*i**2 + 51*i + 19. Let j(p) = z*a(p) + 22*o(p). Factor j(f).
-4*(f + 2)**2*(4*f + 1)
Suppose 4*i = b, 3*i = 2*b - 0*i - 25. Let x = b + -16. Factor 8*d**4 + 12*d**x - 28*d**3 + 8*d**2 + 0*d**4.
4*d**2*(d - 1)*(5*d - 2)
Let m = 7 - -28. Let y be (-21)/m + (-536)/(-10). Factor -y*t**2 + 21*t**2 - 6*t + 29*t**2.
-3*t*(t + 2)
Let k = -13 - -13. Let m(d) be the second derivative of 3/4*d**4 + 3/4*d**2 - 5*d + 1/20*d**6 + k + 3/10*d**5 + d**3. Factor m(l).
3*(l + 1)**4/2
Let r(f) be the first derivative of 5/3*f**3 + 45/2*f**2 - 7 - 50*f. Factor r(i).
5*(i - 1)*(i + 10)
Suppose -s + 2 + 0 = 0. Suppose 34 - 22 = s*u. Factor u*k**3 - 9*k**2 + 6*k - 3/2 - 3/2*k**4.
-3*(k - 1)**4/2
Let q be (224/(-84))/(16/(-2)). Factor q*z**2 + 2/9*z + 0 + 1/9*z**3.
z*(z + 1)*(z + 2)/9
Let w(s) be the third derivative of s**6/30 + 9*s**5/5 + 17*s**4/2 + 50*s**3/3 - s**2 + 17. Let w(u) = 0. What is u?
-25, -1
Suppose -4*c**2 + 0 - 8/3*c + 4/3*c**4 + 0*c**3 = 0. What is c?
-1, 0, 2
Factor 8/17*w - 2/17*w**3 + 4/17*w**2 - 16/17.
-2*(w - 2)**2*(w + 2)/17
Let v(k) be the first derivative of 32*k + 8*k**2 - 24 + 2/3*k**3. Solve v(l) = 0.
-4
Let v(p) be the second derivative of 0 - 1/4*p**5 - 11/6*p**4 - 12*p - 4*p**2 - 14/3*p**3. Suppose v(q) = 0. Calculate q.
-2, -2/5
Suppose -83 = -4*d - 415. Let x = d - -88. Factor 0*c**3 - 3/2*c**x + 3/2*c - 3*c**2 + 0 + 3*c**4.
-3*c*(c - 1)**