3.
2*(n + 1)**3*(n + 2)
Let y(z) be the second derivative of -z**10/40320 + z**9/60480 + z**8/13440 - z**4/12 - 2*z. Let i(p) be the third derivative of y(p). Factor i(s).
-s**3*(s - 1)*(3*s + 2)/4
Let o(l) be the second derivative of l**5/35 + 8*l**4/21 + 2*l**3 + 36*l**2/7 - 31*l - 2. Determine f so that o(f) = 0.
-3, -2
Factor 4*o**3 - 16*o**2 + 10*o + 7*o - 5*o.
4*o*(o - 3)*(o - 1)
Let p(k) be the first derivative of 2/45*k**5 - 1/9*k**4 - 4/27*k**3 + 2/9*k + 1/9*k**2 + 1/27*k**6 - 2. Factor p(z).
2*(z - 1)**2*(z + 1)**3/9
Suppose -10*g + 21 = -9. Factor 1/4*p**2 - 1/2*p**g + 0*p + 1/4*p**4 + 0.
p**2*(p - 1)**2/4
Let s(o) = -3*o**2 + o. Suppose -4 = -2*m, -f = 5*m - 6 - 7. Let z(t) = f - 4 + 2 - 4*t**2. Let p(v) = -3*s(v) + 2*z(v). Factor p(q).
(q - 2)*(q - 1)
Let -1/3*y**2 + 10/3*y - 25/3 = 0. What is y?
5
Suppose -20*n - 1205 = -5205. What is u in 125/2*u**5 + 38*u + 139*u**2 + n*u**4 + 485/2*u**3 + 4 = 0?
-1, -2/5
Let a be -3*(24/(-9) + 2). Let w be ((-6)/(-4))/(2/4). Suppose -w*y**a + 5*y**2 + 3*y - y = 0. Calculate y.
-1, 0
Suppose 0 = 5*z - z - 8. Factor -2*s**2 - 2*s**2 + s**z + 2*s + s**3.
s*(s - 2)*(s - 1)
Let y(j) be the second derivative of -2*j**6/15 - j**5/5 + 4*j**4/3 + 8*j**3/3 - 6*j - 1. Factor y(p).
-4*p*(p - 2)*(p + 1)*(p + 2)
Let y(w) be the third derivative of w**5/35 - w**4/8 - w**3/7 - 28*w**2. Factor y(t).
3*(t - 2)*(4*t + 1)/7
Let d(i) be the second derivative of i**4/18 + 2*i**3/9 + i**2/3 - 5*i. Suppose d(b) = 0. What is b?
-1
Let x(d) be the second derivative of 3/25*d**5 + 4/5*d**2 + 1/75*d**6 - 3*d + 13/30*d**4 + 0 + 4/5*d**3. Factor x(i).
2*(i + 1)**2*(i + 2)**2/5
Let w(p) = p**4 - 8*p**2 + 2. Let o(r) = r**3 - 1. Let f(i) = -4*o(i) - 2*w(i). Find d, given that f(d) = 0.
-4, 0, 2
Let v(b) be the first derivative of 0*b**3 + 4 + 0*b + 1/150*b**5 - 1/2*b**2 + 0*b**4. Let k(g) be the second derivative of v(g). Factor k(a).
2*a**2/5
Let h(y) = -17*y**4 - 69*y**3 - 116*y**2 - 80*y - 16. Let w(z) = -42*z**4 - 172*z**3 - 290*z**2 - 200*z - 40. Let q(t) = 12*h(t) - 5*w(t). Factor q(v).
2*(v + 1)*(v + 2)**2*(3*v + 1)
Let h(b) be the second derivative of -b**4/24 + b**2/4 - 9*b. Determine r so that h(r) = 0.
-1, 1
Let o(z) = z**4 - 11*z**3 - 36*z**2 - 37*z - 19. Let b = 19 - 16. Let u(q) = q**4 + q**3 + q - 1. Let a(y) = b*u(y) - o(y). Factor a(s).
2*(s + 1)*(s + 2)**3
Suppose -2*c - 3 = -4*c - 3*g, 2*c - 3*g = 33. Let w = -5 + c. Factor -3*r**4 + 2*r**4 + 2*r**w + r**3 - r**5 - r**2.
-r**2*(r - 1)**2*(r + 1)
Let v(o) be the second derivative of o**3/6 + 5*o**2 + 2*o. Let t be v(0). Determine k, given that -9/4*k**5 + 39/4*k**4 - 6*k**2 - t*k**3 + 12*k - 4 = 0.
-1, 2/3, 2
Factor 0 - 1/3*a**4 + 2/3*a**2 + 0*a + 1/3*a**3.
-a**2*(a - 2)*(a + 1)/3
Let k(g) be the third derivative of g**8/84 + 2*g**2. Suppose k(s) = 0. What is s?
0
Let m(o) = -o + 15. Let d be m(12). Factor k**5 - 2*k**d - 2*k**5 - k**3 + 4*k**5.
3*k**3*(k - 1)*(k + 1)
Let d be 2/(-6) + (-8)/(-16). Let m(k) be the first derivative of 1 + 1/15*k**5 + 1/9*k**3 + 0*k**2 - d*k**4 + 0*k. Suppose m(v) = 0. Calculate v.
0, 1
Determine h, given that -1/2*h**4 + 3/4*h**5 + 3*h**2 - 1/4*h - 1/2 - 5/2*h**3 = 0.
-2, -1/3, 1
Let b(o) = o**3 - 6*o**2 + 2*o - 8. Let z = 0 - -6. Let t be b(z). Factor t*d**2 - 2*d**2 - d**4 - d**2.
-d**2*(d - 1)*(d + 1)
Let g be -4 + (1 - -2) + 3. Factor 2 + 10*k**3 + 4*k - k**g - 2 + 15*k**2.
2*k*(k + 1)*(5*k + 2)
Let c = -431 - -434. Find k, given that 0 + 0*k - 2/3*k**c + 2/3*k**2 = 0.
0, 1
Suppose 5*m - 3*d + 0 = 3, 2*m - 3*d = 3. Let a(g) be the first derivative of 0*g + m*g**3 - 1/2*g**4 + g**2 - 2. Factor a(s).
-2*s*(s - 1)*(s + 1)
Let p = 1/2 + 1/6. Solve 2/3 + p*n**2 + 4/3*n = 0.
-1
Suppose 0 - 4/15*p**3 + 0*p + 2/15*p**2 + 2/15*p**4 = 0. What is p?
0, 1
Find d, given that 8/11 - 24/11*d - 6/11*d**3 + 2*d**2 = 0.
2/3, 1, 2
Solve 0 + 0*b - 2/3*b**2 - 2/3*b**3 = 0.
-1, 0
Let u(f) be the second derivative of -f**7/252 - f**6/180 + f**5/60 - 35*f. Suppose u(a) = 0. What is a?
-2, 0, 1
Let t(c) be the second derivative of -c**5/300 - 2*c**2 + 5*c. Let a(k) be the first derivative of t(k). Determine y so that a(y) = 0.
0
Let v be -6*(0 - (-1)/(-2)). Factor -2*l**4 - 6*l**2 - l**3 - 2*l - 4*l**v - l**3.
-2*l*(l + 1)**3
Suppose -d - 48 = -z + 3*d, 5*d + 45 = z. Suppose m = -4*m + z. Let 3*y**2 - 2*y**3 + 3*y**2 - m*y**2 - 4*y = 0. Calculate y.
-2, -1, 0
Let i(z) be the first derivative of -z**4/20 + 4*z**3/5 - 24*z**2/5 + 64*z/5 + 1. Let i(v) = 0. Calculate v.
4
Find h such that 0*h + 4/5*h**2 - 2/5*h**5 + 2/5*h**3 - 4/5*h**4 + 0 = 0.
-2, -1, 0, 1
Let p(c) = -40*c**3 + 2*c**2 - 4*c - 4. Let t be p(3). Let x be t/(-495) - (-2)/9. Factor -x*z - 6/5*z**2 - 8/5 - 1/5*z**3.
-(z + 2)**3/5
Let b(p) be the third derivative of p**6/720 - p**5/90 + 5*p**4/144 - p**3/18 - 4*p**2. Factor b(y).
(y - 2)*(y - 1)**2/6
Let -23*i**3 + 30*i - 5*i**4 - 2*i**3 - 10 - 45*i**2 - 65*i = 0. What is i?
-2, -1
Let u = -12 + 16. Factor 0*f**2 + 3/2*f**3 - 3/2*f - 3/4 + 3/4*f**u.
3*(f - 1)*(f + 1)**3/4
Let c(x) be the first derivative of x**4/12 + 7*x**3/9 + 5*x**2/2 + 3*x - 10. Factor c(g).
(g + 1)*(g + 3)**2/3
Let f = 1 - 2. Let l(k) = -k**3 + 2*k**2 - 1. Let j be l(f). Let 10/11*s - 4/11 + 14/11*s**j = 0. What is s?
-1, 2/7
Let l(o) be the first derivative of -2 + 3/2*o**2 + 3/4*o**4 + 0*o - 2*o**3. Factor l(k).
3*k*(k - 1)**2
Let o(c) be the second derivative of c**4/24 + c**3/6 + 10*c. Let o(q) = 0. Calculate q.
-2, 0
Solve -4/9*a**4 + 2/9*a - 2/9*a**5 + 4/9*a**2 + 0 + 0*a**3 = 0.
-1, 0, 1
Let p = 7 - 5. Factor -v**4 - 3*v**3 + p*v**3 + 0*v**3.
-v**3*(v + 1)
Let p = -25 + 39. Suppose s = 3*s - p. Let -8*q**3 - s*q**2 - 5*q**4 + 2*q**4 + 4*q**4 - 2*q - 4*q**4 = 0. What is q?
-1, -2/3, 0
Suppose 0 = -4*d - 0*d - 12. Let h = d - -3. Factor -1/3*p**5 - 1/3*p + 4/3*p**4 - 2*p**3 + 4/3*p**2 + h.
-p*(p - 1)**4/3
Let r be -3 + 6 + (-2 - 1). Let l(g) = -g**2 - g + 3. Let z be l(r). Factor 0 + 8/11*c + 2/11*c**4 - 6/11*c**z + 0*c**2.
2*c*(c - 2)**2*(c + 1)/11
Let i(f) = f**2 + f + 1. Let v(q) = -6*q**2 - 12*q - 6. Let m(r) = 8*i(r) + v(r). Factor m(d).
2*(d - 1)**2
Let y = -11 + 14. Let f(h) be the first derivative of 3 - 8/7*h**2 - 10/21*h**y - 8/7*h - 1/14*h**4. Let f(b) = 0. Calculate b.
-2, -1
Let a be (-10)/2*(-1 + 7 + -7). Let l(o) be the second derivative of 1/20*o**6 + 0*o**3 - 3/40*o**a + 0*o**2 + 0 - o + 1/24*o**4 - 1/84*o**7. Solve l(k) = 0.
0, 1
Let k(u) be the first derivative of u**6/2 - 9*u**5/5 + 9*u**4/4 - u**3 + 1. Factor k(y).
3*y**2*(y - 1)**3
Determine k so that 0*k - 2/7*k**5 + 2/7*k**3 - 4/7*k**4 + 0 + 4/7*k**2 = 0.
-2, -1, 0, 1
Let v(p) be the first derivative of -10*p**6/33 - 18*p**5/55 - p**4/11 + 3. Let v(b) = 0. Calculate b.
-1/2, -2/5, 0
Suppose 5*f + 9 = 8*f. Let x(v) be the second derivative of 8/3*v**4 - 17/9*v**f - 3/2*v**5 + 2*v + 0 + 2/3*v**2. Solve x(n) = 0.
1/3, 2/5
Let g(r) = r**2 + 33*r + 230. Let n be g(-10). Find z such that -8/7*z**4 + n - 2/7*z**5 - 12/7*z**3 - 2/7*z - 8/7*z**2 = 0.
-1, 0
Let m be 342/(-96) + 6/2. Let w = m + 13/16. Solve -1/4*z**2 + 0 + 1/2*z - w*z**3 = 0 for z.
-2, 0, 1
Suppose 2 = -3*t - 16. Let k be 10/(-16)*t/15. What is g in -k*g**2 + 0*g + 1/4 = 0?
-1, 1
Let h = -209/16 + 4457/336. Let w = 1/21 + h. Factor -1/4*f**2 + 0*f + 0 + w*f**3.
f**2*(f - 1)/4
Let i = 418/21 + -116/7. What is d in -i*d - 8/3*d**2 - 2/3 = 0?
-1, -1/4
Let k = 5 + -8. Let r = k + -2. Let i(c) = -3*c**3 + 4*c**2 - 4*c + 10. Let w(u) = -2*u**3 + 3*u**2 - 3*u + 7. Let x(d) = r*i(d) + 7*w(d). Factor x(b).
(b - 1)*(b + 1)**2
Let j(y) = -27*y**3 - 33*y**2 + 9*y + 33. Let k(a) = 13*a**3 + 17*a**2 - 4*a - 16. Let h(x) = 4*j(x) + 9*k(x). Factor h(r).
3*(r + 1)*(r + 2)*(3*r - 2)
Let q(w) = 13*w**4 - 31*w**3 + 24*w**2 - 7*w. Let p(a) = 4*a**4 - 10*a**3 + 8*a**2 - 2*a. Let v(h) = -7*p(h) + 2*q(h). Let v(k) = 0. Calculate k.
0, 2
Suppose -16*j + 18*j - 4 = 0. Determine x so that -30*x**3 - 28*x + 13*x + 12*x**j - 3*x**5 + 15*x**4 + 18*x**2 + 3 = 0.
1
Let j = 2 - 2. Let o = 2 + j. Solve -x**o + 5/3*x - 2/3 = 0 for x.
2/3, 1
Let w(i) = i**3 - 5*i**2 - 6*i + 3. Let p be w(6). Let z = 0 + p. Solve 3*k**5 + 2*k + 4*k**2 + z*k**5 - 4*k**4 + 0*k**4 - 8*k**3 = 0 for k.
-1, -1/3, 0, 1
Suppose 2*z = -9*t + 4*t - 88, 4*t = -z - 71. Let y be 70/9 + (-4)/t. 