84 - y**7/455 - y**6/260 - y**5/390 + 4*y**2. Factor j(f).
-2*f**2*(f + 1)**3/13
Let v(g) be the third derivative of -g**6/480 - 11*g**5/80 - 121*g**4/32 - 1331*g**3/24 + 50*g**2. Factor v(d).
-(d + 11)**3/4
Let c(t) be the second derivative of t**8/6720 + t**7/1120 + t**6/720 - t**3/3 - 9*t. Let s(r) be the second derivative of c(r). Factor s(l).
l**2*(l + 1)*(l + 2)/4
Let g = 15 - 13. Solve -1/4*p**3 - 1/4*p**4 + 1/4*p + 0 + 1/4*p**g = 0.
-1, 0, 1
Let r(m) be the first derivative of 4 + 8/21*m**3 - 1/14*m**4 + 1/7*m**2 - 8/35*m**5 + 0*m. Let r(y) = 0. Calculate y.
-1, -1/4, 0, 1
Suppose 5*a + 2*i - 6 = 0, 0 = 5*a - i - 0 - 12. Find u, given that -2*u**2 - 3*u**2 + 2*u**3 + 7*u**a - u**3 - u**5 - 2*u**4 = 0.
-2, -1, 0, 1
Let f(l) be the second derivative of l**6/15 + 2*l**5/5 + 5*l**4/6 + 2*l**3/3 + 5*l. Find a, given that f(a) = 0.
-2, -1, 0
Let o(a) be the third derivative of -3*a**8/112 - a**7/35 + a**6/4 - 7*a**4/8 + a**3 + 55*a**2. Solve o(t) = 0 for t.
-2, -1, 1/3, 1
Let d(i) = -19*i**4 - 27*i**3 + 26*i**2 + 15*i + 5. Let s(b) = -1 + b**3 - 16*b**4 - b**2 + 24*b**4 - 7*b**4. Let w(v) = -2*d(v) - 6*s(v). Solve w(x) = 0.
-2, -1/4, 1
Let k be (4/54)/((-4)/(-6))*6. Suppose 1/3*h**3 + 0 - k*h**2 + 1/3*h = 0. Calculate h.
0, 1
Let j = -2563/7 - -367. Suppose j*p**3 + 2/7*p**5 + 0 - 2/7*p**2 + 0*p - 6/7*p**4 = 0. What is p?
0, 1
Let w(o) be the first derivative of 1 + o**4 + 0*o**3 + 1/3*o**6 + 0*o**2 + 6/5*o**5 + 0*o. Factor w(f).
2*f**3*(f + 1)*(f + 2)
Factor 2*u + 0 + 2/11*u**2.
2*u*(u + 11)/11
Suppose -3*n + 0*z - 18 = 3*z, 0 = -3*n - 4*z - 23. Let q be n/(-3) + (-10)/(-30). Factor q*l**2 + 2/3 + 4/3*l.
2*(l + 1)**2/3
Let i(f) = 2 + 10*f**3 - 4*f + 6*f**3 - 15*f**3. Let q(v) = v. Let x(h) = -4*i(h) - 4*q(h). Let x(p) = 0. Calculate p.
-2, 1
Let s be (-5)/(-3) + (-6)/9. Suppose 3*r - 4*x - s = 0, 0*r + 3*x - 3 = r. Suppose -8 + 2*y**r - 2*y + 8 = 0. What is y?
-1, 0, 1
Suppose 5*z + 0*z - 245 = 0. Suppose 5*f + 76 = 5*u - z, -f - 97 = -4*u. Factor -d - u*d**3 - 17/2*d**2 - 45/2*d**4 + 0.
-d*(3*d + 1)**2*(5*d + 2)/2
Factor 30/7*f + 24/7*f**2 + 12/7 + 6/7*f**3.
6*(f + 1)**2*(f + 2)/7
Let h = 437/540 + -1/108. Factor -2/5*y**2 - h + 6/5*y.
-2*(y - 2)*(y - 1)/5
Suppose 3*n - 5 = -4*j + 11, 0 = -2*n - 3*j + 12. Let k**3 - 5/4*k**2 - 1/4*k**4 + n + 1/2*k = 0. Calculate k.
0, 1, 2
Let a(i) be the third derivative of 1/330*i**5 - 3*i**2 - 1/33*i**4 + 0 + 4/33*i**3 + 0*i. Factor a(l).
2*(l - 2)**2/11
Let u(f) be the first derivative of -f**6/315 + f**5/140 + f**4/84 + 2*f**3/3 - 2. Let b(n) be the third derivative of u(n). Factor b(g).
-2*(g - 1)*(4*g + 1)/7
Let r(l) be the second derivative of 3/10*l**5 + 6*l**2 - 5*l + 1/10*l**6 + 0 - 2*l**3 - 3/4*l**4. Factor r(w).
3*(w - 1)**2*(w + 2)**2
Let a(i) = 2*i**2 + 9*i - 3. Let f(c) be the third derivative of c**5/30 + 5*c**4/12 - 2*c**3/3 + 2*c**2. Let x(l) = -6*a(l) + 5*f(l). Factor x(k).
-2*(k + 1)**2
Suppose -138/5*c**2 - 4/5 - 42/5*c - 166/5*c**3 - 66/5*c**4 = 0. What is c?
-1, -1/3, -2/11
Factor 0 + 1/6*l**3 + 0*l - 1/3*l**2.
l**2*(l - 2)/6
Let x(a) be the third derivative of a**8/112 - a**7/70 - a**6/8 + a**5/20 + a**4 + 2*a**3 - 30*a**2. Factor x(w).
3*(w - 2)**2*(w + 1)**3
Determine j, given that -1/6*j**4 + 0*j**2 + 0 + 1/6*j**5 + 0*j + 0*j**3 = 0.
0, 1
Let u(c) be the second derivative of -3*c**5/70 - c**4/21 + c**3/21 + 7*c. What is n in u(n) = 0?
-1, 0, 1/3
Let g(v) be the first derivative of v**8/1680 + 2*v**3/3 - 2. Let o(a) be the third derivative of g(a). Factor o(d).
d**4
Let a = -11/37 - -697/2220. Let q(u) be the third derivative of 1/3*u**3 + 0*u + 0 - a*u**6 - u**2 + 1/12*u**4 - 1/30*u**5. Let q(d) = 0. What is d?
-1, 1
Let n(u) = u**2 + 2*u. Let l be n(-3). Factor -d**2 + 3 - 4*d - 2 + l*d + 1.
-(d - 1)*(d + 2)
Let y(f) be the third derivative of -f**6/120 + f**5/20 + 31*f**2. Solve y(d) = 0.
0, 3
Suppose -5*d - 30 = -5*n, 2*n + 4*d + 7 + 5 = 0. Factor 6*b**2 - 2*b**2 - 4*b**3 + n*b**4 - 2*b**2 + 0*b**2.
2*b**2*(b - 1)**2
Let b(a) = -a**5 - 5*a**4 + 5*a**3 - 3*a**2. Let f(y) = 3*y**5 + 14*y**4 - 14*y**3 + 8*y**2. Let v(s) = 11*b(s) + 4*f(s). Solve v(j) = 0 for j.
-1, 0, 1
Let u = 3 - -2. Let r = u - 3. Factor 4/3 - 4/3*q + 1/3*q**r.
(q - 2)**2/3
Let u(m) be the third derivative of 0 + 4*m**2 - 1/20*m**5 + 0*m + 1/8*m**4 + 0*m**3. Find a, given that u(a) = 0.
0, 1
Let p(d) be the first derivative of 0*d + 6*d**5 - 1 - 8*d**4 - 2/3*d**3 + 2*d**2. Determine h so that p(h) = 0.
-1/3, 0, 2/5, 1
Let v be ((-16)/12)/((-10)/6). Solve 0*w - 12/5*w**4 - v*w**2 + 12/5*w**3 + 0 + 4/5*w**5 = 0.
0, 1
Suppose p + 7 = 2*o, p + 14 = 11. Suppose -7*h**3 + 1 + 3*h**4 + 8*h**o - 9/2*h - 1/2*h**5 = 0. Calculate h.
1, 2
Suppose 340*a = 357*a - 51. Factor 2/5*t**a - 2/5*t + 0 - 7/5*t**4 + 7/5*t**2.
-t*(t - 1)*(t + 1)*(7*t - 2)/5
Suppose 7*g - 18 - 10 = 0. Factor 3/2*m**5 + m**2 + 0*m - 1/2*m**3 + 0 - 2*m**g.
m**2*(m - 1)**2*(3*m + 2)/2
Let p(u) = 7*u**2 + 10*u + 19. Let k(h) = -6*h**2 - 10*h - 20. Let w(s) = -6*k(s) - 5*p(s). Find r such that w(r) = 0.
-5
Let p(a) be the first derivative of a**5/180 - a**4/24 + a**3/9 + a**2/2 + 4. Let u(f) be the second derivative of p(f). Suppose u(s) = 0. What is s?
1, 2
Let y(p) be the second derivative of -1/3*p**2 + 0*p**4 + 2/9*p**3 + 0 - 3*p - 1/15*p**5 + 1/45*p**6. Solve y(c) = 0.
-1, 1
Let l(j) = 7*j + 14. Let r be l(-2). Factor 3/2*o**3 + 0 + 0*o**2 + r*o + 3/2*o**5 - 3*o**4.
3*o**3*(o - 1)**2/2
Let a be 3 + -1 - (-2 - -1). Let d be (4/a)/(2/6). Find y such that 30*y**2 - 21*y**2 - 4*y**d + y**4 - 6*y = 0.
-2, 0, 1
Suppose -4*t - 4*w = 4 - 0, 5*t - 19 = w. Let d(n) be the first derivative of -1 - 1/16*n**4 + 0*n - 1/8*n**2 - 1/6*n**t. Factor d(o).
-o*(o + 1)**2/4
Let h(n) be the third derivative of -n**7/13860 + n**6/1980 + n**4/6 + n**2. Let c(r) be the second derivative of h(r). Factor c(p).
-2*p*(p - 2)/11
Let a(b) be the second derivative of 2/75*b**6 - 3*b + 0 - 1/105*b**7 + 0*b**2 + 1/15*b**3 - 1/15*b**4 + 0*b**5. Factor a(q).
-2*q*(q - 1)**3*(q + 1)/5
Let v(g) be the third derivative of -g**7/630 - g**6/72 - g**5/20 - 7*g**4/72 - g**3/9 + 18*g**2. Factor v(o).
-(o + 1)**3*(o + 2)/3
Factor 16*s**2 + 16*s + 12*s**2 + 5*s + 9*s**3 - 4*s**2 + 6.
3*(s + 1)**2*(3*s + 2)
Let f(m) be the third derivative of m**7/525 - m**6/50 + 13*m**5/150 - m**4/5 + 4*m**3/15 + 25*m**2. Factor f(g).
2*(g - 2)**2*(g - 1)**2/5
Let a(g) = 8*g**3 + 56*g**2 - 4*g. Let i(q) = -q**3 + q**2 - q. Let d(f) = a(f) - 12*i(f). Determine m so that d(m) = 0.
-2, -1/5, 0
Let n(v) = v**3 + 10*v**2 + v + 12. Suppose 5*y - w + 45 = 0, 10 + 0 = -2*w. Let z be n(y). Factor 9*h**2 + 5*h**4 - z*h + 2 - 12*h**3 - 2.
h*(h - 1)**2*(5*h - 2)
Let z(y) be the third derivative of -y**7/525 + y**6/150 - y**5/150 + 2*y**2. Let z(l) = 0. What is l?
0, 1
Let v = -12 - -12. Factor 2/3 + 2/3*b**4 + v*b**3 - 4/3*b**2 + 0*b.
2*(b - 1)**2*(b + 1)**2/3
Let w(c) be the third derivative of c**8/784 + c**7/98 - 3*c**6/280 - 17*c**5/140 - 5*c**4/28 - 55*c**2. Suppose w(r) = 0. What is r?
-5, -1, 0, 2
Suppose 11 = 3*o + 2. Factor -6 - 2*n + 0*n**2 + o + n**2.
(n - 3)*(n + 1)
Let v(s) be the third derivative of s**6/360 - s**3/2 + 3*s**2. Let h(c) be the first derivative of v(c). Factor h(j).
j**2
Let o be (-3 + 1)*(2 + -4). Let j(m) = m**2 - 4*m + 1. Let l be j(5). Factor l*q**4 + 2*q**2 - q**5 - q**5 + 6*q**3 + o*q**5.
2*q**2*(q + 1)**3
Factor 6/13*v + 2/13 + 2/13*v**3 + 6/13*v**2.
2*(v + 1)**3/13
Suppose -26 = -4*z - 18. Let m(i) be the second derivative of -1/2*i**z - 1/12*i**3 + 0 + 1/40*i**5 + 1/8*i**4 + 2*i - 1/60*i**6. Suppose m(w) = 0. What is w?
-1, 1, 2
Suppose a + 282 = -3*s + s, -3*s - 4*a - 428 = 0. Let d = -1256/9 - s. Factor 2/3*o**2 + d + 10/9*o.
2*(o + 1)*(3*o + 2)/9
Let k = 108 + -322/3. Find u such that -2/9*u**3 + k*u**2 - 4/9*u + 0 = 0.
0, 1, 2
Let i(n) be the third derivative of -n**6/180 - 2*n**5/45 - n**4/9 - 8*n**2. Factor i(g).
-2*g*(g + 2)**2/3
Let t(g) = -g**5 + g**4 + g**2 + g - 1. Let f(m) = 21*m**4 + 36*m**3 + 27*m**2 + 3*m - 3. Let a(x) = -f(x) + 3*t(x). Find h, given that a(h) = 0.
-2, 0
Let u(z) be the first derivative of -4*z**3/15 - z**2 - 4*z/5 - 1. Factor u(p).
-2*(p + 2)*(2*p + 1)/5
Let c(z) be the second derivative of 2/9*z**3 + 1/9*z**4 - 1/15*z**5 + 0 - 4*z - 2/3*z**2. Fact