w*(w - 1)**3*(w + 1)/5
Let b(g) be the third derivative of g**8/168 - g**7/35 + 14*g**2. Let b(p) = 0. Calculate p.
0, 3
Let a be (-20)/(-42) + (-8)/24. Suppose 1/7*i**2 + a + 2/7*i = 0. What is i?
-1
Let r(o) = o**2 - 4*o + 4. Let i be r(4). Suppose -6 = -0*x - x. Factor -x*g - g**3 - 12*g**i - 11*g**3 - 15*g**2 + 9*g**4.
-3*g*(g + 1)**2*(g + 2)
Let q(i) be the second derivative of 0 + 2*i + 1/20*i**6 + 1/4*i**2 - 1/6*i**3 + 1/20*i**5 - 1/6*i**4. Factor q(k).
(k - 1)*(k + 1)**2*(3*k - 1)/2
Let r be (-1)/2 - (-1)/2. Suppose -14 = -2*c - 2*m, 3*c - 13 = -0*c + m. Factor 0*w + 2/5*w**c - 2/5*w**3 + r - 2/5*w**2 + 2/5*w**4.
2*w**2*(w - 1)*(w + 1)**2/5
Suppose -5*w - 10 = 2*r, 0 = -r - 0*r - 5*w. Let k(v) = 2 - 1 - 13*v + 13*v + v**2. Let j(x) = -8*x**2 + 2*x - 10. Let h(z) = r*k(z) - j(z). Factor h(y).
-2*y*(y + 1)
Suppose 0 = 4*i + 4*d + 4, -5 = -3*i - 0*d - d. Determine o so that -2*o + 6 - i*o**2 + 0*o + 5*o = 0.
-1, 2
Let w(m) be the first derivative of m**6/180 + m**5/60 - m**4/6 - m**3/3 - 5. Let l(f) be the third derivative of w(f). Determine h, given that l(h) = 0.
-2, 1
Let v = -19 + 19. Let q(c) be the third derivative of 0*c + 0*c**4 + 0*c**3 - c**2 + 8/105*c**7 + 1/60*c**5 + 1/15*c**6 + v. Factor q(l).
l**2*(4*l + 1)**2
Let b(k) = k**2 + k. Let x(h) = -6*h**3 - 13*h**2 - 9*h - 6. Let a(u) = -u**3 - u**2 - 1. Let m(q) = 4*a(q) - x(q). Let v(d) = 3*b(d) - m(d). Factor v(i).
-2*(i + 1)**3
Let t(f) = 2*f - 16. Let q be t(9). Let s = -2218/7 - -318. Solve 0 - s*u**3 + 8/7*u**q + 2/7*u**4 + 0*u = 0.
0, 2
Factor k**5 + 5*k**5 - 11*k**5 + 25*k**3 + 20*k**4.
-5*k**3*(k - 5)*(k + 1)
Let h = -13 - -15. Let g(a) be the first derivative of 5*a**2 + h*a**4 - 3 - 16/3*a**3 - 2*a. What is n in g(n) = 0?
1/2, 1
Let b = -69/44 + 20/11. Let s(u) be the first derivative of -b*u**2 + 1 + 1/12*u**3 + 1/4*u. Suppose s(r) = 0. Calculate r.
1
Let y = 710/7 - 101. Determine f, given that 0 + 3/7*f**3 + y*f**2 - 3/7*f - 3/7*f**4 = 0.
-1, 0, 1
Let n(z) = -z**3 - 7*z**2 - z - 5. Let y be n(-7). Suppose 1/4*k**y + 1 - k = 0. Calculate k.
2
Suppose 0 = 5*y - 2*h - 8, -3*y - 4*h + 7 = -3*h. Factor 22*g**y - g**3 + 0*g**3 + 8 - 28*g - 4*g**3.
-(g - 2)**2*(5*g - 2)
Let z(p) be the third derivative of p**6/30 + p**5/15 - 5*p**2. Determine h so that z(h) = 0.
-1, 0
Factor -3*h**2 - 23*h**4 + 5*h - 3*h**3 + 0*h**2 - 2*h + 26*h**4.
3*h*(h - 1)**2*(h + 1)
Let r(m) be the first derivative of -4*m**5/35 + 4*m**3/21 - 11. Factor r(v).
-4*v**2*(v - 1)*(v + 1)/7
Let m(x) = x**3 + 11*x**2 + 11*x - 14. Let d be m(-10). Let h = 24 + d. Factor o - 1/2*o**3 + h + 1/2*o**2.
-o*(o - 2)*(o + 1)/2
Let g(p) be the first derivative of 2/3*p**3 - 1/2*p**2 - 1 - p. Factor g(m).
(m - 1)*(2*m + 1)
Let l be 1*0/(-3) - 0. Suppose 0 = 2*k + 3*i - l*i - 10, i + 6 = 4*k. Let t - t + t**k = 0. What is t?
0
Let q(o) be the third derivative of -o**6/240 + 3*o**5/80 - o**4/8 + o**3/2 + 3*o**2. Let l(d) be the first derivative of q(d). Solve l(u) = 0 for u.
1, 2
Let t(k) be the third derivative of 0*k**3 + 1/420*k**7 + 0 + 6*k**2 - 1/30*k**5 + 1/672*k**8 - 1/40*k**6 + 1/6*k**4 + 0*k. Determine f so that t(f) = 0.
-2, 0, 1, 2
Let q(u) = -3*u**4 - 21*u**3 + 12*u**2 + 6*u. Let b(m) = 4*m**4 + 21*m**3 - 13*m**2 - 5*m. Let v(l) = 6*b(l) + 5*q(l). Find h, given that v(h) = 0.
-3, 0, 2/3
Let i = 1113/2 + -556. Factor -3/2*k + i - 2*k**2.
-(k + 1)*(4*k - 1)/2
Let r(s) = -7*s**3 + 5*s**2 - 3*s + 5. Let w(v) = -v + 15. Let g be w(10). Let o(j) = 4*j**3 - 3*j**2 + 2*j - 3. Let m(q) = g*o(q) + 3*r(q). Factor m(z).
-z*(z - 1)*(z + 1)
Let b(f) be the second derivative of f**8/840 + f**7/420 + 4*f**3/3 - 7*f. Let p(k) be the second derivative of b(k). Factor p(h).
2*h**3*(h + 1)
Let t(f) be the third derivative of f**6/24 - f**5/3 + 5*f**4/6 - 21*f**2. Find z, given that t(z) = 0.
0, 2
Let i(o) be the third derivative of -o**7/945 - o**6/270 - o**5/270 - 7*o**2. Suppose i(w) = 0. What is w?
-1, 0
What is w in 0 + 4/7*w - 8/7*w**3 - 2*w**2 = 0?
-2, 0, 1/4
Let z be ((-48)/9)/((-1)/3). Suppose 3*n = -n - z. Let o(a) = -a**3 - a + 2. Let v(g) = g**3 + 2*g - 3. Let r(w) = n*v(w) - 5*o(w). Factor r(u).
(u - 1)**2*(u + 2)
Factor 2/5*o**2 + 10 - 4*o.
2*(o - 5)**2/5
Let f(h) be the second derivative of -2*h + 1/20*h**5 - 1/6*h**4 + 5/42*h**7 + 4/15*h**6 + 0 + 0*h**3 + 0*h**2. Factor f(d).
d**2*(d + 1)**2*(5*d - 2)
Let u = -11 - 5. Let w be 1 - (-3 + u/(-10)). Factor -15*p**3 - 12*p**2 - w*p + 0.
-3*p*(5*p + 2)**2/5
Let j be (-2)/(-8) + (220/(-112) - -2). Factor -j*g + 2/7*g**2 + 0.
2*g*(g - 1)/7
Let z be 3 + -2*(-1)/(-2). Let u(t) be the second derivative of 0 + 1/6*t**3 + t + 0*t**z - 1/20*t**5 + 0*t**4. Factor u(s).
-s*(s - 1)*(s + 1)
Let v(r) be the second derivative of r**8/1176 - r**6/210 + r**4/84 + r**2 + 2*r. Let o(p) be the first derivative of v(p). Factor o(t).
2*t*(t - 1)**2*(t + 1)**2/7
Let d(a) = -6*a**3 - 9*a**2 + 18*a. Let v(h) = -h**3 + h**2 - h. Let t(g) = d(g) - 9*v(g). Factor t(p).
3*p*(p - 3)**2
Let r(n) = -14*n**4 + 45*n**3 - 16*n**2 + 6*n - 6. Let u(p) = 15*p**4 - 45*p**3 + 15*p**2 - 5*p + 5. Let x(h) = -5*r(h) - 6*u(h). What is t in x(t) = 0?
0, 1/4, 2
Suppose -2/9*l**2 + 8/3*l - 8 = 0. What is l?
6
Factor -3*v - 17*v - 8 + 4*v**4 - 11*v**2 + 4*v**3 - v**2.
4*(v - 2)*(v + 1)**3
Let k(g) = -35*g**3 - 15*g - 30. Let w(t) = 9*t**3 + 4*t + 8. Let j(y) = 4*k(y) + 15*w(y). Let j(p) = 0. Calculate p.
0
Let a = -11 + 25. Let x be a/6*(-2)/(-7). Factor 4/3*h + 0*h**2 + x - 4/3*h**3 - 2/3*h**4.
-2*(h - 1)*(h + 1)**3/3
Let u(g) be the third derivative of g**5/24 - 5*g**4/16 + 15*g**2. Factor u(m).
5*m*(m - 3)/2
Let d(c) be the third derivative of -1/105*c**7 - 8*c**2 + 1/12*c**4 - 1/60*c**6 + 0 + 0*c**3 + 0*c + 1/30*c**5. Factor d(i).
-2*i*(i - 1)*(i + 1)**2
Let d be 1/(2*(-2)/(-12)). Let a(p) be the first derivative of -1/3*p**d + 1/12*p**6 - 1 + 0*p**4 + 1/5*p**5 - 1/4*p**2 + 0*p. Find l, given that a(l) = 0.
-1, 0, 1
Let k = -3421/30 - -586/5. Let w(b) be the first derivative of -k*b**3 + 2*b + 7/8*b**4 + 2*b**2 + 4. Factor w(y).
(y - 2)*(y - 1)*(7*y + 2)/2
Let a(u) be the third derivative of 4*u**2 + 0 + 0*u**3 + 11/60*u**6 - 121/420*u**7 + 0*u + 0*u**4 - 1/30*u**5. What is i in a(i) = 0?
0, 2/11
Let k(x) be the first derivative of 4*x**3/9 + 8*x**2/3 + 16*x/3 + 65. Factor k(q).
4*(q + 2)**2/3
Let m(n) = 3 - 1 + 8*n - 2*n**2 + n**2. Let t be m(5). Let t*d**2 - 27*d + 7*d - 4*d**3 + 3 + 1 = 0. Calculate d.
1/4, 2
Suppose 6 = 3*r, -3*c - 3*r = -16 + 1. Suppose -1/2*j**c - 4 - 3*j**2 - 6*j = 0. Calculate j.
-2
Factor -2*p**5 - 2*p**5 - 8*p**2 + 12*p**3 + 0*p**5.
-4*p**2*(p - 1)**2*(p + 2)
Let m(t) = t**3 + 6*t**2 - 8*t - 5. Let h be m(-7). Suppose h*g + 2*g = 8. Factor -4*j**5 - g*j**3 + 5*j**5 - 4*j**4 - 3*j**5.
-2*j**3*(j + 1)**2
Suppose 3*z = 5*c - 30, -c - 6 = -2*c - 2*z. Let y(r) be the third derivative of r**2 - 2/3*r**3 + 0 + 1/3*r**4 + 11/60*r**5 + 0*r - 1/8*r**c. Solve y(l) = 0.
-2/3, 2/5, 1
Let u be -4 + ((-3)/10)/((-24)/340). Factor 0 - 1/4*n - 1/4*n**4 + 1/4*n**3 + u*n**2.
-n*(n - 1)**2*(n + 1)/4
Let h(o) be the second derivative of -o**9/2016 - o**8/560 - o**7/560 - o**3/2 - 5*o. Let a(s) be the second derivative of h(s). Factor a(y).
-3*y**3*(y + 1)**2/2
Suppose 0 = 3*o - 3*b, 0*o = 5*o + 2*b - 28. Let l(f) be the first derivative of 0*f - 2/35*f**5 - 2/7*f**3 + 2 - 3/14*f**o - 1/7*f**2. Factor l(c).
-2*c*(c + 1)**3/7
Let d(t) be the first derivative of t**5/20 + 3*t**4/16 + t**3/4 + t**2/8 + 4. Determine s, given that d(s) = 0.
-1, 0
Let l(z) = -3*z**4 + 4*z**2 + 3*z. Let o(c) = -c**5 - c**3 - c**2 - c. Let k(f) = -2*l(f) - 2*o(f). Suppose k(h) = 0. What is h?
-2, -1, 0, 1
Let p(i) be the first derivative of 2/3*i**3 - 4 - 8/3*i + 3/2*i**4 - 8/3*i**2. Find n, given that p(n) = 0.
-2/3, 1
Let s(v) be the first derivative of -v**6/120 + v**5/30 + v**4/6 - 2*v**3/3 + 6. Let l(q) be the third derivative of s(q). Determine a, given that l(a) = 0.
-2/3, 2
Let y(n) = 3*n**3 + 6*n**2 + 11*n + 8. Let m(c) = 2*c**3 + 4*c**2 + 7*c + 5. Let u(g) = -8*m(g) + 5*y(g). Factor u(x).
-x*(x + 1)**2
Let y(m) be the third derivative of -1/40*m**4 + 1/100*m**5 + 0 + 1/200*m**6 + 0*m - 8*m**2 - 1/10*m**3. Factor y(x).
3*(x - 1)*(x + 1)**2/5
Suppose -m = -5*l - 27, 4*m - 3 + 5 = -2*l. Find o such that 3*o**3 + 2*o**2