**5/80 - t**4/24 + t**3/3 + t. Let p(j) be the second derivative of k(j). Find s such that p(s) = 0.
-2, -1
Let z(k) be the third derivative of 0 - 2*k**2 + 1/156*k**4 + 0*k - 1/390*k**5 + 2/39*k**3. Factor z(s).
-2*(s - 2)*(s + 1)/13
Let i be (-7)/14 + (-274)/4. Let m = -344/5 - i. Solve -1/5*b - 1/5*b**2 + m*b**3 + 1/5 = 0.
-1, 1
Let w(l) be the third derivative of 0*l**4 + 1/360*l**6 + 0 - 1/1008*l**8 + 0*l + 0*l**3 + 3*l**2 + 0*l**7 + 0*l**5. Factor w(n).
-n**3*(n - 1)*(n + 1)/3
Let x(d) = -25*d**5 + 111*d**3 + 50*d**2 - 86*d - 39. Let m(t) = 5*t**5 - 22*t**3 - 10*t**2 + 17*t + 8. Let q(f) = 11*m(f) + 2*x(f). Factor q(j).
5*(j - 2)*(j - 1)*(j + 1)**3
Suppose -6*n = 3*r - n + 60, -5*r + 2*n = 131. Let m = -20 - r. Suppose -8/5*a**3 - 4/5 - 2*a**m + 24/5*a**4 + 18/5*a - 4*a**2 = 0. What is a?
-1, 2/5, 1
Let q(c) = -4*c**3 + 12*c**2 + 8. Let s(b) be the first derivative of -b**4/4 + b**3/3 - b**2/2 + b - 1. Let t(z) = -q(z) + 6*s(z). Factor t(i).
-2*(i + 1)**3
Let w(y) be the first derivative of 0*y - 4 + 2/3*y**3 + 1/2*y**2 + 1/4*y**4. Factor w(j).
j*(j + 1)**2
Let y(h) be the third derivative of h**6/480 - h**4/96 + 6*h**2. Determine i so that y(i) = 0.
-1, 0, 1
Let v(a) = a**3 - 4*a**2 + 4*a. Let l be v(3). Factor 2*u + 12 - 2*u + 202*u**l - 205*u**3 - 9*u**2.
-3*(u - 1)*(u + 2)**2
Suppose 5*o = o + 16. Let b(k) be the first derivative of -2*k**3 - 2/5*k**5 - 3 - 20*k**2 + 40*k**o - 20*k**6 + 8*k. Find w such that b(w) = 0.
-1, -2/3, 1/4, 2/5, 1
Let u(q) = -q**3 - 5*q**2 + 7*q + 9. Let w be u(-6). Suppose 12 + w = 3*v. Solve 2*j**3 - j**2 - v*j**4 + 4*j**4 - 4*j**3 = 0.
-1, 0
Let f = -587/12 - -49. Let x(o) be the first derivative of -1/6*o**3 + f*o**6 - 3/10*o**5 + 2 + 3/8*o**4 + 0*o**2 + 0*o. Factor x(i).
i**2*(i - 1)**3/2
Let x = -66 - -111. Let o = x + -134/3. Find d, given that 0 + 0*d + o*d**3 + 0*d**2 = 0.
0
Suppose 0 + 2/5*i**2 + 4/5*i = 0. Calculate i.
-2, 0
Let q(i) = i**3 + 5*i**2 + 3*i - 2. Let k be q(-4). Suppose 4*u - 4 = 2*u. Factor 0*b**u + b**k - 4*b**3 + 5*b**3.
b**2*(b + 1)
Let d(h) be the third derivative of h**8/7560 - h**7/3780 - h**6/1620 + h**5/540 + 2*h**3/3 + 3*h**2. Let a(c) be the first derivative of d(c). Factor a(f).
2*f*(f - 1)**2*(f + 1)/9
Let h be 1 - 2*(-2)/2. Let f(x) = x**4 - x**3 - x + 1. Let z(j) = 2*j**4 - 4*j**3 + 3*j**2 - 2*j + 1. Let m(t) = h*f(t) - z(t). Factor m(o).
(o - 1)**2*(o + 1)*(o + 2)
Let s(f) be the second derivative of -1/21*f**7 + 0*f**6 + 0 + 1/5*f**5 - 1/3*f**3 + 0*f**4 + 0*f**2 - 2*f. Factor s(z).
-2*z*(z - 1)**2*(z + 1)**2
Suppose -4*c + 10 = -0*u + 5*u, -4*u - 4*c + 8 = 0. Factor 4*s**3 + 6*s**u + 1/4 + 9/4*s.
(s + 1)*(4*s + 1)**2/4
Let n(c) = 8*c**3 + 8*c**2 - 10*c. Suppose 5*h = 7*h - 20. Let z(d) = -d**3 - d**2 + d. Let i(v) = h*z(v) + n(v). Solve i(l) = 0 for l.
-1, 0
Let w(x) = -18*x**3 + 9*x**2 + 7*x + 13. Let d(h) be the second derivative of -h**5/20 + h**4/12 + h**2/2 + h. Let y(g) = -22*d(g) + 2*w(g). Factor y(z).
-2*(z - 1)*(z + 1)*(7*z + 2)
Let d(t) = t**3 + 8*t**2 - 11*t - 9. Let q be d(-9). Let r be 48/(-200)*(-60)/q. Factor -2/5*s + 8/5*s**4 - 12/5*s**3 + 0 - 2/5*s**5 + r*s**2.
-2*s*(s - 1)**4/5
Let m(j) be the first derivative of 0*j**2 + 3/5*j**5 + 0*j - 5/6*j**6 + 1/2*j**4 - 6 + 0*j**3. Factor m(a).
-a**3*(a - 1)*(5*a + 2)
Let u = -338/5 - -68. Let 48/5*s**2 + 32/5 + u*s**4 + 64/5*s + 16/5*s**3 = 0. Calculate s.
-2
Let s be 4/16 - 7/(-4). Factor -s + 5*l**2 + 2*l + 4*l - 3*l.
(l + 1)*(5*l - 2)
Let d(w) = -w - 1. Let b be d(1). Let f(i) = -4*i**2 - 7*i + 9. Let n(l) = l**2 - 1. Let x(v) = b*f(v) - 14*n(v). Factor x(y).
-2*(y - 2)*(3*y - 1)
Let z(g) be the third derivative of -g**6/120 - g**5/30 + g**4/6 + 4*g**3/3 - 20*g**2. Determine i, given that z(i) = 0.
-2, 2
Solve 16/3 + 4/3*n**2 + 16/3*n = 0.
-2
Let d = 8 - 5. Factor 5*y**5 - y**2 + 13*y**4 - y**3 + 10*y**d + 0*y + 4*y - 6*y.
y*(y + 1)**3*(5*y - 2)
Let a be -26*44/(-160) - (-4)/(-10). Factor -3/4*j**4 + 21/4*j + 15/4*j**3 - a*j**2 - 3/2.
-3*(j - 2)*(j - 1)**3/4
Let d(t) be the second derivative of -2*t**6/15 + t**5/5 + 2*t**4/3 + 3*t. Factor d(o).
-4*o**2*(o - 2)*(o + 1)
Find j, given that -18/11*j**3 - 58/11*j**2 + 0 - 12/11*j = 0.
-3, -2/9, 0
Let w(b) = -12*b**2 - 8*b + 11. Let a(m) = m**2 - 1. Let h(x) = -44*a(x) - 4*w(x). Find c such that h(c) = 0.
-8, 0
Let s = 16 - 11. Let c(h) be the first derivative of 0*h - 1 + 0*h**2 + 2/9*h**3 + 1/3*h**4 - 2/5*h**s. Find i, given that c(i) = 0.
-1/3, 0, 1
Let w(u) be the first derivative of u**5/100 + u**4/20 + u**3/10 - u**2 - 4. Let j(r) be the second derivative of w(r). Factor j(d).
3*(d + 1)**2/5
Let b(s) = -4*s**2 + 2*s + 2. Let z(i) = -23*i**2 + 12*i + 11. Let f = 21 - 15. Let n(p) = f*z(p) - 34*b(p). Factor n(t).
-2*(t - 1)**2
Let d(j) = -j**3 - j + 1. Let l(c) = 5*c**3 - 45*c**2 + 227*c - 377. Let t(i) = 2*d(i) + l(i). What is r in t(r) = 0?
5
Let w(m) be the second derivative of 0*m**3 - 1/5*m**5 - 1/6*m**4 + 0*m**2 + 3*m + 0 - 1/15*m**6. What is k in w(k) = 0?
-1, 0
Factor -6*o**2 + 7*o**3 - 9*o**3 - 2 + 10.
-2*(o - 1)*(o + 2)**2
Let u(y) be the first derivative of y**5/10 - y**4/3 + y**3/3 - 2*y + 4. Let r(f) be the first derivative of u(f). Factor r(z).
2*z*(z - 1)**2
Factor -2 - 9/2*a**2 - 1/4*a**4 - 5*a - 7/4*a**3.
-(a + 1)*(a + 2)**3/4
Suppose -2*v + 0*v - 4*o = 0, 2*v - 4*o = 0. Let t(d) be the third derivative of v + 2*d**2 + 0*d**3 + 0*d + 0*d**5 + 1/60*d**6 - 1/12*d**4. Factor t(x).
2*x*(x - 1)*(x + 1)
Let p(m) be the first derivative of m**6/2 - 9*m**4/4 + 2*m**3 + 8. Let p(x) = 0. What is x?
-2, 0, 1
Suppose -2*q - 4*z + 68 = 0, -q + 34 = 2*z + 2*z. Let c = q - 31. Factor 0 + 0*h**c + 4/3*h + 2/3*h**4 - 2*h**2.
2*h*(h - 1)**2*(h + 2)/3
Solve -1/4*d**4 + 0*d - 1/4*d**3 + 1/4*d**5 + 1/4*d**2 + 0 = 0.
-1, 0, 1
Suppose 2 + 26 = 4*p. Suppose 4 = 2*g + d, 5*g + 0*d = -4*d + p. Solve 0*a + 0 - 2/5*a**g + 2/5*a**2 = 0.
0, 1
Let i(k) be the third derivative of k**7/84 + k**6/120 - k**5/8 + k**4/12 + k**3/3 + 60*k**2. Factor i(o).
(o - 1)**2*(o + 2)*(5*o + 2)/2
Let f(h) be the second derivative of 0*h**2 + 1/27*h**3 - 1/27*h**4 + 1/90*h**5 + 7*h + 0. Factor f(u).
2*u*(u - 1)**2/9
Let i be 2 + -2 - ((-2)/(-4) + -1). Find b such that 1/2*b**3 + i - 1/2*b - 1/2*b**2 = 0.
-1, 1
Let b = -6 + 12. Let m be ((-24)/(-50))/(b/20). Let -2/5*i**2 - 8/5*i - m = 0. What is i?
-2
Let v be 12/(-8) + 21/(-6). Let g = v - -8. Solve 2*s + 2/5*s**g + 8/5*s**2 + 4/5 = 0 for s.
-2, -1
Let o be 4/4 + (0 - -1). Let p be o/(-4)*-44 + 1. Suppose 5*x + 35 - 9 + 3*x**2 + 1 - p*x = 0. Calculate x.
3
Let p(o) be the first derivative of -o**7/672 - o**6/480 + o**5/240 - 5*o**3/3 + 4. Let r(j) be the third derivative of p(j). Factor r(y).
-y*(y + 1)*(5*y - 2)/4
Let g be (4/(-16))/((-21)/24). Let r(q) be the first derivative of 5/7*q**2 + 2 - g*q + 5/7*q**4 - 20/21*q**3 - 2/7*q**5 + 1/21*q**6. Let r(o) = 0. Calculate o.
1
Solve 3*a - 3/2*a**2 - 3/2 = 0.
1
Factor 3/4*o**4 - 3/2*o + 0 + 0*o**3 - 9/4*o**2.
3*o*(o - 2)*(o + 1)**2/4
Suppose 1 + 1/3*s**3 + 7/3*s + 5/3*s**2 = 0. Calculate s.
-3, -1
Let z(c) be the third derivative of -c**7/420 + c**6/48 - c**5/20 - c**4/12 + 2*c**3/3 - 3*c**2. Factor z(p).
-(p - 2)**3*(p + 1)/2
Let d(r) = 7*r**2 + 4*r - 3. Let p(l) = -6*l**2 - 3*l + 3. Let b(j) = -6*d(j) - 5*p(j). Factor b(q).
-3*(q + 1)*(4*q - 1)
Let l = 0 - -3. Determine z, given that 5*z**4 + 5*z**l - 4*z**3 + 3*z - 3*z**4 - 4*z - 2*z**2 = 0.
-1, -1/2, 0, 1
Let g be 2/(-7) + ((-1380)/112)/(-23). Factor -1/2*i**2 - g*i + 1/4.
-(i + 1)*(2*i - 1)/4
Let v(u) = -u**2 + 9*u + 3. Let l be v(7). Solve -9*h**2 + l*h**3 + 12*h**3 + 4*h - 10*h**4 + 0*h - 11*h**2 = 0.
0, 2/5, 1/2, 2
Let i(h) = -14*h**4 + 18*h**3 - 4*h**2 + 7. Let y(z) = -2 - 3 + 0 + 6. Let n(w) = -2*i(w) + 14*y(w). Let n(d) = 0. What is d?
0, 2/7, 1
Let b(z) be the first derivative of z**6/15 + 3*z**5/25 - z**4/10 - 4*z**3/15 + z/5 + 11. Determine j so that b(j) = 0.
-1, 1/2, 1
Suppose 81*g - 83*g = 2*j - 8, -4*g + 12 = 2*j. Let -8/3*a**3 - 4*a**j - 8/3*a - 2/3 - 2/3*a**4 = 0. Calculate a.
-1
Let m(z) be the third derivative of -5*z**8/336 + z**7/42 + z**6/8 - 5*z**5/12 + 5*z**4/12 + 4*z**2. Determine p, given that m(p) = 0.
-2, 0, 1
Let f = 35 - 32. Suppose -3*o + 4*o - 2 = 0. Factor 10/9*n**f - 8/3*n**2 - 4/9 + o*n.
2*(n - 1)**