i(b) be the second derivative of 0 + 0*b**3 - 3*b + p*b**5 + 1/24*b**4 + 0*b**2 + 1/60*b**6. Determine j, given that i(j) = 0.
-1, 0
Let u(t) be the third derivative of t**8/112 + t**7/70 - t**6/20 - t**5/10 + t**4/8 + t**3/2 + 2*t**2. Suppose u(y) = 0. Calculate y.
-1, 1
Solve 124 - s**4 - 2*s**3 - s**2 - 124 = 0.
-1, 0
Let h = 6 + 1. Let s(k) = 2*k**2 + 0 - 1 + 28*k**3 + 3*k**2 - 32*k**3. Let w(j) = -12*j**3 + 14*j**2 + j - 3. Let b(p) = h*s(p) - 2*w(p). Factor b(i).
-(i - 1)**2*(4*i + 1)
Let z(j) be the first derivative of -1/4*j**4 - j + 1/3*j**3 + 2 + 1/2*j**2. Factor z(d).
-(d - 1)**2*(d + 1)
Factor -2*p + 2*p**5 - 17*p**3 + p + 19*p**3 - 3*p**5.
-p*(p - 1)**2*(p + 1)**2
Let k(m) = -m**2 - 1. Let h(p) = -p**4 + 5*p**2 + 5. Let x(d) = -h(d) - 5*k(d). Factor x(v).
v**4
Let x(n) be the second derivative of -n**6/30 + n**5/30 + n**4/12 - n**3/9 + 9*n. Factor x(r).
-r*(r - 1)*(r + 1)*(3*r - 2)/3
Let o(b) be the first derivative of b**8/6720 - b**6/1440 - 2*b**3/3 - 2. Let i(a) be the third derivative of o(a). Factor i(w).
w**2*(w - 1)*(w + 1)/4
Find s, given that 0*s + 1/4*s**3 - 1/4*s**4 + 0 + 0*s**2 = 0.
0, 1
Suppose 2*m - 97 = -u, -4*m + 5*u + 164 = u. Let o be 2/5 + m/10. Solve 0 + 7/3*d**2 - d**o - 7/3*d**4 + 1/3*d**3 + 2/3*d = 0.
-2, -1, -1/3, 0, 1
Suppose -c + 6*c = 25. Let f(r) be the third derivative of 1/4*r**4 + 2/3*r**3 + 0*r - 1/30*r**c - 1/105*r**7 + 0 - 1/20*r**6 + 3*r**2. Factor f(o).
-2*(o - 1)*(o + 1)**2*(o + 2)
Let g(u) be the second derivative of u**7/42 - u**6/30 - u**5/20 + u**4/12 + 11*u. Factor g(a).
a**2*(a - 1)**2*(a + 1)
Let h = 4 - 1. Suppose -4*w + h*v = -6, 4*w - w + 3*v - 15 = 0. Determine g, given that 5*g**2 + 4*g - 3*g**3 + g**3 - w*g**2 = 0.
-1, 0, 2
Let u(q) be the second derivative of -q**6/105 - 2*q**5/35 - 5*q**4/42 - 2*q**3/21 + 4*q. Factor u(f).
-2*f*(f + 1)**2*(f + 2)/7
Suppose 3 - 18 = -5*m, 2*x - 5*m = -23. Let f = x - -5. Solve 5*u**4 - 2*u**5 + 2*u**3 - 2*u**2 - 3*u**4 + 1 - f = 0 for u.
-1, 0, 1
Let c(n) be the third derivative of -2*n**7/105 - 7*n**6/30 - 6*n**5/5 - 10*n**4/3 - 16*n**3/3 + 58*n**2. Suppose c(k) = 0. Calculate k.
-2, -1
Let d(k) be the second derivative of -3*k**5/110 + 49*k**4/66 - 208*k**3/33 + 64*k**2/11 + 24*k. Factor d(n).
-2*(n - 8)**2*(3*n - 1)/11
Let f(a) = -a**4 + a**3 - a**2 - a + 1. Suppose 0*s + 1 = -s. Let t(i) = 3*i**3 - i**2 - 3*i. Let v(g) = s*f(g) + t(g). Determine m so that v(m) = 0.
-1, 1
Let p(h) = 5*h**4 + 5*h**3 - 7*h**2 - 3*h + 2. Let i(g) = 10*g**4 + 10*g**3 - 15*g**2 - 5*g + 5. Let u(f) = -2*i(f) + 5*p(f). Factor u(k).
5*k*(k - 1)*(k + 1)**2
Let y(d) = d**3 + 6*d**2 - 6*d + 10. Let u(t) = 6*t**3 + 2*t + 1. Let c be u(-1). Let i be y(c). Factor 5*z**2 - 5*z**2 - 4*z**2 + 2*z - 6*z**i + 4 - 4*z**2.
-2*(z + 1)**2*(3*z - 2)
Suppose -2*w - w = -6. Let r be 7/4 + 1/4. Factor -10*t**3 + 4*t**2 + w*t**3 - r*t**3 - 4 + 10*t.
-2*(t - 1)*(t + 1)*(5*t - 2)
Let j(l) be the third derivative of -l**6/216 + 7*l**5/90 - 4*l**4/9 + 16*l**3/27 - l**2. Suppose j(c) = 0. Calculate c.
2/5, 4
Factor 5*w**2 - 16*w + 20 + 15*w - 24*w.
5*(w - 4)*(w - 1)
Let h = 7943/5 + -1581. Suppose 294/5*s**4 - 364/5*s**3 + h*s**2 - 8/5 + 8*s = 0. What is s?
-1/3, 2/7, 1
Let u be 10/(-15) + 8/3. Factor -q + 9 + 2*q - 5*q - 3*q**u - 2*q.
-3*(q - 1)*(q + 3)
Let f(r) be the first derivative of -2 + 0*r**3 + 1/2*r**4 - 3*r**2 - 4*r. Factor f(h).
2*(h - 2)*(h + 1)**2
Let h(s) be the third derivative of -5*s**2 - 1/60*s**4 + 0 - 1/525*s**7 + 0*s**3 + 0*s + 1/150*s**5 + 1/300*s**6. Suppose h(k) = 0. Calculate k.
-1, 0, 1
Let r(q) be the third derivative of q**6/40 - q**5/10 - q**4/2 + 4*q**3 - 13*q**2. Let r(a) = 0. What is a?
-2, 2
Let p = -12 + 17. Let u(i) be the third derivative of 0*i - 1/525*i**7 + 0*i**3 - 1/50*i**p - 1/60*i**4 - 2*i**2 + 0 - 1/100*i**6. Factor u(c).
-2*c*(c + 1)**3/5
Let b(y) = -4*y**2 - 5*y + 11. Let s(f) = 2*f**2 + 3*f - 5. Let t(w) = 6*b(w) + 10*s(w). Suppose t(l) = 0. Calculate l.
-2, 2
Let o(b) be the third derivative of 2*b**7/105 - b**6/15 + 20*b**2. Factor o(f).
4*f**3*(f - 2)
Factor -9/7*v**3 + 3/7*v**4 - 6/7*v - 15/7*v**2 + 0 + 3/7*v**5.
3*v*(v - 2)*(v + 1)**3/7
Let b(h) be the second derivative of h**5/25 - 2*h**4/15 + 2*h**3/15 + 3*h. Factor b(m).
4*m*(m - 1)**2/5
Let a be ((-6)/(-30))/((-8)/(-190)). Let y = a - 87/20. Factor y*g**3 + 0*g**2 + 0*g + 0.
2*g**3/5
Let k be (-1)/2 - 24/(-8). Let w(b) be the second derivative of 0 - 3*b**2 + 1/10*b**6 - k*b**3 + 3*b - 3/4*b**4 + 3/20*b**5. Let w(o) = 0. Calculate o.
-1, 2
Let y(n) be the third derivative of 7/108*n**4 + 5/108*n**6 - 16/945*n**7 + 0 - 1/27*n**3 + 1/378*n**8 + 3*n**2 - 19/270*n**5 + 0*n. Factor y(z).
2*(z - 1)**3*(2*z - 1)**2/9
Let c be (-3)/27 - 14/(-18). Let w(v) be the second derivative of 0*v**2 + 5/6*v**4 - 3*v - 2/5*v**5 - c*v**3 + 1/15*v**6 + 0. Let w(p) = 0. Calculate p.
0, 1, 2
Let g(x) be the second derivative of x**5/50 - x**3/15 + x. Factor g(k).
2*k*(k - 1)*(k + 1)/5
Factor -6/5*n - 2/5 - 6/5*n**2 - 2/5*n**3.
-2*(n + 1)**3/5
Let t(v) be the first derivative of -v**8/84 + v**7/35 + v**6/30 - 3*v**2 - 5. Let w(j) be the second derivative of t(j). Factor w(q).
-2*q**3*(q - 2)*(2*q + 1)
Let f(s) = -2*s**3 + 12*s**2 + 16*s - 14. Let g be f(7). Factor 0*l + 0*l**3 - 3/7*l**5 + g*l**4 + 0 + 0*l**2.
-3*l**5/7
Let s(h) be the second derivative of 0 - 3*h - 1/7*h**2 - 4/21*h**3 - 1/14*h**4. Factor s(b).
-2*(b + 1)*(3*b + 1)/7
Let p(j) be the third derivative of -3/70*j**7 + 0*j + 1/20*j**6 - 2*j**2 + 0*j**3 + 1/20*j**5 + 0*j**4 + 0. Solve p(d) = 0 for d.
-1/3, 0, 1
Let c be 3*-1*10/(-15). Let y = 4 - c. Find r, given that -48*r**3 - 18*r**4 - 2*r - 5*r - 44*r**2 + 0*r - 9*r - y = 0.
-1, -1/3
Let b(v) be the second derivative of 5*v**7/42 - 10*v**6/3 + 63*v**5/2 - 245*v**4/3 - 1715*v**3/6 - 19*v. Solve b(f) = 0 for f.
-1, 0, 7
Let r(x) be the second derivative of -5*x**5/2 + 15*x**4/2 - 8*x**3 + 4*x**2 + 6*x. Factor r(w).
-2*(w - 1)*(5*w - 2)**2
Let h(d) = 9*d**5 + 6*d**4 - 14*d**2 - d. Let s(j) = -8*j**5 - 7*j**4 + 13*j**2 + 2*j. Let k(w) = 3*h(w) + 4*s(w). Factor k(g).
-5*g*(g - 1)*(g + 1)**3
Let r = 41/10 - 18/5. Factor -1/2*l**3 + r*l + 3/4*l**2 + 0.
-l*(l - 2)*(2*l + 1)/4
Suppose -5*g + 4*b - 15 = 0, -3*g = -8*g + b. Suppose 39*m**2 - 6 - 9 - 15*m**3 - 12*m + 2 + g = 0. What is m?
-2/5, 1, 2
Let n(f) = f**2 + f + 4. Let k(q) = -3*q**2 - 3*q - 9. Let p be 3/6*0 + 16. Let t = 10 - p. Let c(j) = t*k(j) - 15*n(j). Factor c(u).
3*(u - 1)*(u + 2)
Suppose -5*s = -10 - 10. Factor -8*j - s*j**3 - 16*j**2 + 7*j**2 - 3*j**2.
-4*j*(j + 1)*(j + 2)
Let r(u) be the second derivative of 5*u**7/42 - u**6/2 + 3*u**5/4 - 5*u**4/12 - 7*u. Determine v so that r(v) = 0.
0, 1
Let b(n) be the first derivative of 1/4*n**2 + 1/4*n + 1/12*n**3 + 1. Factor b(m).
(m + 1)**2/4
Let o(t) be the second derivative of t**4/21 + t**3/14 - t**2/14 + 7*t. Factor o(f).
(f + 1)*(4*f - 1)/7
Let u(q) be the first derivative of -7 - 4/5*q**2 + 1/10*q**4 - 4/5*q + 1/15*q**3. Factor u(s).
(s - 2)*(s + 2)*(2*s + 1)/5
Let l(j) be the third derivative of 1/12*j**4 + j**2 + 1/3*j**3 + 0*j + 0 + 0*j**5 - 1/180*j**6. Let h(r) be the first derivative of l(r). Factor h(k).
-2*(k - 1)*(k + 1)
What is q in 0 + 0*q + 3/2*q**2 = 0?
0
Let m(h) be the first derivative of 7*h**6/160 - 9*h**5/80 + h**4/16 - h**2/2 - 7. Let x(p) be the second derivative of m(p). Solve x(r) = 0 for r.
0, 2/7, 1
Suppose 0 = -3*p - 0*p + 15. Let m(h) be the second derivative of 2/15*h**p - 1/18*h**4 + 1/3*h**2 - 4/9*h**3 + 2*h + 0. Factor m(s).
2*(s - 1)*(s + 1)*(4*s - 1)/3
Let p(h) be the third derivative of -h**6/80 + 3*h**5/80 - h**3/8 + 31*h**2. Factor p(q).
-3*(q - 1)**2*(2*q + 1)/4
Factor 28/5*q - 1/5*q**3 - 1/5*q**4 + 12/5*q**2 + 16/5.
-(q - 4)*(q + 1)*(q + 2)**2/5
Factor -2/15*g**2 + 8/15 + 0*g.
-2*(g - 2)*(g + 2)/15
Determine x, given that -1458/7 + 486/7*x - 54/7*x**2 + 2/7*x**3 = 0.
9
Let x(l) be the third derivative of 9*l**2 + 1/20*l**5 + 0*l**3 + 0 + 0*l + 3/40*l**4 + 7/600*l**6 + 1/1050*l**7. Suppose x(c) = 0. Calculate c.
-3, -1, 0
Solve -3*w + 22 + 32 + w**2 - 52 = 0.
1, 2
Factor 0*f**3 - 8/5*f + 6/5*f**2 + 3/5 - 1/5*f**4.
-(f - 1)**3*(f + 3)/5
Let c(x) be the second derivative of 1/12*x**4 - 1/20*x**5 + 1/3*x**3 + 0 + 4*x + 0*x**2. Let c(f) = 0. What is f?