rd derivative of -1/24*m**4 + 1/30*m**5 - 1/105*m**7 + 0*m**3 + 0 + m**2 + 1/336*m**8 + 0*m + 0*m**6. Factor z(b).
b*(b - 1)**3*(b + 1)
Let h(z) = 4*z**5 - 5*z**4 - z**3 + 8*z**2 + 3. Let s(i) = i**4 + i**3 + 1. Let y(b) = h(b) - 3*s(b). Factor y(t).
4*t**2*(t - 2)*(t - 1)*(t + 1)
Let i(m) = -m**3 - 6*m**2 - 4*m + 7. Let j be i(-5). Find p such that -4 + 4*p + 0*p**j - 4*p**2 + 3*p**2 = 0.
2
Let x(w) be the second derivative of -5*w**4/12 - 17*w**3/42 - w**2/7 + 25*w. Factor x(s).
-(5*s + 1)*(7*s + 2)/7
Let d be -6 + (-8)/(-3) + 4. Factor d*i**2 + 0 + 2*i.
2*i*(i + 3)/3
Let r(p) be the third derivative of -9/40*p**6 + 5*p**2 + p**3 + 0*p + 11/8*p**4 + 3/5*p**5 + 0. Factor r(w).
-3*(w - 2)*(3*w + 1)**2
Let u(k) = k**5 - k**3 - k. Let s(q) = -q**5 - 14*q**4 - 29*q**3 - 4*q**2 + 29*q + 18. Let v(r) = s(r) - u(r). Suppose v(i) = 0. Calculate i.
-3, -1, 1
Let p(n) be the third derivative of -1/15*n**6 + 0*n + 0 + 2*n**3 - 7*n**2 - 1/3*n**5 + 2/3*n**4. Factor p(j).
-4*(j - 1)*(j + 3)*(2*j + 1)
Let m(c) be the third derivative of c**7/1050 - c**6/300 - c**5/100 + 9*c**2. Determine g so that m(g) = 0.
-1, 0, 3
Let p(a) be the third derivative of -a**6/420 - a**5/210 + a**4/84 + a**3/3 - 2*a**2. Let u(w) be the first derivative of p(w). Solve u(x) = 0 for x.
-1, 1/3
Suppose -6 = -5*m + 4. Suppose 0*i + i = m. Find v such that -5*v**3 - 5*v**4 + 3*v**4 - v**3 - i*v - 6*v**2 = 0.
-1, 0
Let l(z) be the second derivative of -z**6/255 - z**5/85 + z**4/34 + 8*z**3/51 + 4*z**2/17 - 18*z. Suppose l(q) = 0. Calculate q.
-2, -1, 2
Let z(y) = 7*y**2 - 3*y**3 + 0*y**3 + 3*y**3 - 5*y - 2*y**4 - 5. Let r(a) = 6*a**4 - 22*a**2 + 16*a + 16. Let k(i) = 5*r(i) + 16*z(i). Factor k(l).
-2*l**2*(l - 1)*(l + 1)
Let t(k) be the first derivative of -3*k**5/5 + 3*k**4/2 - k**3 + 4. Find s such that t(s) = 0.
0, 1
Let v(i) = -i - 4. Let u be v(-6). Factor 8*o**u + 4*o - 8*o**2 + 2*o**2 + 2.
2*(o + 1)**2
Factor 3*v**2 - 2*v**3 + 13*v**4 + v + 4*v**5 + 4*v**2 + 0*v + 17*v**3.
v*(v + 1)**3*(4*v + 1)
Let x = -24 - -26. Suppose -3*i - 2*n = 8, -i - 8 = 4*i + x*n. Factor i + 8*f**3 + 8/5*f**2 + 10*f**4 + 0*f.
2*f**2*(5*f + 2)**2/5
Let x(i) be the first derivative of 1/9*i**3 + 0*i + 3 + 0*i**2. What is k in x(k) = 0?
0
Let n(p) = -3*p**4 + 7*p**3 - p**2 + p - 4. Let d(g) = 6*g**4 - 13*g**3 + g**2 - g + 7. Let t(b) = 4*d(b) + 7*n(b). Factor t(r).
3*r*(r - 1)**2*(r + 1)
Let r be (-52)/(-20) - 1 - (-8)/20. Factor 1/4*b**3 + 3/4*b**r - 1/4*b - 1/4*b**4 - 1/2.
-(b - 2)*(b - 1)*(b + 1)**2/4
Let o(g) = -2*g**2 - g + 5. Let v(a) = a**2 + a - 3. Let k(s) = 3*o(s) + 5*v(s). Solve k(j) = 0 for j.
0, 2
Let t = 6 - 3. Let p(f) be the third derivative of 0 + 0*f - 1/210*f**5 - f**2 + 1/21*f**4 - 4/21*f**t. Determine y, given that p(y) = 0.
2
Let q(h) be the first derivative of h**8/10920 + h**7/5460 - h**6/2340 - h**5/780 + h**3/3 - 3. Let n(l) be the third derivative of q(l). Factor n(c).
2*c*(c - 1)*(c + 1)**2/13
Suppose -4*m = -8*m + 44. Factor 11*g + m*g**3 + 10*g**3 - 48*g**2 + g.
3*g*(g - 2)*(7*g - 2)
Let v be (-24)/20*(-10)/4. Suppose 2*i + v*i = 0. Solve 1/2*l**2 + i - 1/2*l = 0.
0, 1
Let v(p) = p**3. Let j(t) = 4*t**3 - 24*t**2 + 48*t. Let f(y) = j(y) - v(y). Factor f(n).
3*n*(n - 4)**2
Let m = -544/7 + 78. Let i = 0 - -4. Find r such that 0*r**3 - m*r**i + 0*r + 4/7*r**2 - 2/7 = 0.
-1, 1
Suppose 0*l + 2*l = 0. Factor l + 2/5*v**2 + 4/5*v**3 + 2/5*v**4 + 0*v.
2*v**2*(v + 1)**2/5
Let v(b) be the second derivative of -1/3*b**2 + 0 - 8*b - 2/9*b**3 - 1/18*b**4. Factor v(t).
-2*(t + 1)**2/3
Determine y, given that 1/3 + 0*y - 2/3*y**2 + 1/3*y**4 + 0*y**3 = 0.
-1, 1
Determine f, given that 68*f**2 - 145*f**3 - 12 + 13*f**3 + 4 - 8 + 80*f = 0.
-2/3, 2/11, 1
Let w(h) = 3*h**2 + 1. Let p be w(-1). Suppose p*c - 23 = -4*d + c, 3*c = -3*d + 21. Suppose -5/3*g**d - 2/3*g**3 - 4/3*g - 1/3 = 0. Calculate g.
-1, -1/2
Solve 0 + 6/11*b**2 - 2/11*b**4 + 0*b**3 - 4/11*b = 0.
-2, 0, 1
Factor 2/3 - 1/3*z**2 - 1/3*z.
-(z - 1)*(z + 2)/3
Let j(g) be the second derivative of g**5/60 + g**4/12 + g**3/9 + 20*g. Suppose j(o) = 0. Calculate o.
-2, -1, 0
Let g(t) = 4*t**2 - 19*t + 22. Let d(b) = 4*b**2 - 18*b + 20. Let w(j) = -5*d(j) + 6*g(j). Factor w(m).
4*(m - 4)*(m - 2)
Solve 125*g**2 - 12*g - 126*g**2 + 10*g = 0.
-2, 0
Let n be (60/250*-10)/(1 - 3). Factor 0*x**2 + 9/5*x - 3/5*x**3 - n.
-3*(x - 1)**2*(x + 2)/5
Factor 2/15*l - 8/5 + 8/5*l**2 - 2/15*l**3.
-2*(l - 12)*(l - 1)*(l + 1)/15
Let u(l) be the first derivative of -10*l**5 - 10*l**4 + 14*l**3 + 20*l**2 + 8*l - 8. Solve u(x) = 0 for x.
-1, -2/5, 1
Factor 10/7*d**4 + 0*d**2 + 0 + 0*d + 6/7*d**5 + 4/7*d**3.
2*d**3*(d + 1)*(3*d + 2)/7
Let d(a) = -50*a**5 - 46*a**4 - 12*a**3 - 8*a + 8. Let r(i) = 17*i**5 + 15*i**4 + 4*i**3 + 3*i - 3. Let b(m) = -3*d(m) - 8*r(m). Find n, given that b(n) = 0.
-1, -2/7, 0
Let o = 20/39 - 9/26. Solve 0 - o*k**3 + 1/3*k**2 + 0*k = 0.
0, 2
Let s(k) = -k**2 + 6*k - 5. Let i be s(5). Let b be 5/(-15)*(-12)/8. Find p, given that 0 + 1/2*p**3 + i*p + b*p**2 = 0.
-1, 0
Let s be ((-6)/(-7))/((128/(-28))/(-4)). Factor 0 + 3/4*o**4 - 3/4*o - s*o**2 + 3/4*o**3.
3*o*(o - 1)*(o + 1)**2/4
Let o(k) be the third derivative of -k**7/105 - k**6/10 - 4*k**5/15 + k**4/2 + 3*k**3 + 3*k**2. Find y, given that o(y) = 0.
-3, -1, 1
Let k(h) = h**4 + h**3 - h**2 - h. Let b(c) = -9*c**4 - 9*c**3 + 5*c**2 + 5*c. Let t(d) = b(d) + 5*k(d). Find x such that t(x) = 0.
-1, 0
Let p(w) be the second derivative of 3*w**5/2 + 5*w**4/12 - 5*w**3 - 5*w**2/2 - 20*w. Determine u so that p(u) = 0.
-1, -1/6, 1
Let h(f) = 7*f**4 + 11*f**3 + 2*f**2 - 2*f + 6. Let y(d) = -d**4 - d**3 + d**2 + d - 1. Let g(u) = -5*h(u) - 30*y(u). Factor g(l).
-5*l*(l + 1)*(l + 2)**2
Let h(m) be the second derivative of m**5/16 - m**4/48 - 5*m**3/24 + m**2/8 + 19*m. Factor h(k).
(k - 1)*(k + 1)*(5*k - 1)/4
Let b(r) = -r**3 - 6*r**2 - 5*r + 3. Let m(f) = 3*f**3 + 17*f**2 + 14*f - 8. Let x(l) = -8*b(l) - 3*m(l). Factor x(n).
-n*(n + 1)*(n + 2)
Let i be (0 + (-3)/9)*-9. Let x(p) be the first derivative of -p - 1/3*p**i + 1 - p**2. Factor x(r).
-(r + 1)**2
Let g(v) be the second derivative of v**7/3360 - v**6/720 - v**3/2 + 4*v. Let t(y) be the second derivative of g(y). Factor t(b).
b**2*(b - 2)/4
Let o(h) be the second derivative of 0*h**2 + 1/21*h**4 - 3*h + 1/70*h**5 + 1/21*h**3 + 0. Factor o(x).
2*x*(x + 1)**2/7
Suppose -115*o + 117*o = 8. Factor -2*u**3 - 24/13*u**2 - 12/13*u**o - 8/13*u + 0 - 2/13*u**5.
-2*u*(u + 1)**2*(u + 2)**2/13
Let d = 9/8 - 25/24. Let o(u) be the second derivative of -d*u**4 + 3*u - 1/40*u**5 - 1/12*u**3 + 0*u**2 + 0. Let o(z) = 0. What is z?
-1, 0
Let m be -2 - (3 - 1)/1. Let x = m + 16/3. Factor -2/3 + 2*w**2 + 2/3*w + x*w**4 - 10/3*w**3.
2*(w - 1)**3*(2*w + 1)/3
Factor -3*z**2 - 7 + 0*z + 2 - 9*z - 1.
-3*(z + 1)*(z + 2)
Let q(n) = n**2 + 1. Let i be q(1). Factor 2*j**3 + j**2 - 3*j**3 + i*j + 12 - 12.
-j*(j - 2)*(j + 1)
Let f(r) = -r**2 - 10*r - 7. Let p be f(-9). Determine s so that -s + s**3 - 2*s**3 + 3*s**p - s**2 = 0.
0, 1
Suppose -4 + 7 = 3*s. Let j(i) be the first derivative of 0*i**5 + 0*i - s + 0*i**3 + 1/30*i**6 + 0*i**2 - 1/20*i**4. Suppose j(r) = 0. What is r?
-1, 0, 1
Let n(z) be the first derivative of 16*z**6/21 + 16*z**5/35 + z**4/14 + 14. Find u, given that n(u) = 0.
-1/4, 0
Let f(w) = w - 5. Let j be f(8). Suppose 2 = -j*r + 4*s, 6*s - s = -r + 12. Factor r*b**2 - 2*b - 1 - b**2 - 2*b**2 + 4*b.
-(b - 1)**2
Let x = 18 + -9. Suppose 0 = -d + 4*d - x. Factor 4*f**2 + f**2 + d*f**3 + 3*f + 4 - 5 - 2*f.
(f + 1)**2*(3*f - 1)
Factor r - r + 3*r**2 - 3*r.
3*r*(r - 1)
Let u = -2/29 - -33/58. Let 0*x + 0 + u*x**2 = 0. What is x?
0
Solve -2/15 - 4/15*p + 2/5*p**2 = 0.
-1/3, 1
Suppose -2*v + 4*z + 16 = 0, 13*v - 8*v - 16 = 2*z. Factor -2/13*x**v + 0 - 2/13*x.
-2*x*(x + 1)/13
Let m(a) be the second derivative of -a**5/20 + a**4/12 + a**3/3 - 12*a. Factor m(z).
-z*(z - 2)*(z + 1)
Let b(v) be the second derivative of v**5/80 - v**4/48 - 5*v**3/24 - 3*v**2/8 - 9*v. Let b(w) = 0. Calculate w.
-1, 3
Let h = 0 - 0. Suppose j + 9 = 5*p - 2*j, h = -3*p - j + 11. Determine q so that -3*q**4 + p*q**2 + 3*q + 3*q**3 + 0*q**3 - 5*q**3 - q**3 = 0.
-1, 0, 1
Solve 1/2*n**3 - n + 1/2*n**5 + 3/2*n**4 + 0 - 3/2*n**2 = 0 for n.
-2, -1, 0, 1
Let x(r) be the second derivative of