o - 4. Let m(p) = -n(p) - 4*t(p). Factor m(f).
-3*f*(3*f + 2)*(5*f - 2)**2
Let t(s) = -3*s**4 + 9*s**3 + 5*s**2 - 12*s. Let i(w) = 3*w**4 - 9*w**3 - 4*w**2 + 12*w. Let g(m) = -5*i(m) - 4*t(m). Solve g(x) = 0 for x.
-1, 0, 2
Let d(z) be the third derivative of z**5/330 - z**4/22 + 3*z**3/11 - 3*z**2. Determine y so that d(y) = 0.
3
Suppose -12 = -3*p + 3*a - 5*a, 0 = -p + 4*a - 10. Factor 36*x - 4*x**2 + 3*x**3 + 22 + 2 - x**p + 23*x**2.
3*(x + 2)**3
Suppose p = 2, 0 = -5*b + 5*p + 5 + 5. Suppose -1/3*x**b - 1/3*x**3 + 0*x + 0 + 1/3*x**5 + 1/3*x**2 = 0. What is x?
-1, 0, 1
Suppose -2*w - 12 = -5*w. Suppose -c + 22 = 3*o + 3*c, 3*o - w*c = -10. Factor 0 - i**o + 0*i + 7/2*i**3.
i**2*(7*i - 2)/2
Let k(s) be the first derivative of s**6/240 + s**5/120 + 5*s**2/2 - 1. Let w(m) be the second derivative of k(m). Solve w(r) = 0 for r.
-1, 0
Let f(n) = -18*n - 162. Let g be f(-9). Factor -10/3*z**4 + 16/3*z**3 + 8/3*z**2 + g + 0*z.
-2*z**2*(z - 2)*(5*z + 2)/3
Let z be 66/14 + 52/(-14) + 4. Let b(m) be the second derivative of 49/40*m**z + 1/3*m**3 + 7/6*m**4 + 0*m**2 - 3*m + 0. Find o such that b(o) = 0.
-2/7, 0
Suppose 3*d - 23 = -j, -5*d - 2*j = 2*j - 50. Determine b, given that 3*b**2 + 5 + 4*b**3 - d - 6*b**3 = 0.
-1/2, 1
Let y(f) be the third derivative of -f**6/1260 + f**5/420 - 7*f**3/6 + 3*f**2. Let s(r) be the first derivative of y(r). Determine h so that s(h) = 0.
0, 1
Let i(g) be the first derivative of -1/3*g**6 - 2/15*g**5 + 0*g**4 + 0*g + 1 + 0*g**3 + 0*g**2. Find j, given that i(j) = 0.
-1/3, 0
Factor 2 - 2*j**2 + 5*j**3 + 7*j - 3*j**3 - 9*j**3.
-(j - 1)*(j + 1)*(7*j + 2)
Determine b so that 10/3*b**4 - 4/3*b**3 - 4/3*b**5 - 2/3 + 8/3*b - 8/3*b**2 = 0.
-1, 1/2, 1
Let f(g) = -3*g**2 + 9*g + 2. Let p(i) = -4*i**2 + 8*i + 3. Let c(l) = -3*f(l) + 2*p(l). Let o be c(11). Factor -1/2*t**2 + 1/4*t**3 + 1/4*t + o.
t*(t - 1)**2/4
Let z(w) be the second derivative of 0 + 1/60*w**5 - 3*w - 2/3*w**3 - 1/360*w**6 + 0*w**2 + 0*w**4. Let i(p) be the second derivative of z(p). Factor i(r).
-r*(r - 2)
Let r(m) be the third derivative of -1/336*m**8 + 1/70*m**7 + 0*m + 0*m**4 + 0*m**3 + 0 + 0*m**5 - 1/60*m**6 + 5*m**2. Find b, given that r(b) = 0.
0, 1, 2
Let s = 493/1323 - 11/49. Let b(h) be the first derivative of 5/18*h**4 + 2 + 0*h + 0*h**2 + 8/45*h**5 + s*h**3 + 1/27*h**6. Let b(t) = 0. What is t?
-2, -1, 0
Let p(q) = q**3 - 6*q**2 + 9*q + 10. Let x(s) = -15*s**3 + 85*s**2 - 125*s - 140. Let k(w) = 85*p(w) + 6*x(w). Factor k(b).
-5*(b - 2)*(b + 1)**2
Factor -2/3*u**4 + 2/3*u**2 + 0 + 0*u + 0*u**3.
-2*u**2*(u - 1)*(u + 1)/3
Let y(h) be the third derivative of 0*h**3 + 0*h**4 + h**2 + 0 - 1/60*h**5 - 1/42*h**7 - 1/30*h**6 + 0*h - 1/168*h**8. Find v such that y(v) = 0.
-1, -1/2, 0
Solve -4/5 + 2/5*r**2 - 2/5*r = 0.
-1, 2
Let v be (-12)/(-15)*(-10)/(-4). Factor -4 - 2*s**3 + 4*s**2 - v*s**3 + 3*s**3 - s**2.
-(s - 2)**2*(s + 1)
Suppose 8*f = 5*f. Factor 0*v**4 + 1/4*v**5 + 1/4*v + 0*v**2 - 1/2*v**3 + f.
v*(v - 1)**2*(v + 1)**2/4
Let f(t) be the third derivative of t**7/1470 - t**6/840 + 4*t**2. Factor f(w).
w**3*(w - 1)/7
Suppose 35 = 5*z - 0*z + 5*t, 0 = -5*z - 3*t + 29. Suppose i = z*i. Factor i*l**4 - 1/3*l**5 + 0*l**2 - 1/3*l + 2/3*l**3 + 0.
-l*(l - 1)**2*(l + 1)**2/3
Let v(c) be the first derivative of 2*c**4 + 2*c**2 + 2*c - 14/3*c**3 - 2. Suppose v(j) = 0. Calculate j.
-1/4, 1
Let y(p) = -p + 10. Let a be y(5). Let f = 7 - a. Suppose 0 - f*r**4 + 0*r - 1/2*r**2 + 3/4*r**5 + 7/4*r**3 = 0. Calculate r.
0, 2/3, 1
Let y(a) = a**3 - a**2 + 1. Let f(w) = -3*w**3 + 5*w**2 - 4. Let i(c) = f(c) + 4*y(c). Factor i(q).
q**2*(q + 1)
Suppose 3*q + 2 = f + 4, 3*q + 4*f = 22. Let g(c) = -c - 1. Let m(t) = -t**2 + 1. Let s(l) = q*m(l) + g(l). Suppose s(u) = 0. Calculate u.
-1, 1/2
Let i = 6 - 6. Suppose -4*c + 5*c = i. Let 1/5*b + 1/5*b**5 + 0*b**4 + c*b**2 - 2/5*b**3 + 0 = 0. What is b?
-1, 0, 1
Suppose 5*g = -3*w - 5, 2*g = 3*w - 2*w - 13. Factor -3*l**4 - 3*l**4 + w*l**4 - 6*l**3 - l**4 - 6*l**2 - 2*l.
-2*l*(l + 1)**3
Factor -2 - 8/3*z - 2/3*z**2.
-2*(z + 1)*(z + 3)/3
Factor 4/19*b + 2/19*b**2 + 2/19.
2*(b + 1)**2/19
Let q(t) be the first derivative of -t**4/4 + 2*t**3/3 - t**2/2 - 8. Factor q(j).
-j*(j - 1)**2
Let u(q) be the first derivative of q**6/240 - q**5/40 + q**4/16 - q**3/12 + q**2/2 + 5. Let h(z) be the second derivative of u(z). What is r in h(r) = 0?
1
Let z(k) be the second derivative of k**7/168 - k**6/120 - k**5/40 - 7*k. Factor z(t).
t**3*(t - 2)*(t + 1)/4
Suppose -6 - 14 = -5*z. Find d, given that 3/4*d**3 - 1/4*d**2 + 1/4*d**z + 0 - 1/2*d - 1/4*d**5 = 0.
-1, 0, 1, 2
Let h = -50 - -601/12. Let g(m) be the second derivative of 0 + 0*m**2 + 1/24*m**4 - h*m**3 - m. Find d, given that g(d) = 0.
0, 1
Let c(t) = -t**3 - 5*t**2 - 3*t - 15. Let x be c(-5). Let r = 2 + 12. Solve -6*n**5 + x*n**3 - r*n**4 + 10*n + 2 - n**3 + 9*n**2 - 3*n**3 + 3*n**2 = 0 for n.
-1, -1/3, 1
Let z = 1 + -1. Suppose z = 5*j - 2 - 23. Solve -2*p - 4*p**2 - 4*p**3 - 3*p**3 + j*p**3 = 0 for p.
-1, 0
Suppose -5*v = -4*v - 5. Let w(g) be the third derivative of 0 - 1/180*g**6 + 2*g**2 + 0*g**3 + 1/180*g**v + 0*g + 1/630*g**7 + 0*g**4. Factor w(u).
u**2*(u - 1)**2/3
Let j = -53 + 57. Let s(h) be the first derivative of -7/12*h**j + 1 - 2/15*h**5 + 0*h + 2/9*h**3 + 0*h**2 + 7/18*h**6. Determine k, given that s(k) = 0.
-1, 0, 2/7, 1
Let i(u) be the first derivative of 4*u**3/21 + 2*u**2/7 - 8*u/7 - 5. Factor i(h).
4*(h - 1)*(h + 2)/7
Suppose 5*w - 6 = 3*w. Determine p, given that 3/2*p**2 + 3/2*p + 1/2*p**w + 1/2 = 0.
-1
Let c(a) = -78*a**2 + 39*a - 4. Let d(y) = y**2 + y. Let o(s) = c(s) - 3*d(s). Factor o(w).
-(9*w - 2)**2
Let b = -4/545 + 7666/4905. Factor -b*r**3 + 8/3*r**2 - 2/3*r - 4/9.
-2*(r - 1)**2*(7*r + 2)/9
Let r(l) be the first derivative of -l**3/18 + 3*l**2/2 - 27*l/2 + 3. Let r(v) = 0. What is v?
9
Let r(w) be the first derivative of -w**6/30 - 2*w**5/25 - w**4/20 - 5. Find q, given that r(q) = 0.
-1, 0
Let i(h) = h**5 - h**4 - h**3 + h**2 - h. Let n(x) = 24*x**5 - 29*x**4 - 35*x**3 - 9*x**2 + x. Let y(s) = -2*i(s) - 2*n(s). Factor y(d).
-2*d**2*(d - 2)*(5*d + 2)**2
Factor 3*p**2 + 15*p - 15*p - 3.
3*(p - 1)*(p + 1)
Let j be 0 - (-8)/(3 - 1). Find s such that 4*s**3 - 2*s**3 - s**4 + 3*s**j = 0.
-1, 0
Let j be (-12)/(-24)*(-6)/(-9). Factor -j*c**4 - c**3 + 2/3 + c - 1/3*c**2.
-(c - 1)*(c + 1)**2*(c + 2)/3
Let z be 5/(-4)*(-2 + (-63)/(-35)). Let 3/4*v**4 - 1/2*v**3 - 1/4 - z*v**5 + 3/4*v - 1/2*v**2 = 0. What is v?
-1, 1
Let n be (-6)/4*2*(-2)/3. Let l(s) be the first derivative of 4/3*s**3 + 1/2*s**n - 3/4*s**4 + 3 - 2*s. Let l(w) = 0. What is w?
-2/3, 1
Let b(n) be the second derivative of -n**7/42 + 3*n**6/70 + 2*n**5/7 - n**4/7 + 35*n. Solve b(s) = 0.
-2, 0, 2/7, 3
Let 2/3 + 1/3*u**5 - 7/3*u + 8/3*u**2 - 2/3*u**4 - 2/3*u**3 = 0. Calculate u.
-2, 1
Factor 18/5*h - 2/5*h**2 - 28/5.
-2*(h - 7)*(h - 2)/5
Let l(k) be the second derivative of k**6/30 + 3*k**5/20 + k**4/4 + k**3/6 - 8*k. Factor l(z).
z*(z + 1)**3
Determine t, given that 3*t**3 + 9/2*t**2 + 3/4*t**4 + 3*t + 3/4 = 0.
-1
Suppose 2*q = 9 + 7. Suppose -4*j + f + 10 = 0, 5*j = f + 5 + q. Factor -5*s**4 - 2*s**2 - s**j + 5*s**3 - 2*s**2 + 2*s**5 + 3*s**2.
s**2*(s - 1)**2*(2*s - 1)
Let y = -13 - -17. Let p(i) be the first derivative of 5/12*i**y + 1/3*i**2 + 7/9*i**3 + 0*i + 2. Suppose p(j) = 0. Calculate j.
-1, -2/5, 0
Let l(m) = m + 11. Let j be l(-9). Find u such that u**2 - j*u**3 + 0*u - u**2 + 4*u - 2*u**2 = 0.
-2, 0, 1
Factor -2 + 1/2*o**3 - 7/2*o - o**2.
(o - 4)*(o + 1)**2/2
Let 2/3*v**3 + 0 - 2/3*v**2 + 0*v = 0. Calculate v.
0, 1
Suppose 0 = 10*m - 0 + 40. Let y be (-1)/(-1)*m/(-8). Solve -y*g + 1/2*g**3 - 1 + g**2 = 0.
-2, -1, 1
Let p = 11 - 9. Let y be (-3)/(-54)*p*6. Factor y + 4/3*h**2 + 3*h.
(h + 2)*(4*h + 1)/3
Let y(a) be the second derivative of a**10/120960 - a**9/60480 + a**4/4 + 4*a. Let j(t) be the third derivative of y(t). Factor j(m).
m**4*(m - 1)/4
Suppose -5*z = 2*o - 8, 6 = 3*z - z - 2*o. Suppose 2*v - 33 = -5*l + 5*v, -2*l - 5*v + 7 = 0. Factor l*t**3 - 2*t + 2*t**5 + 9*t**4 + t**4 - 2*t**z + 2*t**5.
2*t*(t + 1)**3*(2*t - 1)
Suppose -170 + 24 = -2*r. Suppose 3*o - 84 - 38 = -5*p, 0 = 3*p + 2*o - r. Factor 88*z + 25*z**4 + 10*z**3 - 132*z**2 - 16 + 23*z**4 + p*z**4 - 23*z**4.
2*(z - 