 Determine p so that 3*p**5 + 2*p**4 - 3 + 3*p - 6*p**3 - p**5 - 5*p**4 + 6*p**n + p**5 = 0.
-1, 1
Factor -20*m**3 - m**2 - m**4 + 42*m**3 - 24*m**3.
-m**2*(m + 1)**2
Suppose 18*k = 21*k - 18. Let q(j) be the first derivative of 2/3*j**k - 1/3*j**3 + 0*j**2 + 3/2*j**4 - 4 + 0*j - 9/5*j**5. Solve q(i) = 0.
0, 1/4, 1
Let w(v) = v**3 - v**2 - 1. Let m(n) = 16*n**3 - 25*n**2 + 3*n + 5. Let b(h) = -m(h) + w(h). Suppose b(y) = 0. What is y?
-2/5, 1
Let y(a) be the second derivative of a**4/42 - 2*a**3/21 + a**2/7 - 10*a. Determine n so that y(n) = 0.
1
Let q(d) be the third derivative of 7*d**6/900 + d**5/225 - 14*d**2. Suppose q(l) = 0. Calculate l.
-2/7, 0
Let s(p) be the third derivative of -p**8/224 + p**7/168 + p**6/80 - 15*p**2. Factor s(g).
-g**3*(6*g**2 - 5*g - 6)/4
Let u(f) = f + 5. Let h be u(-2). Suppose 0*c**2 + 1/4*c**4 - 1/2*c**h + 0*c + 0 = 0. What is c?
0, 2
Let m = 2 + 0. Let b(n) = n**2 - 3*n - 2. Let x(v) = v**2 - 4*v - 3. Let q(k) = m*x(k) - 3*b(k). Factor q(i).
-i*(i - 1)
Let u(d) be the first derivative of 8/7*d - 3 + 2/21*d**3 - 4/7*d**2. Solve u(n) = 0 for n.
2
Let j(r) be the second derivative of 3*r**5/160 + r**4/16 + r**3/16 + 10*r. Determine o so that j(o) = 0.
-1, 0
Let u be (-50)/(-40) + 6/8. Factor -11*i**2 - 12*i**u + 2*i**5 + 21*i**2 - 2*i**3 + 2*i**4.
2*i**2*(i - 1)*(i + 1)**2
Let q(b) be the first derivative of -b**7/147 - 2*b**6/105 + b**4/21 + b**3/21 - 4*b + 10. Let w(d) be the first derivative of q(d). Let w(k) = 0. Calculate k.
-1, 0, 1
Let u = -19 + 19. Let p(t) be the third derivative of -1/360*t**6 + u + 0*t + 0*t**3 + 1/72*t**4 - 2*t**2 + 1/180*t**5 - 1/630*t**7. Factor p(b).
-b*(b - 1)*(b + 1)**2/3
Let r be (442 + 7)/(7/4). Let c = r - 256. Suppose -6/7*x**4 + 4/7*x - c*x**3 + 6/7*x**2 + 0 = 0. Calculate x.
-1, -2/3, 0, 1
Let i(p) be the first derivative of -p**4/5 + 16*p**3/15 - 6*p**2/5 - 7. Factor i(q).
-4*q*(q - 3)*(q - 1)/5
Factor 1/4*i**3 - i - i**2 + 1/4*i**4 + 0.
i*(i - 2)*(i + 1)*(i + 2)/4
Let w = -1679/40 + 42. Let z(g) be the third derivative of 0*g + 1/60*g**5 + w*g**6 + 1/336*g**8 + 3*g**2 + 0*g**3 + 0 + 1/70*g**7 + 0*g**4. Factor z(t).
t**2*(t + 1)**3
Let s(j) = 15*j**4 - 15*j**2. Let y(w) = -7*w**4 + 8*w**2. Let k(o) = 4*s(o) + 9*y(o). Factor k(t).
-3*t**2*(t - 2)*(t + 2)
Let z(n) be the second derivative of 0*n**4 - 1/70*n**5 + 0*n**2 + 0*n**3 - 1/105*n**6 + 0 + 4*n. What is d in z(d) = 0?
-1, 0
Let p = -18 + 18. Let n(z) be the second derivative of 1/16*z**4 + 0 + 2*z + 1/24*z**3 + 3/80*z**5 + p*z**2 + 1/120*z**6. Factor n(c).
c*(c + 1)**3/4
Suppose -8/3*t**2 + 2*t + 0 + 2/3*t**3 = 0. What is t?
0, 1, 3
Let y = -11 - -2. Let w be y/(-4) - (-7)/(-28). Factor -2*i**2 - 4*i**3 - w*i**4 + 0*i + 2*i - 2*i.
-2*i**2*(i + 1)**2
Factor -18*q - 20*q + 17*q - 2*q**2 - 3*q.
-2*q*(q + 12)
Let h = -283/4 - -1609/20. Let u = h + -19/2. Solve 0*b + u*b**2 - 1/5 = 0 for b.
-1, 1
Factor 2 - 3*d**2 + d**3 - d + 6*d**3 - 6*d**3 + d**2.
(d - 2)*(d - 1)*(d + 1)
Let h(w) be the third derivative of 5*w**8/1008 - w**7/42 + w**5/9 + 7*w**2 - 2*w. What is m in h(m) = 0?
-1, 0, 2
Let g(d) = -3*d**4 + 2*d**3 + 6*d + 11. Let b be -1 + (3/3 - -3). Let t(r) = r**4 - r**3 - 2*r - 4. Let x(n) = b*g(n) + 8*t(n). Factor x(z).
-(z - 1)*(z + 1)**3
Let r(n) = n**2 - 6*n + 4. Let h be r(6). Suppose 0 = h*i - 14 - 2. Find z such that 2*z**2 - 4*z**3 - 2*z**2 + 2*z**i + 2*z**2 = 0.
0, 1
Suppose -3*f + 6*f = -3*s - 3, -s = -f + 7. Factor 0 + 1/4*c**f - 1/4*c**4 + 0*c**2 + 0*c.
-c**3*(c - 1)/4
Let m(v) be the second derivative of -8/3*v**3 + 1/3*v**4 + 6*v**2 + 0 + 7*v. Suppose m(o) = 0. What is o?
1, 3
Let m(f) = -6*f**2 + 6. Let o(r) = -r + 14. Let v be o(12). Let q(h) = 5*h**2 - h - 6. Let i(x) = v*m(x) + 3*q(x). Suppose i(c) = 0. Calculate c.
-1, 2
Factor 722/5*o**2 + 40 + 2/5*o**5 + 326/5*o**3 + 46/5*o**4 + 128*o.
2*(o + 1)**3*(o + 10)**2/5
Let j(z) be the first derivative of -z**4/42 - z**3/7 - 2*z**2/7 + 2*z - 6. Let n(d) be the first derivative of j(d). Factor n(m).
-2*(m + 1)*(m + 2)/7
Let y(h) be the first derivative of 0*h**4 + 1 - 1/2*h**2 + 1/120*h**6 + 0*h**3 + 0*h + 1/60*h**5. Let u(q) be the second derivative of y(q). Factor u(l).
l**2*(l + 1)
Let f(o) be the second derivative of 4*o - 1/48*o**4 + 0 - 1/12*o**3 - 1/8*o**2. Find x, given that f(x) = 0.
-1
Let d(r) = -5*r**2 + 6*r + 7. Let m(j) = 36*j**2 - 42*j - 48. Let l(w) = -15*d(w) - 2*m(w). Let l(k) = 0. What is k?
-1, 3
Let 8*q - 33 - 90*q**5 - 196*q**4 + 33 - 114*q**3 = 0. What is q?
-1, -2/5, 0, 2/9
Let g(u) = -11*u**2 - 13*u - 15. Let w(d) be the third derivative of d**5/12 + d**4/4 + 7*d**3/6 - 2*d**2. Let q(j) = 6*g(j) + 13*w(j). Factor q(r).
-(r - 1)*(r + 1)
Let w be (-1 + (-39)/12)*-4. Suppose -5*m + 0*m + w = q, 0 = -4*q + 2*m + 2. Solve 1/2*v + v**q + 0 + 1/2*v**3 = 0.
-1, 0
Let l(n) = n**3 + n**2 - 13*n - 17. Let f be l(-3). Solve -2/3 + 0*m**f - m - 1/3*m**5 + 4/3*m**3 + 2/3*m**2 = 0 for m.
-1, 1, 2
Suppose 1 = -4*v - 4*t + t, -9 = 3*t. Let f be 4/10 - 0/(-1). Determine a, given that 4/5*a - 4/5*a**3 + 0*a**v - 2/5 + f*a**4 = 0.
-1, 1
Factor -3/7*n**2 + 18/7*n + 0 - 3/7*n**3.
-3*n*(n - 2)*(n + 3)/7
Let s(m) be the third derivative of m**7/70 - m**6/5 + 11*m**5/10 - 3*m**4 + 9*m**3/2 - 6*m**2. Factor s(a).
3*(a - 3)**2*(a - 1)**2
Let m(p) be the third derivative of -5*p**2 + 0*p + 0 + 0*p**3 + 1/160*p**6 + 0*p**4 + 1/140*p**7 - 1/80*p**5. Let m(b) = 0. Calculate b.
-1, 0, 1/2
Let p(r) be the third derivative of 5*r**8/336 - r**7/21 + r**5/6 - 5*r**4/24 + 3*r**2. Determine b so that p(b) = 0.
-1, 0, 1
Let a(s) be the third derivative of -s**8/21 + 8*s**7/105 + s**6/10 - 4*s**5/15 + s**4/6 - 3*s**2. Solve a(u) = 0 for u.
-1, 0, 1/2, 1
Suppose 3*i = 4*i - 2*c + 5, -5*c + 10 = -3*i. Suppose 0 = -i*w, 4*z - 5 - 7 = -2*w. Solve -5*b**3 + z*b**3 + 4*b**3 = 0 for b.
0
Let o(l) be the third derivative of -l**6/1080 - 11*l**5/540 - l**4/9 + 2*l**3/3 - 3*l**2. Factor o(y).
-(y - 1)*(y + 6)**2/9
Let n(l) be the first derivative of -4*l**3/3 + 16*l**2 - 64*l - 2. Factor n(y).
-4*(y - 4)**2
Suppose 4*r + 14 = 22. Let y be (-2)/(-2)*2/8. Factor 0 - y*f**3 - 1/4*f - 1/2*f**r.
-f*(f + 1)**2/4
Let q(k) be the second derivative of -2*k**6/15 - 4*k**5/5 - 5*k**4/3 - 4*k**3/3 + 20*k. Suppose q(l) = 0. What is l?
-2, -1, 0
Let w(u) = -u**2 + u + 6. Let n(f) = 0*f + 26 + 3*f - f**2 - 2 - 2*f**2. Let a(i) = 2*n(i) - 9*w(i). Factor a(p).
3*(p - 2)*(p + 1)
Let v(a) be the first derivative of 1/12*a**3 + 0*a - 10 - 1/2*a**2. Factor v(u).
u*(u - 4)/4
Suppose -5*v + 2 = -2*d, 2*v - 4*d = -v - 10. Suppose -4*t + 3*t + v = 0. Let 2/5*c**t + 8/5 - 8/5*c = 0. Calculate c.
2
Factor 0*n**2 - 2*n**3 + 6*n**2 - 2*n**2 - 2*n.
-2*n*(n - 1)**2
Let m(b) = b**5 - b**4 + b**3 + b**2 + b. Let l(n) = -6*n**5 - 12*n**4 - 30*n**3 - 24*n**2 - 9*n. Let t(w) = l(w) + 3*m(w). What is d in t(d) = 0?
-2, -1, 0
Solve -2*d**5 + 8/5*d - 4/5*d**4 + 6*d**3 + 0 + 32/5*d**2 = 0.
-1, -2/5, 0, 2
Let w(c) = -c**3 + 4*c**2 - c - 1. Let k be w(3). Suppose 4*o - 1 = -2*u + 11, k*o - 3*u = 15. Factor -3*h**o + 0*h + 0*h + 3*h.
-3*h*(h - 1)*(h + 1)
Let t(q) be the third derivative of -q**7/315 - q**6/90 + q**4/18 + q**3/9 + 4*q**2. Factor t(l).
-2*(l - 1)*(l + 1)**3/3
Let f(y) be the second derivative of y**6/105 + 17*y**5/70 + 40*y**4/21 + 64*y**3/21 + 9*y + 3. Factor f(x).
2*x*(x + 1)*(x + 8)**2/7
Let t be (-3)/((3/7)/((-156)/273)). Let -2/7*b**t - 2/7*b + 2/7*b**2 + 2/7*b**3 + 0 = 0. Calculate b.
-1, 0, 1
Factor 75 - y**2 + 6*y**2 - 2*y**2 + 30*y + 0*y**2.
3*(y + 5)**2
Let k(o) = 2*o - 2. Let r be k(6). Suppose -2*b - 2*h - 4 = -4*b, -2*h - r = -5*b. Factor -2/9*m**b - 2/9*m + 0.
-2*m*(m + 1)/9
Let n(z) be the first derivative of -1 - 1/4*z**4 - 1/3*z**3 + 0*z + 1/5*z**5 + 1/2*z**2. Factor n(c).
c*(c - 1)**2*(c + 1)
Let h(p) = p**2 - 2*p - 1. Let d(w) = 4*w**2 - 8*w - 5. Let n(j) = 2*d(j) - 9*h(j). Factor n(f).
-(f - 1)**2
Let v(g) be the third derivative of 1/30*g**4 + 1/150*g**5 + 3*g**2 + 0*g + 0 + 1/15*g**3. Factor v(p).
2*(p + 1)**2/5
Let t(w) = w**2 - w + 1. Let z(y) be the second derivative of -y**4/4 + y**3/3 - y**2 - 4*y. Let m(q) = -2*t(q) - z(q). Suppose m(l) = 0. Calculate l.
0
Let u(t) be the second derivative of -t**6/1440 - t**5/160 - t**4/48 + 2*t**3/3 + 3*t. Let s(h) be the second derivative o