k**4 - 3*k**3 - 3*k**2 + 3*k + 6. Let t(r) = 10*r**4 + 4*r**3 + 4*r**2 - 4*r - 7. Let y(u) = -7*c(u) - 6*t(u). Factor y(a).
3*a*(a - 1)**2*(a + 1)
Let o(p) be the third derivative of -p**5/100 + 10*p**2. Factor o(t).
-3*t**2/5
Let g be (-48)/(-45) + ((-12)/5)/6. Factor -1/3*p**2 + 0 + g*p - 1/3*p**3.
-p*(p - 1)*(p + 2)/3
Let x(k) be the second derivative of -3*k**5/5 + 14*k**4/3 - 40*k**3/3 + 16*k**2 + 4*k. Factor x(w).
-4*(w - 2)**2*(3*w - 2)
Factor -1/5 - 9261/5*j**3 - 1323/5*j**2 - 63/5*j.
-(21*j + 1)**3/5
Let 12*g**4 + 18*g**2 + 33*g**3 + 29*g**4 - 32*g**4 = 0. What is g?
-3, -2/3, 0
Suppose 5*k - 2*t = 29, 0 = -k - 4*t - t + 22. Suppose k*z - 15 = 2*z. What is u in -u**2 + 0*u**2 + u + u**3 + z*u**2 = 0?
-1, 0
Let o = 1016/5 + -202. Factor 2*d + 14/5*d**2 + 2/5 + o*d**3.
2*(d + 1)**2*(3*d + 1)/5
Let y(b) be the third derivative of -4*b**7/525 + 3*b**6/100 - b**5/25 + b**4/60 + b**2. Determine t so that y(t) = 0.
0, 1/4, 1
Let p be 6/(-12) - 2/(24/(-6)). Solve 7/3*t**3 - 2/3*t**2 + 4/3*t**4 + 0 + p*t = 0.
-2, 0, 1/4
Determine w so that -52 - 10*w - 2*w - 4*w**2 + 44 = 0.
-2, -1
Let v(w) = -w**2 + w. Let i be v(0). Factor 1/4 - 1/4*k**2 + i*k.
-(k - 1)*(k + 1)/4
Let s(k) be the third derivative of k**5/30 + 5*k**4/12 - 28*k**2. Factor s(d).
2*d*(d + 5)
Let h(d) be the third derivative of d**7/11340 - d**6/540 + d**5/60 - d**4/8 - 2*d**2. Let t(a) be the second derivative of h(a). Let t(q) = 0. Calculate q.
3
Let o(v) be the first derivative of -v**3/3 + v**2 - 3. Factor o(w).
-w*(w - 2)
Let x(c) be the third derivative of c**6/30 - 13*c**5/15 + 35*c**4/6 + 98*c**3/3 + 26*c**2. Factor x(i).
4*(i - 7)**2*(i + 1)
Factor 0 - 11/4*o + 1/4*o**2.
o*(o - 11)/4
Let i = 1346/3069 - -2/341. Factor 2/9*r**2 + i + 2/3*r.
2*(r + 1)*(r + 2)/9
Let v(a) be the first derivative of 16/3*a**3 + 3*a**4 + 3 + 0*a + 2*a**2. Suppose v(w) = 0. Calculate w.
-1, -1/3, 0
Let a(n) be the third derivative of -n**5/180 + 2*n**3/9 + n**2 - 4*n. Factor a(u).
-(u - 2)*(u + 2)/3
Let l(m) be the second derivative of 9*m**5/80 - m**4/4 + m**3/8 - 8*m. What is d in l(d) = 0?
0, 1/3, 1
Let t(c) = -c**2 + c + 2. Let w be t(3). Let h be (-10)/w*(4 - 2). Find l, given that 2*l**2 - 16/5*l**4 - 8/5*l**h + 2/5*l - 2/5*l**3 - 2/5 = 0.
-1, 1/2
Factor -b**2 + 12 + 16*b**3 - 16*b + b**2 - 4*b**4 - 8*b**2.
-4*(b - 3)*(b - 1)**2*(b + 1)
Let j = 3 + 0. Factor d**2 - d**2 + d**3 + 2*d**4 + d**j.
2*d**3*(d + 1)
Let x(r) = r**2 - 2*r + 1. Let p(m) = -10*m**2 + 22*m - 12. Let u(k) = -2*p(k) - 22*x(k). Factor u(q).
-2*(q - 1)*(q + 1)
Let i(k) be the first derivative of k**3 + 3 - 3/2*k**2 - 1/4*k**4 + k. Suppose i(z) = 0. What is z?
1
Factor -10*h - 29*h**2 + 2*h**3 - 5*h**3 + 2*h**3 + 36*h**2.
-h*(h - 5)*(h - 2)
Let c(f) = -f**3 + 5*f**2 + 2. Let g be c(5). Let v = 3 + 4. Solve -v*a**2 + g*a + a**2 + a**2 = 0.
0, 2/5
Determine z so that 8/7 + 8/7*z + 2/7*z**2 = 0.
-2
Determine f so that -5/3 + 2/3*f**2 - 3*f = 0.
-1/2, 5
Let z = -6 - -11. Let f(d) be the third derivative of 1/630*d**7 + 0*d**4 + 0*d + 2*d**2 + 0 + 0*d**3 + 1/180*d**6 + 1/180*d**z. Factor f(g).
g**2*(g + 1)**2/3
Factor -4 + 15*x**2 + 1 + 2*x - 3*x**3 + 12*x**3 + x.
3*(x + 1)**2*(3*x - 1)
Let s(y) be the third derivative of -7/240*y**6 - 3/32*y**4 - 4*y**2 - 1/15*y**5 + 0 - 1/140*y**7 + 0*y - 1/1344*y**8 - 1/12*y**3. Suppose s(z) = 0. What is z?
-2, -1
Determine h so that -14/3*h**2 + 2/3*h**3 + 10*h - 6 = 0.
1, 3
Let y(p) be the first derivative of -p**6/180 + p**5/45 - p**4/36 + 3*p**2/2 - 5. Let r(g) be the second derivative of y(g). Solve r(n) = 0.
0, 1
Let c(s) be the first derivative of -s**4/2 + 14*s**3/3 - 15*s**2 + 18*s - 11. Determine p so that c(p) = 0.
1, 3
Solve -5*p**2 - 4*p + p**2 + 5*p**2 + p**2 = 0 for p.
0, 2
Let b(p) be the third derivative of -5*p**8/336 - 2*p**7/21 - 5*p**6/24 - p**5/6 + 6*p**2. Factor b(k).
-5*k**2*(k + 1)**2*(k + 2)
Let q(t) = -t**2 - t. Let y(g) = -5*g**2 - 9*g. Let x(c) = -5*c**2 - 8*c. Let l(v) = -6*x(v) + 5*y(v). Let i(z) = l(z) + 2*q(z). Factor i(u).
u*(3*u + 1)
Let s(r) = -r**2 - r. Let p be s(2). Let z be p/9*-3 + 2. Factor 2*b**5 - 2*b**z - 3*b**5 - b**5.
-2*b**4*(b + 1)
Let j(n) be the third derivative of -n**5/180 - n**4/6 - 2*n**3 - n**2. Factor j(t).
-(t + 6)**2/3
Suppose -3*r - 45*k + 47*k = 6, 3*r - 6 = -2*k. Factor r*h**2 + 1/2*h**5 + 0*h + 0*h**4 + 0 - 1/2*h**3.
h**3*(h - 1)*(h + 1)/2
Let i(n) = -n**3 - 16*n**2 - 16*n - 12. Let v be i(-15). Factor 0 - 2/11*c**v + 2/11*c + 0*c**2.
-2*c*(c - 1)*(c + 1)/11
Let q(v) be the third derivative of 2*v**7/35 + v**6/6 - 4*v**5/15 - 2*v**4/3 + 2*v**2. Determine w so that q(w) = 0.
-2, -2/3, 0, 1
Solve -12/5*q - 11/5*q**2 - 4/5 - 3/5*q**3 = 0 for q.
-2, -1, -2/3
Factor 3*l - 1/4*l**4 - 13/4*l**2 - 1 + 3/2*l**3.
-(l - 2)**2*(l - 1)**2/4
Let h(g) be the third derivative of 0*g + 1/84*g**4 - 1/210*g**5 + 0 + 1/735*g**7 - g**2 - 1/420*g**6 + 0*g**3. Factor h(s).
2*s*(s - 1)**2*(s + 1)/7
Let a(f) be the first derivative of 2*f**6/45 - f**5/15 - f**4/12 + 2*f**3/9 - f**2/6 - 3*f - 3. Let j(l) be the first derivative of a(l). Factor j(h).
(h - 1)*(h + 1)*(2*h - 1)**2/3
Suppose -3*w + 8*w - 20 = 0. Let u(c) be the first derivative of 12/7*c**3 + 16/7*c + 20/7*c**2 + 3 + 1/2*c**w + 2/35*c**5. Factor u(m).
2*(m + 1)*(m + 2)**3/7
Suppose 2*c - w = -3*w + 10, -c + w = -13. Let x be -1 - (0 + (-15)/c). Factor 0 + 1/3*v**3 + 1/3*v + x*v**2.
v*(v + 1)**2/3
Let d(z) be the first derivative of 1/3*z**3 + 0*z**2 + 1/18*z**4 + 1/60*z**5 + 0*z + 1/540*z**6 + 4. Let v(x) be the third derivative of d(x). Factor v(o).
2*(o + 1)*(o + 2)/3
Let s(v) be the third derivative of v**8/84 - v**6/30 + 3*v**2 - 9*v. Suppose s(a) = 0. Calculate a.
-1, 0, 1
Let f(s) = s**3 - 4*s**2 - 20*s - 12. Let w(u) = -4*u**3 + 12*u**2 + 60*u + 36. Let m(t) = 8*f(t) + 3*w(t). Factor m(n).
-4*(n - 3)*(n + 1)**2
Let p(h) = -3*h**3 + 21*h**2 - 24*h + 6. Let t(i) = i**3 - 1. Let s(z) = -p(z) + 3*t(z). Suppose s(b) = 0. What is b?
1, 3/2
Let d be ((-9)/(-6))/((-4)/(-8)). Let v(n) = n**3 + n**2 + n. Let q(b) = -13*b**2 - 27*b - 10*b**2 - b**2 + 46*b**3 - 4. Let j(u) = d*v(u) + q(u). Factor j(o).
(o - 1)*(7*o + 2)**2
Let q(g) = 6*g**3 - 12*g**2 + 2*g - 4. Let y be -3 + 4/(1 + -5). Let j(s) = -2 + 12*s**3 - 23*s**2 + 5*s - s - 5. Let d(k) = y*j(k) + 7*q(k). Factor d(i).
-2*i*(i - 1)*(3*i - 1)
Let w = -1/65 + 3/26. Let k(m) be the second derivative of -1/6*m**4 + 0 - 2*m + 0*m**3 + 1/15*m**6 + 1/21*m**7 - w*m**5 + 0*m**2. Let k(o) = 0. What is o?
-1, 0, 1
Find q such that -8/5*q**3 + 2/5*q**4 + 12/5*q**2 + 2/5 - 8/5*q = 0.
1
Suppose -2*q + 0*q + 4 = 0. Factor 0*i - i + 2*i**2 - q*i**4 + 2*i - i**5.
-i*(i - 1)*(i + 1)**3
Let k(z) = 9*z**4 - 14*z**3 + 4*z**2 - 6*z. Let n(b) = 26*b**4 - 41*b**3 + 12*b**2 - 17*b. Let o(v) = 17*k(v) - 6*n(v). Let o(a) = 0. What is a?
0, 2/3, 2
Suppose 0*a - a - 4 = 0. Let w = a + 6. Let 2/7 - 2/7*j**w + 0*j = 0. What is j?
-1, 1
Suppose -2*n = 3*q + 6 + 6, -3*q = 3*n + 12. Factor -1/2*a - 3*a**3 + n - 5/4*a**4 - 9/4*a**2.
-a*(a + 1)**2*(5*a + 2)/4
Let g = -20/23 - -323/345. Let f(i) be the second derivative of i - 1/6*i**4 + 1/3*i**3 + 0*i**2 + 0 + g*i**6 - 3/10*i**5 + 2/21*i**7. What is b in f(b) = 0?
-1, 0, 1/2, 1
Factor 8/5 - 2*q + 2/5*q**2.
2*(q - 4)*(q - 1)/5
Let m(f) be the third derivative of f**7/84 - f**6/360 - f**5/60 + f**3/3 + f**2. Let i(g) be the first derivative of m(g). Factor i(r).
r*(2*r - 1)*(5*r + 2)
Factor 10*s**3 - 64*s - 5*s**4 + 64*s - 5*s**2.
-5*s**2*(s - 1)**2
Let c(s) = 48*s**4 - 84*s**3 + 92*s + 20. Let i(o) = 7*o**4 - 12*o**3 + 13*o + 3. Let a(p) = -3*c(p) + 20*i(p). What is d in a(d) = 0?
-1, 0, 2
Let t(j) = j + 2. Let a be t(4). Factor 0*v - v**2 - v + a*v - 1 - 3*v.
-(v - 1)**2
Let s = 26 - 26. Let v(d) be the first derivative of 0*d**2 + s*d + 1/4*d**4 + 0*d**3 + 1. Factor v(j).
j**3
Let v = 672 + -6037/9. Let h = 82/45 - v. Factor -h*y**2 - 4/5*y + 4/5*y**3 + 4/5*y**4 - 1/5.
(y - 1)*(y + 1)*(2*y + 1)**2/5
Let d(s) be the second derivative of -s**4/6 - 4*s**3/3 - 12*s. What is c in d(c) = 0?
-4, 0
Let j(n) be the second derivative of -n**4/12 - n**3/6 + n**2 + 6*n. Factor j(t).
-(t - 1)*(t + 2)
Let d(t) be the second derivative of t**4/60 - t**3/15 - 3*t**2/10 - 3*t. Find j, given that d(j) = 0.
-1, 3
Factor -2/3*w**2 + 0 + 2*w