 = -6*o**4 + 9*o**3 - 3*o + 6. Let v(r) = -14*r**4 - 8*r**4 + 17 - 10*r + 26*r**3 + 5*r**4. Let d(n) = 8*f(n) - 3*v(n). Factor d(k).
3*(k - 1)**3*(k + 1)
Let g(p) = 6*p**5 + 34*p**4 + 18*p**3 + 30*p**2 + 16*p. Let r(v) = -v**4 + v**3 - v**2 - v. Suppose 5*z + 2 = 7*z. Let f(b) = z*g(b) + 12*r(b). Factor f(q).
2*q*(q + 1)**3*(3*q + 2)
Let t(l) be the third derivative of -l**6/280 + l**5/35 + 5*l**4/56 + 36*l**2. Factor t(m).
-3*m*(m - 5)*(m + 1)/7
Let d = 29986/5 - 5928. Let g = 70 - d. Factor -2/5*c**4 - g*c**3 + 2/5*c**5 - 2/5 + 4/5*c**2 + 2/5*c.
2*(c - 1)**3*(c + 1)**2/5
Let r(i) = -10*i**4 + 93*i**3 - 323*i**2 + 400*i - 160. Let o(a) = -5*a**4 + 46*a**3 - 161*a**2 + 200*a - 80. Let b(l) = -7*o(l) + 4*r(l). Factor b(m).
-5*(m - 4)**2*(m - 1)**2
Let o(h) be the second derivative of 1/7*h**2 - 7*h - 1/42*h**4 + 0 + 0*h**3. Factor o(v).
-2*(v - 1)*(v + 1)/7
Find y such that -2/3 - 2/3*y**2 - 4/3*y = 0.
-1
Let s(z) = 3*z**5 + 2*z**4 + 2*z**2 + 2*z - 2. Let t(w) = 10*w**5 + 7*w**4 + 7*w**2 + 7*w - 7. Let v(x) = -21*s(x) + 6*t(x). Factor v(r).
-3*r**5
Let z(i) be the second derivative of -i**6/6 + 3*i**5/4 - 2*i. Find n such that z(n) = 0.
0, 3
Suppose -q = -0 - 23. Suppose 3*m + 30 = 5*o + 3, -5*o + q = -2*m. Factor -c**2 + 2*c**3 + 0*c**2 + 0*c**o + 3*c**2.
2*c**2*(c + 1)
Let b = -6 + 9. Let w = 0 + b. Let -2*r**5 - 3*r**3 + 3*r**w - 2*r + 4*r**3 = 0. What is r?
-1, 0, 1
Let s(r) = r**3 - 3*r**2 - 3*r. Let m be s(4). Suppose -2 = c - m. Factor -2/3*h**c - 2/3*h**3 + 0 + 0*h.
-2*h**2*(h + 1)/3
Solve -4*o - 3*o**3 + 5*o**3 + 0*o + 2*o**2 = 0 for o.
-2, 0, 1
Let o be 0 + 11/2 + -1. Let f be 1/(-2)*(5 - 15). Factor 16 + 21*s**4 - o*s**f - 24*s**2 - 20*s**3 + 24*s.
-(s - 2)**3*(3*s + 2)**2/2
Factor -10/13*o - 2/13*o**3 - 4/13 - 8/13*o**2.
-2*(o + 1)**2*(o + 2)/13
Factor 0 + 26/15*m**3 - 4/5*m**4 + 2/15*m**5 + 8/15*m - 8/5*m**2.
2*m*(m - 2)**2*(m - 1)**2/15
Let x = 1/42 + 1/7. Factor -x*y**3 - 1/6*y**2 + 0 + 1/6*y**4 + 0*y + 1/6*y**5.
y**2*(y - 1)*(y + 1)**2/6
Factor 19/4*x**2 - 1/4*x**3 - 25 - 20*x.
-(x - 10)**2*(x + 1)/4
Let m(k) = -7*k + 24. Let b be m(3). Let 0*z + 0 - 3/7*z**4 + 3/7*z**2 + 0*z**b = 0. Calculate z.
-1, 0, 1
Let z(s) = s**3 + s**2 - s + 1. Let a(u) = -6*u**3 - 4*u**2 + 7*u - 5. Let y(q) = -4*a(q) - 20*z(q). Factor y(c).
4*c*(c - 2)*(c + 1)
Factor f - 7*f**4 - 14*f**2 + 17*f**4 - 6*f**3 + 11 - 7 + 5*f.
2*(f - 1)**2*(f + 1)*(5*f + 2)
Let z = 27661/60 + -461. Let l(g) be the third derivative of -1/6*g**3 - 2*g**2 + 1/210*g**7 - 1/12*g**4 + z*g**6 + 0*g**5 + 0 + 0*g. Factor l(q).
(q - 1)*(q + 1)**3
Let z = -158 + 164. Let x(r) be the third derivative of 1/35*r**7 - 1/120*r**z + 3/224*r**8 + 0*r**3 - 1/30*r**5 + 0 + 0*r - 2*r**2 + 1/48*r**4. Factor x(y).
y*(y + 1)**2*(3*y - 1)**2/2
Suppose r + 5*z = -18, 5*z + 22 = -2*r + 3*r. Factor 31*t**4 + 38*t**3 + 19*t**4 + 3*t**2 + r*t**3 + 5*t**2.
2*t**2*(5*t + 2)**2
Let v(y) be the third derivative of -y**5/150 + y**4/10 - 3*y**3/5 - 8*y**2. Find t, given that v(t) = 0.
3
Let v(i) be the first derivative of -2*i**2 + 0*i**4 + 1/40*i**6 + 1 + 1/20*i**5 + 0*i**3 + 0*i. Let u(s) be the second derivative of v(s). Factor u(o).
3*o**2*(o + 1)
Let h(y) be the first derivative of -y**6/57 + 2*y**5/95 + y**4/38 - 2*y**3/57 + 25. Factor h(g).
-2*g**2*(g - 1)**2*(g + 1)/19
Let q = 8765/7 - 1260. Let h = 200/21 + q. Factor 7/3*j**2 + 1/3 + j**3 + h*j.
(j + 1)**2*(3*j + 1)/3
Let w(a) = -3*a**2 - 5*a + 2. Let j(f) = -12*f**2 - 21*f + 9. Let z(r) = 2*j(r) - 9*w(r). Suppose z(c) = 0. Calculate c.
-1, 0
Let q(h) be the second derivative of h**6/6 + 3*h**5/4 + 5*h**4/6 + 4*h. Factor q(n).
5*n**2*(n + 1)*(n + 2)
Let h(d) be the third derivative of d**5/120 + d**4/48 + 15*d**2. Solve h(v) = 0 for v.
-1, 0
Let m(i) be the third derivative of -i**5/330 + 5*i**4/44 + 16*i**3/33 + 7*i**2 - 2*i. Factor m(x).
-2*(x - 16)*(x + 1)/11
Suppose -1/2*m**3 + 1/4*m**4 + 0*m**2 - 1/4 + 1/2*m = 0. What is m?
-1, 1
Let m(c) be the first derivative of 1/10*c**4 - 1/30*c**6 - 1/5*c - 1/10*c**2 + 2/15*c**3 - 1 - 1/25*c**5. Factor m(z).
-(z - 1)**2*(z + 1)**3/5
Suppose 2*z + 56 = 9*z. Suppose -4*w**3 + z*w**2 - 20*w**5 - 13*w**4 - 16*w**4 - 3*w**4 = 0. Calculate w.
-1, 0, 2/5
Factor 1 + 5*m**2 - 12 - 6*m + 4 + 8.
(m - 1)*(5*m - 1)
Suppose 0*p + 4 = 2*p. Factor 2/3*b - 1/3*b**p - 1/3.
-(b - 1)**2/3
Let h(f) = 28*f**3 - 115*f**2 + 144*f - 32. Let r(y) = 42*y**3 - 172*y**2 + 216*y - 48. Let u be 62/(-8) - (-9)/(-36). Let x(q) = u*h(q) + 5*r(q). Factor x(l).
-2*(l - 2)**2*(7*l - 2)
Let t(f) be the second derivative of -f**7/42 + f**6/30 + f**5/20 - f**4/12 + 8*f. Let t(m) = 0. What is m?
-1, 0, 1
Suppose -u = -c - 14, 2*u - 6 = -0*u. Let k = 35/3 + c. Solve k*f**2 - 2*f + 4/3 = 0 for f.
1, 2
Suppose k = -4*k - 30. Let w be (-5)/(-2) - 3/k. Let 0*d + 0*d + 2*d**4 + 3*d**5 + 2*d**w - 3*d**3 = 0. Calculate d.
-1, 0, 1/3
Let h(m) be the second derivative of m**7/630 + m**6/360 - m**5/180 - m**4/72 - 2*m**2 - 5*m. Let b(y) be the first derivative of h(y). Factor b(n).
n*(n - 1)*(n + 1)**2/3
Let w(b) be the second derivative of -5*b**4/4 - b**3 + 7*b. Factor w(o).
-3*o*(5*o + 2)
Suppose -4*m + 12 = 2*u, -10 = -6*m + 2*m - u. Factor -7*k**m + 1 - 1 + 2*k**4 - k**2.
2*k**2*(k - 2)*(k + 2)
Factor 3/2 + h**2 - 7/2*h.
(h - 3)*(2*h - 1)/2
Let j(k) be the second derivative of -k**5/80 + k**4/24 - k**3/24 - 13*k. Factor j(h).
-h*(h - 1)**2/4
Factor 0 + 0*i - 2/5*i**3 - 4/5*i**2.
-2*i**2*(i + 2)/5
Let m(k) be the third derivative of -k**5/120 - 5*k**4/48 - k**3/3 - 7*k**2. Factor m(a).
-(a + 1)*(a + 4)/2
Let m(j) be the second derivative of j**4/72 - 5*j**3/36 + j**2/2 - 20*j. Factor m(b).
(b - 3)*(b - 2)/6
Let z(i) be the second derivative of -5*i**4/12 + 20*i**3 - 360*i**2 + 6*i. Factor z(m).
-5*(m - 12)**2
Let o = -12 - -14. Find r, given that 9*r + 4*r**3 - 4*r**3 + 3*r**3 - 22*r**2 + 27 + 7*r**o = 0.
-1, 3
Factor 9/5*x - 6/5*x**2 + 6/5.
-3*(x - 2)*(2*x + 1)/5
Let v(r) be the second derivative of 3*r + 1/18*r**3 + 1/60*r**5 + 1/18*r**4 + 0 + 0*r**2. What is n in v(n) = 0?
-1, 0
Let x(b) be the first derivative of -b**6/140 - b**5/210 + b**4/28 + b**3/21 - 3*b**2/2 + 3. Let r(k) be the second derivative of x(k). Factor r(l).
-2*(l - 1)*(l + 1)*(3*l + 1)/7
Let q(n) = n**2 - 5*n - 5. Let m be q(6). Suppose -m - 1 = -a. Find k, given that 1 + k**3 - 3*k**4 - k**3 + a*k**3 - 3*k + k**5 + 2*k**2 = 0.
-1, 1
Let f = -1146 - -8028/7. Let u = 3282/7 - 468. Factor u*i**4 + 2/7*i**5 - f*i - 2/7 - 4/7*i**2 + 4/7*i**3.
2*(i - 1)*(i + 1)**4/7
Let c = 20 + -7. Factor -29*l + 13*l + c*l + l**2.
l*(l - 3)
Let w(y) be the first derivative of -y**4/14 + y**2/7 + 6. Factor w(p).
-2*p*(p - 1)*(p + 1)/7
Factor 27*f**3 - f**4 + 26*f**3 - 56*f**3 + 2*f**4 + 2*f**2.
f**2*(f - 2)*(f - 1)
Factor -1/4 + 0*q + 1/4*q**2.
(q - 1)*(q + 1)/4
Suppose 2*v + v + 42 = 0. Let u(c) = -8*c**2 - 12*c + 6. Let z(g) = 3*g**2 + 4*g - 2. Let r(q) = v*z(q) - 5*u(q). Factor r(y).
-2*(y - 1)**2
Suppose 3*z = h - 12, h + 3*h = -2*z + 6. Factor 0 - 4*l**2 - 4/3*l - 3*l**h.
-l*(3*l + 2)**2/3
Let k be -4*1*((-15)/(-5))/(-6). Suppose -3/7*g**k - 1/7*g**3 + 4/7 + 0*g = 0. What is g?
-2, 1
Suppose -3*g = -3, -3*g = o + 3*o - 11. Let 3*c**3 + 3*c**2 - 2*c**3 + o*c**3 + 0*c**3 = 0. What is c?
-1, 0
Factor 64/3 - 16/3*o + 1/3*o**2.
(o - 8)**2/3
Determine n so that -2/5*n**5 - 2/15*n + 8/15*n**3 - 4/5*n**2 + 8/15*n**4 + 4/15 = 0.
-1, -2/3, 1
Let u(j) be the third derivative of j**5/32 - j**4/48 - j**3/12 + 9*j**2. Determine g, given that u(g) = 0.
-2/5, 2/3
Let y(f) = -f - 9. Let l be y(-9). Let u(v) be the second derivative of l + 1/36*v**4 - 1/18*v**3 - v + 0*v**2. Suppose u(c) = 0. Calculate c.
0, 1
Let a(n) be the first derivative of -4*n**5/5 + n**4 + 8*n**3/3 - 4. Factor a(i).
-4*i**2*(i - 2)*(i + 1)
Let l(d) be the second derivative of -9*d**5/100 - 7*d**4/20 - d**3/5 - 44*d. Factor l(h).
-3*h*(h + 2)*(3*h + 1)/5
Let y be 0/((2/(-4))/((-2)/(-8))). Let v(a) be the third derivative of y*a - 1/150*a**5 + 3*a**2 + 0*a**4 + 0*a**3 + 0. Determine d, given that v(d) = 0.
0
Let h be -4 + 2 + 4 - 2. Factor h - 1/4*x**2 + 1/2*x.
-x*(x - 2)/4
Let z = 10 - 12. Let d(o) = 6*o**3 - 6*o**2 - 15*o + 15. Let q(l) = -l**3 + l**2 + 2*l - 2. Let t(m) = z*d(m) - 15*q(m). Let t(b) = 0. Calculate b.
0, 1
Suppose -4*n =