q**5 + 0*q - 1/20*q**4 + 1/525*q**7. Factor n(v).
2*(v - 1)*(v + 1)**2*(v + 2)/5
Let c(w) = -3*w**3 + 6*w**2 - 12. Let q be (16/(-40))/((-1)/(-5)). Let v(y) = -3*y**3 + 7*y**2 - 12. Let d(o) = q*c(o) + 3*v(o). Suppose d(b) = 0. Calculate b.
-1, 2
Find n, given that 16/5*n**4 + 0 - 8*n**2 + 22/5*n**3 + 0*n + 2/5*n**5 = 0.
-5, -4, 0, 1
Let b(h) be the third derivative of -h**7/30 - 13*h**6/60 - 9*h**5/20 - h**4/6 + 2*h**3/3 + 3*h**2 + 21*h. What is z in b(z) = 0?
-2, -1, 2/7
Let v(x) = -x**3 - 11*x**2 - x - 9. Let t be v(-11). Factor 12*z**3 - 32*z**3 - 3*z**2 - 3*z**2 + t*z**2.
-4*z**2*(5*z + 1)
Let m(f) = -7*f**3 - 3*f**2 + 7*f + 3. Let r(z) = 3*z**3 + z**2 - 3*z - 1. Let u(l) = 6*m(l) + 15*r(l). Factor u(o).
3*(o - 1)**2*(o + 1)
Suppose -2*a = -7*a - 60. Let q = a - -14. Factor -2 + 2*p + 2*p**q - 1 - 1.
2*(p - 1)*(p + 2)
Suppose -8*v = -44 + 12. Suppose 2 + h - v*h - 1994*h**2 + 1995*h**2 = 0. Calculate h.
1, 2
Let a be ((-420)/45)/((-4)/3). Let d(u) be the third derivative of 5/96*u**4 - 1/840*u**a + 1/12*u**3 + 0*u - 1/480*u**6 + 0 + 1/80*u**5 - 2*u**2. Factor d(r).
-(r - 2)*(r + 1)**3/4
Let l(d) be the third derivative of 0*d**3 - 12*d**2 - 1/36*d**5 + 0 - 5/72*d**4 + 0*d. Factor l(f).
-5*f*(f + 1)/3
Find d, given that 48/5*d + 6/5*d**5 + 0 + 27/5*d**3 - 24*d**2 + 39/5*d**4 = 0.
-4, 0, 1/2, 1
Let f(c) be the first derivative of c**6/1260 - c**5/210 + c**4/84 - 5*c**3/3 + 20. Let m(q) be the third derivative of f(q). Factor m(t).
2*(t - 1)**2/7
Factor 807*j**3 + 25*j - 812*j**3 + 35*j + 5*j**2.
-5*j*(j - 4)*(j + 3)
Let -20/3*q**4 + 190/3*q - 2/3*q**5 + 64/3*q**2 - 44/3*q**3 + 100/3 = 0. Calculate q.
-5, -1, 2
Let p(u) be the second derivative of u**6/27 - 44*u**5/45 + 41*u**4/6 + 6*u**3 + 50*u. Let p(y) = 0. Calculate y.
-2/5, 0, 9
Factor -1/9*h**2 - 22/9*h + 1/9*h**3 + 40/9.
(h - 4)*(h - 2)*(h + 5)/9
Suppose 0 - 10*t + 52/5*t**2 - 2/5*t**3 = 0. Calculate t.
0, 1, 25
Let r(t) be the third derivative of -2*t**2 + 0*t + 0 + 1/24*t**4 + 1/360*t**6 + 1/18*t**3 + 1/60*t**5. Factor r(c).
(c + 1)**3/3
Let p(r) be the third derivative of r**5/420 + 3*r**4/28 - 20*r**3/21 - 2*r**2 + 41. Solve p(f) = 0.
-20, 2
Let l = -4326/5 + 8667/10. Factor 0 + l*j**5 + 15/2*j**4 - 6*j**2 - 12*j + 9*j**3.
3*j*(j - 1)*(j + 2)**3/2
Suppose 3*a = 3, -4*h + 6 + 8 = -2*a. Find x, given that -7*x + 7*x + 12*x**4 + h*x**5 - 27*x**2 + 16 - x**2 - 4*x**3 = 0.
-2, -1, 1
Let n = 3106 - 3104. Factor 4*p - 2/5*p**n - 10.
-2*(p - 5)**2/5
Let f(v) be the third derivative of v**8/2240 - v**7/280 - v**6/240 + 3*v**5/40 + 7*v**4/24 - 16*v**2. Let x(a) be the second derivative of f(a). Factor x(s).
3*(s - 3)*(s - 1)*(s + 1)
Suppose 5*v - w - 20 = -7, -9*v + 33 = -5*w. Solve 3/5*r - 3/5 - 3/5*r**3 + 3/5*r**v = 0 for r.
-1, 1
Let o(k) be the first derivative of 0*k**6 + 0*k**2 + 1 + 0*k**4 + 1/90*k**5 - 7*k - 1/189*k**7 + 0*k**3. Let x(h) be the first derivative of o(h). Factor x(n).
-2*n**3*(n - 1)*(n + 1)/9
Suppose -12/7*y + 4/7*y**2 + 0 = 0. Calculate y.
0, 3
Let d be (-485)/60 + 8 - (-25)/12. Determine g so that 0*g**3 + 6/5 - 2/5*g**4 + 12/5*g**d - 16/5*g = 0.
-3, 1
Factor 55*u - 39 + 72*u - 3*u**3 - 33*u**2 - 52*u.
-3*(u - 1)**2*(u + 13)
Let d(q) be the first derivative of 2*q**3/9 + 6*q**2 - 38*q/3 - 3. Suppose d(v) = 0. What is v?
-19, 1
Find h such that -4/5*h**3 + 0*h + 0*h**2 + 1/5*h**4 + 0 = 0.
0, 4
Let m = -74/3 + 25. Suppose 1/6*b**3 + 1/6*b + 0 + m*b**2 = 0. What is b?
-1, 0
Suppose -5*v - b = -31, -v + 3*b + 1 = -2*b. Suppose -2*i + v*i - 5*q = 43, -3*i + 31 = -5*q. Factor 33*h**2 - i*h**2 - 24*h - 18*h**2 + 48.
3*(h - 4)**2
Let o(b) be the first derivative of b**4/22 + 28*b**3/33 + 9. Suppose o(r) = 0. Calculate r.
-14, 0
Factor 15 - 5/6*x**3 + 40/3*x**2 + 175/6*x.
-5*(x - 18)*(x + 1)**2/6
What is y in 22/5*y**3 + 2/5*y**5 + 0*y + 12/5*y**4 + 12/5*y**2 + 0 = 0?
-3, -2, -1, 0
Let k(v) = 9*v**3 + 16*v**2 - 28*v - 30. Let f(u) = -14*u**3 - 24*u**2 + 42*u + 44. Let m(a) = -5*f(a) - 8*k(a). Factor m(w).
-2*(w - 2)*(w + 1)*(w + 5)
Let y be (6 - 0/2) + 180 + -184. Let n = 15 - 12. Let 0*p**y - 2/3*p**4 + 0*p - 2/3*p**n + 0 = 0. Calculate p.
-1, 0
Solve 8/3 - 13/9*k**2 + 10/9*k + 1/9*k**3 = 0 for k.
-1, 2, 12
Let z(d) be the third derivative of -d**8/168 - d**7/35 - d**6/20 - d**5/30 - 110*d**2. Factor z(k).
-2*k**2*(k + 1)**3
Let i be 2 + 1 + 179 - 3. Let f be (-2)/(-8) + -8 + i/20. Factor -2/5*w**5 + 6/5*w - 4/5*w**3 - 2/5 - 4/5*w**2 + f*w**4.
-2*(w - 1)**4*(w + 1)/5
Let p(u) be the first derivative of u**4 - 40*u**3 - 283. Factor p(z).
4*z**2*(z - 30)
Let j(y) = -y**4 - y**3 + y**2. Let o(u) = u**5 - u**3 + u**2. Suppose -7*f = 2 - 9. Let x(n) = f*o(n) - j(n). Factor x(p).
p**4*(p + 1)
Let d(j) be the third derivative of j**7/70 - j**6/40 - 7*j**5/20 + j**4/8 + 3*j**3 + 38*j**2 + 4. Solve d(o) = 0.
-2, -1, 1, 3
Let l(b) = 4*b - 10. Let p be 12/(-5)*(-10)/8. Let n be l(p). Solve 8/9 + 8/9*h - 2/9*h**3 - 2/9*h**n = 0.
-2, -1, 2
Let r(t) be the second derivative of t**4/2 + 8*t**3/9 - t**2/3 + 30*t. Let r(c) = 0. What is c?
-1, 1/9
Let w(b) be the third derivative of -b**8/560 + b**7/175 + 3*b**6/100 - b**5/25 - 13*b**4/40 - 3*b**3/5 - 83*b**2. Let w(r) = 0. Calculate r.
-1, 2, 3
Factor 150*p**2 - 24 + 28*p - 9*p**3 - 160*p**2 + 10*p**3.
(p - 6)*(p - 2)**2
Let p(c) = 2*c + 8. Let t be p(-4). Suppose -4*q - 6 = -w - w, t = 5*q - 10. Determine g, given that -w*g + 0 + 0 - 5*g - 12*g**2 - 3*g**3 = 0.
-2, 0
Let j(w) = -w**3 - 4*w**2 + 5*w + 5. Let z be j(-5). Let q be (-1)/z*-1*25. Suppose 16*r**2 - 6*r**4 + 4*r**3 - 2 - 8*r**q - 2 + 4*r**3 - 6*r**4 = 0. What is r?
-1, 1/2, 1
Let g(s) = -10*s**4 + 50*s**3 - 10*s**2 - 95*s. Let q(i) = 5*i**4 - 25*i**3 + 7*i**2 + 47*i. Let r(t) = 2*g(t) + 5*q(t). Suppose r(j) = 0. What is j?
-1, 0, 3
Suppose -4*i - 7*i = 0. Factor f**2 + i*f**2 + 3*f - f - 5*f.
f*(f - 3)
Suppose -3 = 5*y - a - 0, 4*a = 12. Let s(k) be the first derivative of -4 + 3/4*k**4 - 3/2*k**2 + 0*k**3 + y*k. Find b, given that s(b) = 0.
-1, 0, 1
Let k(r) = -13*r**5 - 7*r**4 + 6*r**3 + 7*r**2 + 14*r - 7. Let v(f) = 7*f**5 + 4*f**4 - 3*f**3 - 4*f**2 - 8*f + 4. Let y(t) = -4*k(t) - 7*v(t). Factor y(u).
3*u**3*(u - 1)*(u + 1)
Let t(d) = -7*d**3 - 66*d**2 + 60*d + 128. Let z(p) = 11*p**3 + 132*p**2 - 120*p - 256. Let o(l) = 5*t(l) + 3*z(l). Factor o(b).
-2*(b - 32)*(b - 2)*(b + 1)
Let u be (-10)/(-4) - -2 - (-6)/(-4). Factor -u*a**2 - 1 + 41*a + 6 - 38*a - 2 - 3*a**3.
-3*(a - 1)*(a + 1)**2
Factor 2808*r + 2*r**2 - 2808*r - 4*r**2 - 2*r**3.
-2*r**2*(r + 1)
Suppose 4 = 2*v - y, 0 = 3*v - 14*y + 9*y + 8. Let l(q) be the first derivative of -v + 1/2*q**4 + q**2 + 0*q + 4/3*q**3. Solve l(s) = 0 for s.
-1, 0
Let s(x) be the first derivative of -8*x**5/25 + 27*x**4/10 - 10*x**3/3 - 72*x**2/5 - 32*x/5 + 66. Let s(i) = 0. Calculate i.
-1, -1/4, 4
Let u be 2/(-7) + (-198)/(-189). Let o(y) be the third derivative of u*y**3 - 2/21*y**4 + 1/210*y**5 + 0*y + 0 - 7*y**2. Factor o(r).
2*(r - 4)**2/7
Let i(f) be the third derivative of f**6/60 + f**5/5 + 11*f**4/12 + 2*f**3 + 54*f**2 - f. What is l in i(l) = 0?
-3, -2, -1
Suppose 52 = 252*o + 52. Factor o*a**2 - 1/2*a**3 + 1/2*a**4 - 1/8*a**5 + 0 + 0*a.
-a**3*(a - 2)**2/8
Determine h so that 128*h**2 - 8*h - 116*h**2 - 7*h + 6 - 3*h**3 = 0.
1, 2
Let h(i) be the second derivative of i**7/5880 - 5*i**4/4 + 12*i. Let l(r) be the third derivative of h(r). Suppose l(b) = 0. Calculate b.
0
Let l be 8*(3/(-6) - -2). Factor -d**2 - 6 - 5 - 25 - l*d.
-(d + 6)**2
Let b(m) = m**2 + 13*m + 2. Let s be b(-13). Find u such that 2*u**2 - 20 - 3*u**3 - s*u + 11 + 5*u + 7*u**2 = 0.
-1, 1, 3
Let i be ((-744)/(-930))/(6/15). Let 2/7*y**i - 10/7*y - 12/7 = 0. Calculate y.
-1, 6
Let b(u) be the second derivative of u**8/1344 + u**7/504 - u**6/72 + 29*u**4/12 - 24*u. Let p(x) be the third derivative of b(x). Find t such that p(t) = 0.
-2, 0, 1
Let i(f) be the third derivative of f**7/840 + f**6/48 - 5*f**4/6 + 15*f**2. Let n(x) be the second derivative of i(x). Factor n(v).
3*v*(v + 5)
Factor -5829 - 236*k + 134*k**2 - 135*k**2 - 5890 - 2205.
-(k + 118)**2
Let x(s) be the second derivative of 1/6*s**4 + 0 + 9/7*s**2 + 1/70*s**5 + 5/7*s**3 + 6*s. Find q, given that x(q) = 0.
-3, -1
Let s(w) be the second derivative of 3*w**5/20 + 3*w**4 + 45*w**3/2 + 75*w**2 - 19