et g(q) = -a(q) - 6*h(q). Factor g(f).
-f*(f - 1)*(2*f + 1)
Suppose 3*w = 5*w. Determine n so that w - n**2 + 3*n**2 - 3 - 5*n**2 + 6*n = 0.
1
Let z(f) = -f**4 + 2*f**3. Let b(h) = -43*h**4 + 26*h**3 + 42*h**2 - 40*h + 8. Let r(a) = -b(a) - 7*z(a). Let r(v) = 0. Calculate v.
-1, 2/5, 1
Let y(k) be the third derivative of -k**8/168 + k**7/84 - 31*k**2. Solve y(h) = 0.
0, 5/4
What is h in 152/11*h**2 + 84/11*h**3 + 14/11*h**5 - 48/11*h + 0 - 102/11*h**4 = 0?
-1, 0, 2/7, 2, 6
Let t(f) = -f**3 - 9*f**2 - 11*f - 19. Let w be t(-8). Let j(q) = q**4 - q**2 + 4*q. Let n(s) = -s**4 + s**2 - 5*s. Let o(p) = w*j(p) + 4*n(p). Factor o(v).
v**2*(v - 1)*(v + 1)
Determine z, given that 2*z**2 - z**3 + 3*z - 54*z**4 - 7*z**2 + 55*z**4 + 2*z**3 = 0.
-3, 0, 1
Let q(d) = -d**4 - d**3 - d**2. Let x(n) = -3*n**5 + 3*n**4 + 18*n**3 - 27*n**2 - 36*n. Let p(f) = 3*q(f) - x(f). Let p(j) = 0. What is j?
-2, -1, 0, 2, 3
Let o = -61 + 64. Suppose 4*n = 2*r, -o*r + 20 = 2*r. Suppose 0*a - 2/7 + 2/7*a**n = 0. What is a?
-1, 1
Let v = 9 - 4. Suppose 4*j + j - 25 = -a, -a = -v*j - 55. Factor a*t + 14*t**3 - 19*t**2 + 4*t**4 - 17*t**2 + t**4 - 7*t**4 - 16.
-2*(t - 2)**3*(t - 1)
Let q(c) be the third derivative of 0 + 0*c + 16*c**2 - 57/100*c**5 - 2*c**3 + 8/5*c**4 + 9/200*c**6. Let q(v) = 0. What is v?
2/3, 5
Let f(y) be the third derivative of 2*y**7/315 - 2*y**6/45 - 4*y**5/15 - 11*y**2 + 21*y. Solve f(i) = 0 for i.
-2, 0, 6
Suppose 0 = -3*q + 4*d + 18, -q + d = -4*d - 17. What is n in -5*n**4 + 10/3*n**3 - 5/3*n - 5 + 10*n**q - 5/3*n**5 = 0?
-3, -1, 1
What is s in 50/3 - 8/21*s**3 + 4*s**2 + 440/21*s - 2/21*s**4 = 0?
-5, -1, 7
Let c(b) be the second derivative of b**6/105 - 3*b**5/70 + b**4/21 - 37*b + 1. Factor c(q).
2*q**2*(q - 2)*(q - 1)/7
Let i = 6017/7 - 859. Suppose i*s - 4/7 + 8/7*s**2 = 0. What is s?
-1, 1/2
Let s(n) be the first derivative of 2/25*n**5 - 1/30*n**6 + 0*n - 1/20*n**4 - 18 + 0*n**2 + 0*n**3. Determine u so that s(u) = 0.
0, 1
Let k(j) = -j**3 + 51*j**2 - 55*j + 253. Let f be k(50). Suppose 2/3*g**2 + 2/15*g**f - 2/15*g - 2/3 = 0. What is g?
-5, -1, 1
Let l(v) be the first derivative of 6*v**2 - 5/2*v**3 + 3/8*v**4 - 6*v - 14. Factor l(n).
3*(n - 2)**2*(n - 1)/2
Let k(n) be the second derivative of -n**4/78 - n**3/39 + 3*n + 6. Factor k(z).
-2*z*(z + 1)/13
Let a(d) = d**3 - 34*d**2 + 23*d + 332. Let s be a(33). Factor -2/5*r + 0 - 12/5*r**s.
-2*r*(6*r + 1)/5
Let k be ((3128/69)/(-34))/(2/(-3)). Let n(p) be the first derivative of 13 + 4/21*p**3 - 10/7*p**k + 16/7*p. Find h such that n(h) = 0.
1, 4
Suppose 42 = 6*c + 18. Let g(y) be the first derivative of 0*y - 4 + 1/4*y**c - 4/9*y**3 + 1/6*y**2. Factor g(x).
x*(x - 1)*(3*x - 1)/3
Let j(n) be the second derivative of -51/32*n**4 - 31/16*n**3 - 25*n - 27/160*n**5 + 0 - 15/16*n**2. Factor j(v).
-3*(v + 5)*(3*v + 1)**2/8
Suppose 12 = -9*u + 30. Let g(h) be the first derivative of -1 + 0*h - 3/5*h**5 + h**3 - 3/4*h**4 + 1/2*h**6 + 0*h**u. Solve g(k) = 0.
-1, 0, 1
Factor 2/13*y**2 - 6/13 + 4/13*y.
2*(y - 1)*(y + 3)/13
Find l such that 13/3*l**4 - 1/3*l**5 - 47/3*l**3 - 8*l + 59/3*l**2 + 0 = 0.
0, 1, 3, 8
Let o(u) be the second derivative of -1/20*u**4 + 0 - 8*u + 3/5*u**2 - 1/10*u**3. Factor o(i).
-3*(i - 1)*(i + 2)/5
Let w be (-24)/(-40) + (-42)/(-15) - (-2 + 5). Factor -6/5 + 2/5*b - w*b**3 + 6/5*b**2.
-2*(b - 3)*(b - 1)*(b + 1)/5
Suppose 0 = 33*q + 8*q. Find j such that -1/6*j**5 + q + 1/6*j**3 + 0*j - 1/6*j**2 + 1/6*j**4 = 0.
-1, 0, 1
Let x(g) be the first derivative of g**4 + 128*g**3/15 - 246*g**2/5 - 216*g/5 - 388. Factor x(s).
4*(s - 3)*(s + 9)*(5*s + 2)/5
Factor 3/4*p**3 + 0*p + 0 - 21/8*p**2.
3*p**2*(2*p - 7)/8
Suppose 1 = -3*v + 10. Suppose 3 = -0*i + v*i. Solve 31*z**2 - i - z**3 - 3*z - 15*z**2 - 19*z**2 = 0 for z.
-1
Let y = 464/429 - -36/143. Determine j, given that -4/3*j**3 + y*j + 4/3 - 4/3*j**2 = 0.
-1, 1
Let w be (6 + (-78)/12)*-1. Let y = -243 - -246. Find l, given that 1/6 - 1/6*l - w*l**y - 5/6*l**2 = 0.
-1, 1/3
Factor -44*t**5 - 42*t**5 + 173*t**5 + 32*t**3 - 41*t**5 - 28*t**4 - 50*t**5.
-4*t**3*(t - 1)*(t + 8)
Let u(o) be the second derivative of o**7/8820 + o**6/1260 + o**5/420 - 7*o**4/6 + 6*o. Let x(t) be the third derivative of u(t). Factor x(j).
2*(j + 1)**2/7
Let g(v) be the second derivative of -1/4*v**4 + 3/10*v**5 + 0 - v**3 + 7*v + 0*v**2 + 1/10*v**6. Factor g(o).
3*o*(o - 1)*(o + 1)*(o + 2)
Let f be (3300/280 - 12)*35/(-2). Factor -f*l + 3/8*l**2 + 75/8.
3*(l - 5)**2/8
Let p(c) = c**5 + 18*c**4 + 76*c**3 + 93*c**2 + 34*c - 3. Let v(o) = o**4 - o**3 - 2*o**2 + 1. Let q(t) = -p(t) - 3*v(t). Factor q(b).
-b*(b + 1)**2*(b + 2)*(b + 17)
Let c be (-12)/(-4) - 3 - (-1)/3. Let x(b) = 2*b + 29. Let y be x(-14). Factor -y - c*i**2 - 4/3*i.
-(i + 1)*(i + 3)/3
Let p(v) be the third derivative of v**5/20 - 45*v**4/4 + 2025*v**3/2 + 111*v**2 - 2*v. Factor p(r).
3*(r - 45)**2
Let l = 189 - 109. Factor l*x - 32*x - 30*x - 3*x**2 - 15.
-3*(x - 5)*(x - 1)
Suppose 2*f = 2*x + 16, 4*f - x - 2*x - 29 = 0. Suppose r + 17 = -3*r + f*i, 3*r + 5*i = 31. Factor 0 + 0*m**r + 2/3*m**3 - 2/3*m.
2*m*(m - 1)*(m + 1)/3
Let z(b) be the second derivative of -1/20*b**5 + 0 - 1/4*b**4 - 1/2*b**3 + b + 2*b**2. Let c(t) be the first derivative of z(t). What is i in c(i) = 0?
-1
Let x = -86 - -130. Factor x*j**4 - 18*j**4 - 14*j**4 - 5*j**3 - 17*j**4.
-5*j**3*(j + 1)
Let n(p) be the third derivative of -1/42*p**7 + 5/6*p**3 + 0*p**5 + 0*p - 5/12*p**4 - 10*p**2 + 1/12*p**6 + 0. Suppose n(t) = 0. Calculate t.
-1, 1
What is b in -2/3*b**4 + 4/3*b**3 + 0 - 4/3*b + 2/3*b**2 = 0?
-1, 0, 1, 2
Let a = 30 - 31. Let g be a*5*6/(-10). What is o in 1/4*o**2 - 3/4*o**g + 0 + 1/2*o = 0?
-2/3, 0, 1
Factor -1/4*f - 1/4*f**2 + 3.
-(f - 3)*(f + 4)/4
Let p(o) be the second derivative of -8*o + 0 + 1/180*o**5 - 1/1620*o**6 + 0*o**2 + 0*o**4 - 2/3*o**3. Let t(a) be the second derivative of p(a). Factor t(r).
-2*r*(r - 3)/9
Let l(s) = 6*s**2 - 47*s + 24. Let z(b) = -6 - b**2 + 8*b - 1 + 3. Let t(p) = -6*l(p) - 34*z(p). What is i in t(i) = 0?
1, 4
Let g(i) be the third derivative of i**6/8 - i**5/6 - 5*i**4/2 + 20*i**3/3 + 483*i**2. Determine b so that g(b) = 0.
-2, 2/3, 2
Let r(t) = -10*t**4 + 2*t**3. Let y(s) = s**5 + 51*s**4 - 8*s**3. Let a(q) = -22*r(q) - 4*y(q). Factor a(d).
-4*d**3*(d - 3)*(d - 1)
Let d(t) = -5*t**2 - 179*t - 210. Let s(l) = l**2 + 45*l + 52. Let q(p) = -2*d(p) - 9*s(p). Factor q(i).
(i - 48)*(i + 1)
Let d(b) be the third derivative of 0 - 1/20*b**5 + b**2 + 0*b - 32*b**3 - 2*b**4. Factor d(g).
-3*(g + 8)**2
Let a(z) = 3*z**2 - 2*z - 20. Let b(d) = -3*d**2 + 4*d + 19. Let j(t) = 4*a(t) + 5*b(t). Determine m, given that j(m) = 0.
-1, 5
Let y(k) be the second derivative of -k**5/15 + 2*k**3/3 + 10*k**2 + 2*k + 6. Let i(z) be the first derivative of y(z). Solve i(n) = 0 for n.
-1, 1
Let o(i) = -i**3 + 3*i**2 + 2*i + 4. Let x(y) = -2*y**3 + 3*y**2 + 2*y + 5. Let t(r) = 3*o(r) - 2*x(r). Let w be t(-2). Factor -1/2*v**w + 1 + 1/2*v.
-(v - 2)*(v + 1)/2
Let u(p) be the first derivative of 1/15*p**6 - 1/5*p**4 - 4/25*p**5 + 1/5*p**2 + 8/15*p**3 - 4/5*p - 13. Solve u(r) = 0.
-1, 1, 2
Let u(v) be the first derivative of -v**6/54 - 8*v**5/45 - v**4/6 + 8*v**3/27 + 7*v**2/18 - 85. Let u(d) = 0. Calculate d.
-7, -1, 0, 1
Let x be (-3)/(-2)*-18*9/(-81). Let t(q) be the first derivative of 8 + 1/4*q**3 + x*q + 3/2*q**2. Factor t(j).
3*(j + 2)**2/4
Let f(o) = -o**2 - 55*o + 117. Let i be f(-57). Factor -2/11*p - 4/11*p**2 + 0 - 2/11*p**i.
-2*p*(p + 1)**2/11
Find k, given that -100 + 170/3*k - 32/3*k**2 + 2/3*k**3 = 0.
5, 6
Suppose -1/5*f**5 + 18/5*f - f**4 + 0 + 31/5*f**3 - 43/5*f**2 = 0. What is f?
-9, 0, 1, 2
Let g = 194 + -1744/9. Suppose 13*s - 32 = 5*s. Factor 0*n**2 + g + 4/9*n**3 - 2/9*n**s - 4/9*n.
-2*(n - 1)**3*(n + 1)/9
Let w(b) be the first derivative of b**6/14 + 6*b**5/35 - 3*b**4/14 - 4*b**3/7 + 3*b**2/14 + 6*b/7 + 762. Let w(h) = 0. What is h?
-2, -1, 1
Let g(x) be the first derivative of -5*x**4/4 + 7*x**2/2 - 2*x + 10. Let t(k) = -k**3 + k. Let r(i) = g(i) - 4*t(i). Suppose r(w) = 0. Calculate w.
-2, 1
Let g = -2512 + 7648/3. Let y = g - 548/15. Factor -y*t + 2/5*t**2 + 0.
2*t*(t - 2)/5
Let n(r) be the first derivative of 3*r**5 + 7*r**3 + 0*r + 1/2*r**6 + 27/4*r**4 + 15 + 3*r**2. Factor n(u).
3*u*(u + 1