
Let o(b) = -b**5 - 15*b**4 + 21*b**3 - 13*b**2 - 2*b. Let y(g) = 2*g**5 + 16*g**4 - 20*g**3 + 14*g**2 + 3*g. Let c(a) = -3*o(a) - 2*y(a). Factor c(z).
-z**2*(z - 11)*(z - 1)**2
Let z be (-7 - 3 - -10)/((-1)/2*-2). Factor -2/5*i**4 + 2/5*i**2 + 2/5*i - 2/5*i**3 + z.
-2*i*(i - 1)*(i + 1)**2/5
Let p be (-6312)/(-132) - (2 + 72/(-33)). Factor 2*g**3 + 23*g**2 - 3*g + p*g - 53*g**2 + 3*g**3.
5*g*(g - 3)**2
Let q be (-3)/((-2)/(-6) - (-64)/(-120)). Solve -35 - q*u**3 - 85*u + 70 + 5*u**4 - 75*u**2 - 42 - 23 = 0 for u.
-1, 6
Let m(j) be the third derivative of -j**5/390 - j**4/13 - 20*j**3/39 - 37*j**2 - 2. Factor m(r).
-2*(r + 2)*(r + 10)/13
Factor -3*k**3 - 27/2*k**2 + 3/4*k**4 - 21/4 - 15*k.
3*(k - 7)*(k + 1)**3/4
Suppose -9*g + 63 = 12*g. Let z(w) be the second derivative of -10*w + 0 - g*w**2 + 11/3*w**3 - 19/18*w**4 + 1/10*w**5. Factor z(x).
2*(x - 3)**2*(3*x - 1)/3
Let s = 43 + -41. Determine r so that 14 - 16 - r + r**3 + 0*r**2 + s*r**2 = 0.
-2, -1, 1
Suppose 4*t = 4*u, t - 3*u + 2 = -u. Suppose t + 6 = 4*f. What is s in 2*s + 0 - 1/2*s**f = 0?
0, 4
Let q(v) be the second derivative of -7*v**5/100 - 19*v**4/60 - 4*v**3/15 + 2*v**2/5 + 7*v. Factor q(c).
-(c + 1)*(c + 2)*(7*c - 2)/5
Let s = -36429/2 + 18215. Let 0*z + 0 - s*z**3 - 1/2*z**2 = 0. What is z?
-1, 0
Let p(c) = -13*c**2 + 13*c - 54. Let w(u) = -11*u**2 + 13*u - 51. Let s(y) = -5*p(y) + 6*w(y). Suppose s(f) = 0. What is f?
4, 9
Let k(s) be the first derivative of -s**6/3 - 48*s**5/25 - 4*s**4 - 52*s**3/15 - 3*s**2/5 + 4*s/5 - 80. Let k(v) = 0. What is v?
-2, -1, 1/5
Find l such that -76*l - 21*l**3 + 30*l**3 + 21 + 3 - 18*l**3 + 66*l**2 = 0.
2/3, 6
Let q be 0*(16/6 + -3). Let l(v) be the third derivative of 8/3*v**4 + 8/15*v**5 + 4*v**2 + 0*v + 1/30*v**6 + q*v**3 + 0. Factor l(o).
4*o*(o + 4)**2
Let z(y) be the first derivative of 5*y**7/42 + y**6/2 - 30*y + 4. Let f(s) be the first derivative of z(s). Factor f(h).
5*h**4*(h + 3)
Factor -49/5*k - 23*k**2 + 5*k**3 - 1.
(k - 5)*(5*k + 1)**2/5
Let r(f) be the second derivative of -f**6/6 + f**5 + 5*f**4/12 - 10*f**3/3 + 22*f + 2. Let r(o) = 0. What is o?
-1, 0, 1, 4
Let n = 275 + -267. Let g(k) be the third derivative of -1/60*k**5 + 2/3*k**3 + 0*k**4 + 0*k + n*k**2 + 0. Factor g(w).
-(w - 2)*(w + 2)
Let d = 12 + 4. Factor 13*m**2 - m**3 + 0 + 0 - d*m**2.
-m**2*(m + 3)
Solve -14*n**3 - n**2 + 17320*n**4 - 17124*n**4 - 39*n**2 + 8*n = 0 for n.
-1/2, 0, 2/7
Suppose -3*a + 7 = 13. Let f be 152/80 + 3/a. Factor -f*g + 2/5*g**2 + 0.
2*g*(g - 1)/5
Let p(h) = 4*h**5 - 34*h**4 + 63*h**3 + 735*h**2 + 7*h + 7. Let s(z) = z**5 - 11*z**4 + 21*z**3 + 245*z**2 + 2*z + 2. Let m(i) = -6*p(i) + 21*s(i). Factor m(x).
-3*x**2*(x - 5)*(x + 7)**2
Let n(w) = -w**3 + 11*w**2 - 22*w - 8. Let l be n(8). Determine i, given that 0*i - i**3 - i**3 + l*i**2 + i + i**3 - 8 = 0.
-1, 1, 8
Let r = -2/12797 - -179164/38391. Determine z, given that 0*z**2 + 2/3*z**3 + 4 - r*z = 0.
-3, 1, 2
Factor -5*y**2 - 4928 + 4896 + 3*y**2 + 6*y**2 + 62*y + 28*y**4 - 64*y**3 + 2*y**5.
2*(y - 1)**3*(y + 1)*(y + 16)
Let a(t) = -7*t + 2*t**2 - 2*t**2 - 3*t**2. Let h(l) be the second derivative of -l**4/4 - l**3 + 13*l. Let c(k) = 3*a(k) - 4*h(k). Factor c(r).
3*r*(r + 1)
Factor 0 + 0*s + 1/2*s**2 + 1/4*s**3.
s**2*(s + 2)/4
Let g(o) be the third derivative of o**7/420 - o**6/180 - o**5/10 + o**3/6 - 6*o**2. Let w(y) be the first derivative of g(y). Find r, given that w(r) = 0.
-2, 0, 3
Solve 1/6*z**5 - 2/3*z + 5/6*z**4 + 1/2*z**3 - 5/6*z**2 + 0 = 0.
-4, -1, 0, 1
Let k(o) be the first derivative of -29 + 105*o**2 + 5*o**4 - 45*o - 125/3*o**3. Solve k(n) = 0.
1/4, 3
Let i(w) = w**3 - w. Let q(k) = 7*k**3 - 8*k**2 + 13*k - 12. Let g(t) = 6*i(t) - q(t). Factor g(m).
-(m - 4)*(m - 3)*(m - 1)
Let l(r) be the second derivative of -4*r**6/5 - 4*r**5/5 + 5*r**4/3 + 10*r**3/3 - 25*r. Let y(k) = k**4 - k. Let d(z) = -l(z) - 20*y(z). Solve d(g) = 0.
-5, 0, 1
Let z be (-6)/21 - (-60)/14. Suppose -4*k + 4 = -4*h, 0 = 5*h + k + z*k - 25. Factor y - y + y - h*y**2 - 3*y.
-2*y*(y + 1)
Let y(h) = -h**3 - 43*h**2 + 44*h. Let q be y(-44). Factor -2/7*i**2 + 0 + q*i + 11/7*i**3 - 9/7*i**4.
-i**2*(i - 1)*(9*i - 2)/7
Let l(k) be the second derivative of k**7/16380 + k**6/468 + 5*k**5/156 - 5*k**4/12 + 2*k. Let h(f) be the third derivative of l(f). Factor h(j).
2*(j + 5)**2/13
Let d be 70/84 - 7/(-6). Factor -25/4 - 5/2*h - 1/4*h**d.
-(h + 5)**2/4
Let t(c) = -c**4 + c**2. Let a(p) = p**5 - 4*p**4 + p**3 + 2*p**2. Let k(q) = -a(q) + 2*t(q). Find h such that k(h) = 0.
0, 1
Find q, given that -18/13*q**2 - 2/13*q + 18/13 + 2/13*q**3 = 0.
-1, 1, 9
Let o(r) = r + 7. Let k be o(-5). Let k + 3*x**3 + 3*x + 9*x**2 + 0*x**3 - 15*x - 38 = 0. What is x?
-3, -2, 2
Factor -9*x - 27*x + 252*x**4 + 4*x**3 + 36*x**2 + 245*x**4 - 501*x**4.
-4*x*(x - 3)*(x - 1)*(x + 3)
Solve 386*t**2 - 4*t + 2*t**4 + 2*t**5 - 6*t**3 + 389*t**2 - 785*t**2 = 0 for t.
-1, 0, 2
Let c be 5/4*192/1320. Factor 2/11*o**4 + 0*o + 0*o**2 - c*o**5 + 0 + 4/11*o**3.
-2*o**3*(o - 2)*(o + 1)/11
Let j(n) be the third derivative of -5*n**8/336 - n**7/42 + n**6/4 - n**5/6 - 25*n**4/24 + 5*n**3/2 + 4*n**2 + 4*n. What is h in j(h) = 0?
-3, -1, 1
Factor 122*p**4 + 30*p**2 + 104*p**4 + 27*p**3 - 229*p**4.
-3*p**2*(p - 10)*(p + 1)
Suppose p = 2*w + 2*p - 6, -3*w + 2 = -2*p. Factor -m**3 + 48*m + 3*m**3 + 58*m**2 - 28*m**w - 32 - 48*m**2.
2*(m - 4)**2*(m - 1)
Suppose -6*h = -h - 4*a + 6, h - 22 = -5*a. Let w be h/(-4)*(-1 + -3). Determine u so that 4*u**2 + 4*u**3 - 18*u**2 + 9*u**2 + 48*u - 32 - 19*u**w = 0.
2
Let n(q) = 2*q - 4. Let c be n(4). Suppose 2*m - 2*j = 7*m - 23, c*m + 4*j = 28. Factor -2*z**2 - 3*z**m + 2 - 2 + 4*z**3.
z**2*(z - 2)
Let i = -2 + 5. Suppose -5*a = 4*a - 45. Let -2*w - 7*w**3 - 2*w**3 - 6*w**2 + 2*w + i*w**a = 0. What is w?
-1, 0, 2
Suppose -5*k - 4 = 3*x - 11, -5 = 5*x. Suppose -4*y**5 + 12*y**4 + 8*y**3 - 5*y**5 + 4 - 16*y**k + y**5 = 0. What is y?
-1, -1/2, 1
Determine h so that 1/4*h + 3/8*h**2 - 3/8 - 1/4*h**3 = 0.
-1, 1, 3/2
Let y(r) = 10*r**3 - 40*r**2 - 5. Let b(s) = 11*s**3 - 41*s**2 - 6. Let l(d) = -5*b(d) + 6*y(d). Factor l(w).
5*w**2*(w - 7)
Suppose -10*u + 3*j = -6*u, -u + 23 = 5*j. Let 37*x**u - 16*x**2 - 16*x**3 - 17*x**3 + 16*x = 0. What is x?
0, 2
Let x(m) = 2*m**2 - 5*m. Let s(p) = -6*p - 33. Let v be s(-5). Let a(n) = -2*n**2 + 6*n. Let o(r) = v*a(r) - 4*x(r). Factor o(l).
-2*l*(l - 1)
Let f(d) be the second derivative of d**4/28 + d**3/2 - 27*d**2/7 - 4*d + 6. Determine j so that f(j) = 0.
-9, 2
Factor 37 + 3 - 125*d + 15*d**2 + 55*d.
5*(d - 4)*(3*d - 2)
Let j(a) be the third derivative of -591/20*a**6 + 667/45*a**5 + 8*a**3 + 0*a - 216/7*a**7 + 2025/56*a**8 + 61/3*a**4 + 19*a**2 + 0. Factor j(f).
2*(5*f - 3)**2*(9*f + 2)**3/3
Suppose -2811 = -6*v - 2793. Suppose 0 + 2/5*g**4 + 4/5*g**v - 2/5*g**2 - 4/5*g = 0. What is g?
-2, -1, 0, 1
Let s = 14 + -15. Let o(x) = -x**3 + x - 1. Let r(j) = -2*j**4 + 4*j**3 + 6*j**2 + 4. Let f = -2 - 2. Let g(y) = f*o(y) + s*r(y). Factor g(b).
2*b*(b - 2)*(b + 1)**2
Let y(q) be the first derivative of 5*q**3/3 + 285*q**2/2 - 294. Suppose y(p) = 0. What is p?
-57, 0
Let f(n) = 0*n**3 + 24*n + 6*n - 12 + 6*n**3 - 29*n**2. Let t be (4 - 63/14)*4. Let q(w) = 3*w**3 - 14*w**2 + 15*w - 6. Let v(g) = t*f(g) + 5*q(g). Factor v(k).
3*(k - 2)*(k - 1)**2
Let -6/5 - 2*z**2 + 32/5*z = 0. What is z?
1/5, 3
Let x(j) be the third derivative of j**6/360 - j**5/40 + j**4/12 + 9*j**3 + 45*j**2. Let y(w) be the first derivative of x(w). Determine u, given that y(u) = 0.
1, 2
Let n(v) be the first derivative of -65*v**2 + 9 - 40*v - 7*v**5 + 65/2*v**4 + 25*v**3. Suppose n(g) = 0. Calculate g.
-1, -2/7, 1, 4
Let t be -7 - (-3 + 96/(-22)). Factor 0 - t*h**4 - 2/11*h**5 + 0*h - 2/11*h**3 + 0*h**2.
-2*h**3*(h + 1)**2/11
Let x(g) = 2*g**3 - 27*g**2 - 53*g - 3. Let k(h) = -h**3 + 26*h**2 + 50*h + 2. Let b(c) = 3*k(c) + 2*x(c). Factor b(f).
f*(f + 2)*(f + 22)
Let f = -8 - -11. Let k = -309 + 3401/11. Determine y so that 0 + 0*y + 0*y**f - k*y**4 + 0*y**2 - 2/11*y**5 = 0.
-1, 0
Let q = 128 + -131. Let f(u) = u - 1. Let z(w) = -4*w**2 + 3*w - 3. Let p(j) = q*f(j) + z(j). Factor p(n).
-4*n**2
Let z(w) be the second derivative of 0*w**3 + 1/35*w**5 + 0*w**4 + 22*w + 4/105*w**6 + 2/147*w**7 + 0*w**2 + 0. Suppose z(q) =