g) = -2*g**3 + g - 1. Let n(o) = 5*c(o) + h(o). Factor n(d).
3*(d - 2)**2*(d + 4)
Factor -4*k**4 + 0*k + 0*k**2 - 16/3*k**3 - 2/3*k**5 + 0.
-2*k**3*(k + 2)*(k + 4)/3
Let n(p) = 65*p**3 - 430*p**2 + 780*p - 560. Let u(b) = -5*b**3 + 33*b**2 - 60*b + 43. Let t(z) = -3*n(z) - 40*u(z). Determine c so that t(c) = 0.
2
Factor -36/7*p**3 + 76/7*p + 0 - 6*p**2 + 2/7*p**4.
2*p*(p - 19)*(p - 1)*(p + 2)/7
Suppose 687*o**3 - 24 - 676*o**2 - 223*o**3 + 20 + 98*o**4 - 158*o**4 + 320*o - 44 = 0. What is o?
1/3, 2/5, 1, 6
Let b = -5840 + 5840. Find u, given that u**2 - 5/8*u**3 - 1/2*u + b + 1/8*u**4 = 0.
0, 1, 2
Let h(w) be the first derivative of -3*w**5/160 + w**4/8 - 5*w**3/16 + 3*w**2/8 + 10*w - 1. Let z(x) be the first derivative of h(x). Factor z(q).
-3*(q - 2)*(q - 1)**2/8
Let l(p) be the first derivative of 2/19*p**4 + 4 + 4/19*p**2 - 2/95*p**5 - 4/19*p**3 - 2/19*p. Find d, given that l(d) = 0.
1
Suppose 0*q + 60 = 5*q. Let x be q/(-8) - (-33)/6. Find d, given that 4*d**x + 4 - 12*d**2 - 16*d + 11 + 1 + 2*d**3 + 6*d**3 = 0.
-2, 1
Let s(r) be the first derivative of -26 + 0*r - 1/9*r**3 + 1/6*r**2. Factor s(o).
-o*(o - 1)/3
Let r(u) = -u**2 + 88*u - 1571. Let k be r(63). Let -3*x**2 + 0 - 9/7*x - 15/7*x**3 - 3/7*x**k = 0. Calculate x.
-3, -1, 0
Let h(t) = 12*t**2 + 502*t - 81. Let f be h(-42). Factor 3/8*s + 3/2*s**2 - 3/2 - 3/8*s**f.
-3*(s - 4)*(s - 1)*(s + 1)/8
Let r = 83 - 163/2. Let z(w) = -w**3 - w**2 + 53*w + 102. Let y be z(-2). Factor 3/2*p**2 + y - r*p.
3*p*(p - 1)/2
Let m(y) be the first derivative of 12*y**3 + 34*y**2 + 32*y + 288. Factor m(t).
4*(t + 1)*(9*t + 8)
Solve 12*a**2 + 0 - 55*a + 2 + 13 - 32*a**2 = 0.
-3, 1/4
Let p(s) = -s**5 + s**4 + s - 1. Let d(x) = 2*x**5 - 2*x**3 - x + 1. Let w(q) = -3*d(q) - 3*p(q). Factor w(z).
-3*z**3*(z - 1)*(z + 2)
Let o(x) be the first derivative of -7*x**4/16 + 37*x**3/12 + 29*x**2/4 - 22*x + 338. Suppose o(v) = 0. Calculate v.
-2, 1, 44/7
Let q(f) be the first derivative of -f**5/4 - 5*f**4/6 - 5*f**3/6 - 9*f + 7. Let s(u) be the first derivative of q(u). Factor s(b).
-5*b*(b + 1)**2
Suppose 12/7 + 2/7*r**3 + 8/7*r**2 - 22/7*r = 0. What is r?
-6, 1
Let r = 1308 - 16995/13. Let n(g) be the first derivative of -6/65*g**5 - 4/13*g - 11 - r*g**2 - 11/26*g**4 - 10/13*g**3. Find f, given that n(f) = 0.
-1, -2/3
Let v = 39 - 37. Let j be (3402/49)/(-9) + 8. Find z such that -j*z**v - 8/7 - 8/7*z = 0.
-2
Suppose -20 = 42*k - 47*k. Let d(t) be the second derivative of t**3 + 1/10*t**5 + 1/2*t**4 + t**2 - k*t + 0. Factor d(o).
2*(o + 1)**3
Suppose -3*x + 26 = 4*g - 6, -3*g - x = -19. Suppose m - g*m = -20. Factor 2*t**2 - 3*t + 1 - 1 - m*t**2.
-3*t*(t + 1)
Suppose 16 - 45*l + 8*l**3 + 13*l + 3*l**4 + 12*l**2 - 2*l**4 + 0*l**4 - 5*l**4 = 0. What is l?
-2, 1, 2
Let q(z) be the first derivative of -z**5/10 - 11*z**4/8 + 55*z**3/6 - 73*z**2/4 + 15*z + 715. Suppose q(f) = 0. What is f?
-15, 1, 2
Let k(g) be the second derivative of -g**7/18 - 13*g**6/45 - 9*g**5/20 - g**4/9 + 2*g**3/9 + g - 606. Suppose k(t) = 0. What is t?
-2, -1, 0, 2/7
Let d be (-2 - -1)*5/(-25). Suppose d*m**2 + 0 - 1/5*m = 0. What is m?
0, 1
Let o(j) be the third derivative of -j**9/20160 - j**8/6720 + j**7/280 + j**5/20 + 8*j**2. Let w(m) be the third derivative of o(m). Find p such that w(p) = 0.
-3, 0, 2
Let z(q) be the first derivative of -q**4/24 + q**3/18 + q**2/12 - q/6 + 35. Factor z(l).
-(l - 1)**2*(l + 1)/6
Suppose 0 = -6*x - 35 - 31. Let i = x + 20. Factor -2*n**2 - i*n**2 - 4 + n**2 - 2*n**2 - 4*n**3 - 12*n.
-4*(n + 1)**3
Let d be (0 - -1)/((-9)/(-18)). Let w(o) = d*o**2 - 2*o**2 - 3*o**2. Let f(y) = -y**4 + 4*y**2. Let v(b) = -3*f(b) - 3*w(b). Solve v(r) = 0 for r.
-1, 0, 1
Determine m, given that 52/3*m + 2/3*m**2 + 338/3 = 0.
-13
Let c(t) be the third derivative of t**7/280 - 3*t**5/40 - t**4/4 - 5*t**3/3 - 20*t**2. Let d(s) be the first derivative of c(s). Factor d(z).
3*(z - 2)*(z + 1)**2
Let y(b) = b**3 - 4*b**2 - 2*b + 9. Let f be y(4). Factor 8*d - 2 - d**2 + 6*d**2 - 1 - f.
(d + 2)*(5*d - 2)
Let g(o) be the second derivative of -2*o**6 - 13*o**5/4 + 10*o**4/3 + 35*o**3/6 - 5*o**2 - 712*o. Suppose g(h) = 0. What is h?
-1, 1/4, 2/3
Let d = 233 - 233. Let y be d + 2 - 0 - 0/10. Determine v, given that -1/2 + 1/4*v - 1/4*v**3 + 1/2*v**y = 0.
-1, 1, 2
Let m(b) be the first derivative of 10*b - 17*b**2 - 7/6*b**3 + 44. Factor m(p).
-(p + 10)*(7*p - 2)/2
Let x = 947/2 - 473. Determine j so that 1/2*j**3 + j**2 - 1 - x*j = 0.
-2, -1, 1
Factor 10/7*s**2 + 2/7*s**3 + 0*s + 0.
2*s**2*(s + 5)/7
Let l(y) be the second derivative of -7*y + y**2 - 1/90*y**6 + 1/18*y**3 - 1/36*y**4 - 7/180*y**5 + 0. Let r(a) be the first derivative of l(a). Factor r(f).
-(f + 1)**2*(4*f - 1)/3
Let q(w) be the second derivative of 18*w**7/49 - 216*w**6/35 + 1017*w**5/35 - 1312*w**4/21 + 480*w**3/7 - 256*w**2/7 - 689*w. Find j such that q(j) = 0.
1/3, 1, 4/3, 8
Let u = 1421 + -15625/11. Factor 0 - 2/11*t**2 + u*t.
-2*t*(t - 3)/11
Factor 4/7*n**2 - 20/7*n + 0.
4*n*(n - 5)/7
Determine c, given that -36*c**2 + 6*c - 38*c - 2*c**4 + 11 - 3 - 24 + 6 - 16*c**3 = 0.
-5, -1
Suppose j + 2*b = -8, 4*j = 5*b - 19 + 52. Suppose 3*s = 2*s - 4*p + 14, 5 = -j*s + 3*p. Factor 3*g**s + 4*g**4 - g**4 - 3*g**2.
3*g**4
Let h(y) be the third derivative of 18*y**7/35 + 54*y**6/5 - 114*y**5/5 + 58*y**4/3 - 26*y**3/3 - 34*y**2 - 2*y. Factor h(o).
4*(o + 13)*(3*o - 1)**3
Let v(r) be the second derivative of -2*r**6/135 + 11*r**5/90 - r**4/3 + 4*r**3/27 + 8*r**2/9 - 2*r - 6. Factor v(y).
-2*(y - 2)**3*(2*y + 1)/9
Let 36*w**2 - 12*w - 12*w + 42*w**3 + w**4 - 46*w**4 - 27*w**5 = 0. What is w?
-2, -1, 0, 2/3
Let p(o) = 7*o**3 - 75*o**2 - 20*o - 20. Let w be p(11). Factor 4/3 + 2*y + 2/3*y**w.
2*(y + 1)*(y + 2)/3
Let w(n) be the second derivative of -8*n**2 + 7/5*n**5 - 2/15*n**6 - 5*n**4 + 0 + 30*n + 26/3*n**3. Factor w(m).
-4*(m - 4)*(m - 1)**3
Suppose -2*b + 0 - 8 = -2*s, s - 3*b = 8. Factor 6*m + 1 + 18*m**2 + m**3 - 24*m**s + 9*m**2 - 3*m.
(m + 1)**3
Let b(q) = -q**3 + 9*q**2 - 8*q + 3. Let s be b(8). Suppose -c + 4*i - 4 = 0, c - 2*i - 12 = -s*c. Factor l + 2*l**2 - 2 - l**2 - 4*l + c.
(l - 2)*(l - 1)
Factor 1/3*j**4 - 2*j**3 + 0 + 0*j**2 + 32/3*j.
j*(j - 4)**2*(j + 2)/3
Let p(z) be the first derivative of -z**4/12 + 26*z**3/9 - 169*z**2/6 + 79. Determine k, given that p(k) = 0.
0, 13
Let m(j) = -j**5 - 47*j**4 - 69*j**3 - 3*j**2 - 3*j. Let r(k) = -k**5 + k**4 - k**3 + k**2 + k. Let c(u) = m(u) + 3*r(u). Factor c(s).
-4*s**3*(s + 2)*(s + 9)
Suppose 4*r = r. Let y(p) = -12*p + 1 + 11*p + 2 + 15*p**2 + r. Let z(s) = 136*s**2 - 10*s + 26. Let g(i) = -52*y(i) + 6*z(i). Factor g(l).
4*l*(9*l - 2)
Let g = -85/2 - -48. Let q(d) = 5*d - 15. Let l be q(4). Solve -g*w**2 + 11/2*w**4 - w + 0 - 7/2*w**3 + 9/2*w**l = 0.
-1, -2/9, 0, 1
Factor -39*t**3 + 22*t**2 + 20*t**2 + 3*t**4 + 15*t**2 - 21*t**2.
3*t**2*(t - 12)*(t - 1)
Determine u so that -1/3*u**2 - 14/3 + 5*u = 0.
1, 14
Suppose -3*x - 10 = -5*c, 6*x - 8*x + 2 = c. Let f(b) be the first derivative of -2 - 4/5*b**5 + 4/3*b**3 + b**4 - 2*b**2 + x*b. Find h such that f(h) = 0.
-1, 0, 1
What is g in 2 - 364*g + 361*g - g**4 + 10*g**3 - g**2 - 7*g**3 = 0?
-1, 1, 2
Let h(y) be the second derivative of -y**5/160 + y**4/16 + y**3/3 + 12*y - 2. What is t in h(t) = 0?
-2, 0, 8
Let d(k) be the second derivative of -k**7/84 + k**6/15 + k**5/20 - k**4/2 - 3*k**3/4 - k + 106. Solve d(a) = 0 for a.
-1, 0, 3
Let h(z) be the second derivative of 3*z**6/65 - 15*z**5/26 + 73*z**4/78 + 25*z**3/13 + 14*z**2/13 - 13*z. Determine t so that h(t) = 0.
-1/3, 2, 7
Let x(y) be the second derivative of -3*y**6/20 + 21*y**5/8 - 79*y**4/8 + 65*y**3/4 - 27*y**2/2 - 10*y + 1. Solve x(l) = 0.
2/3, 1, 9
Let w(n) = -17*n**2 + 9*n + 8. Let m(r) be the first derivative of 11*r**3/3 - 3*r**2 - 5*r + 14. Let t(v) = 8*m(v) + 5*w(v). Find u such that t(u) = 0.
0, 1
Let o(n) be the third derivative of n**5/240 - 7*n**4/16 + 147*n**3/8 - 11*n**2. Determine x so that o(x) = 0.
21
Let n(h) be the first derivative of 4*h + 1/5*h**5 + 3/2*h**4 - 1 + 13/3*h**3 + 6*h**2. Suppose n(z) = 0. Calculate z.
-2, -1
Factor 40*j + 2*j**2 + 17 - 17.
2*j*(j + 20)
Let h(q) be the first derivative of 0*q**3 - 2*q**4 - 36/5*q**5 + 0*q**2 - 4 + 0*q. Factor h(p).
-4*p**3*(9*p + 2)
Suppose -w = 5*x,