1/(-6))/(33/(-6) + 5). Let u = -108 + v. Factor 2/3*d + 4/3*d**3 - 1/3 + u*d**2.
(d + 1)**2*(4*d - 1)/3
Let w(v) = 2*v**2 + 71*v - 146. Let q be w(2). Factor 1/3*f**2 - 1/2*f**3 + 0*f + 0 + 1/6*f**q.
f**2*(f - 2)*(f - 1)/6
Let b(j) be the second derivative of -j**7/357 + 2*j**6/255 + j**5/85 - 2*j**4/51 - j**3/51 + 2*j**2/17 + 119*j. Solve b(g) = 0 for g.
-1, 1, 2
Let o = -306/7 + 1843/42. Let p(h) be the third derivative of 10*h**2 + 1/240*h**6 + o*h**4 + 0*h + 1/24*h**5 + 1/3*h**3 + 0. Find z such that p(z) = 0.
-2, -1
Suppose 480*b + 497 = 1937. Suppose 5/4*k**2 + 0 - k - 1/4*k**b = 0. Calculate k.
0, 1, 4
Let m(f) be the second derivative of f**4/120 - f**3/30 - 2*f**2/5 + 416*f. Factor m(c).
(c - 4)*(c + 2)/10
Let t = 1884 + -13156/7. Factor -18/7*j**2 - t + 48/7*j + 2/7*j**3.
2*(j - 4)**2*(j - 1)/7
Let y(o) = 4*o - 14. Let d(b) = -5*b - 1. Let f be d(-1). Let w be y(f). Solve 4/7 - 6/7*i + 2/7*i**w = 0.
1, 2
Let k(m) be the third derivative of -m**6/1140 - m**5/190 + m**4/57 - 93*m**2. Factor k(f).
-2*f*(f - 1)*(f + 4)/19
Let a(l) be the second derivative of -l**5/120 - l**4/36 - l**3/36 - 63*l + 2. Factor a(x).
-x*(x + 1)**2/6
Let v be 129/(-27) + 6/(-27). Let h(a) = a**3 + 6*a**2 + 3*a - 5. Let l be h(v). Determine t so that 6*t**3 - 2*t**l + 4*t**5 - 5*t**5 - 3*t = 0.
-1, 0, 1
Let i(x) = 2*x**2 + 4*x + 2. Let z be i(-4). Suppose -4*b - 4*h = -28, h - z = -5*b - 3. Solve -3*s**5 - 9*s**3 + 1 - 1 + 9*s**4 + 3*s**b + 0*s**5 = 0 for s.
0, 1
Suppose i + 4*q - 10 = 0, 0*i = -3*i - 5*q + 16. Factor -3/2*x**i + 0 + 3/4*x + 3/4*x**3.
3*x*(x - 1)**2/4
Let i(x) be the first derivative of 15*x**6/2 + 51*x**5 - 65*x**4/2 - 220*x**3/3 + 60*x**2 + 164. Solve i(z) = 0 for z.
-6, -1, 0, 2/3
Find k such that -42 + 19*k - 10 - 16*k**2 + 5*k**2 - 49*k + 9*k**2 = 0.
-13, -2
Let x(z) = -2*z**3 - 6*z**2 + 3. Let g be x(-3). Let q(i) be the first derivative of -3/4*i**4 + 0*i - i**3 + g*i**2 - 3. Suppose q(p) = 0. What is p?
-2, 0, 1
Suppose 2*x + 0*x - 14 = 2*h, 3*h + 1 = -x. Let s = 6 - h. Solve -1 + 4*j**2 - 2*j**2 - 4*j - j**4 - 4*j**3 - s*j**2 = 0.
-1
Let t(z) be the first derivative of 2 + 5/7*z**2 + 1/14*z**4 + 4/7*z + 8/21*z**3. Factor t(f).
2*(f + 1)**2*(f + 2)/7
Let x(h) be the second derivative of 2*h**6/5 + 13*h**5/5 + 19*h**4/3 + 22*h**3/3 + 4*h**2 - 2*h + 35. Factor x(v).
4*(v + 1)**2*(v + 2)*(3*v + 1)
Let n(j) = 34*j**3 + 102*j**2 + 104*j + 20. Let m(w) = -69*w**3 - 203*w**2 - 208*w - 39. Let k(z) = -4*m(z) - 9*n(z). Factor k(h).
-2*(h + 2)*(3*h + 1)*(5*h + 6)
Let k(q) = 12*q - 56. Let o be k(5). Solve x**5 + 100*x**2 + 15 + 28*x**o + 76*x**3 + 3*x**5 + 55*x + 1 + 9*x = 0.
-2, -1
Let g = 97 + -175. Let b be (4/14)/(g/(-728)). Factor 2/3*i**2 - b*i + 8/3.
2*(i - 2)**2/3
Factor 29*j - 14*j + 33*j - 4*j**2 + 0*j**2 - 144.
-4*(j - 6)**2
Let s(t) be the first derivative of t**5/45 - t**4/3 + 10*t**3/9 + 50*t**2/9 + 19*t + 12. Let z(x) be the first derivative of s(x). Factor z(v).
4*(v - 5)**2*(v + 1)/9
Factor -3*i**2 - 18*i + 636*i**3 - 1264*i**3 + 634*i**3.
3*i*(i - 2)*(2*i + 3)
Find p such that 5*p**2 - 14 - 290*p + 278 + 21 = 0.
1, 57
Let h(f) be the first derivative of 9*f**6/5 + 36*f**5/5 + 69*f**4/10 - 44*f**3/15 - 36*f**2/5 - 16*f/5 + 188. Solve h(i) = 0 for i.
-2, -1, -2/3, -1/3, 2/3
Suppose 3985*f = 3952*f - 15 + 114. Let -2/5*l**4 - 8/5*l - 2 + 12/5*l**2 + 8/5*l**f = 0. Calculate l.
-1, 1, 5
Factor 14700 - 231*v**2 + 839*v**2 - 114*v**3 + 3*v**4 + 1097*v**2 - 202*v**2 - 7980*v.
3*(v - 14)**2*(v - 5)**2
Let c = 5 + -11. Let f be 2/c - 335/(-15). Factor -20*g**4 + f*g**4 + g**3 + 4*g - 4*g - 2*g**2 - g**5.
-g**2*(g - 2)*(g - 1)*(g + 1)
Let j be 50*((-165)/(-25) + -6). Let r be (-201)/(-360)*3 - (-6)/j. Find a such that r*a**2 - 3/4*a - 9/8*a**3 + 0 = 0.
0, 2/3, 1
Let l be ((-24)/(-100))/(9/15)*-405. Let w = -160 - l. Determine d so that 2/3*d**4 + 0*d + 0 + 2/3*d**5 + 0*d**w - 4/3*d**3 = 0.
-2, 0, 1
Suppose -n - 2 + 22 = 5*l, 3*n + 30 = 3*l. Let z(x) be the first derivative of 9/4*x**4 - 10 + 0*x + 3/2*x**2 + 3*x**3 + 3/5*x**l. Find o such that z(o) = 0.
-1, 0
Let x(l) be the third derivative of l**6/40 - l**5/4 - 17*l**4/8 + 21*l**3/2 - 157*l**2 - 2*l. Let x(r) = 0. What is r?
-3, 1, 7
Let m(p) be the third derivative of p**5/20 - 17*p**4/8 + 21*p**3 - 11*p**2 + 2*p. Determine d so that m(d) = 0.
3, 14
Let m(l) = -2*l**2 + 68*l - 35. Let b(u) = -u**2 + 34*u - 14. Let h(o) = -15*b(o) + 6*m(o). Factor h(n).
3*n*(n - 34)
Let b be 120/25*1/(-2). Let y = -2 - b. What is s in y*s**2 - 2/5*s + 0 = 0?
0, 1
Let g(v) be the first derivative of 2*v**5/5 - v**4/2 - 4*v**3 + 4*v**2 + 16*v - 192. Solve g(z) = 0 for z.
-2, -1, 2
Let s = 35878/33 + -1087. Let k(o) be the first derivative of 1/22*o**4 - s*o**3 + 9 + 4/11*o - 5/22*o**2. Factor k(a).
(a - 4)*(a + 1)*(2*a - 1)/11
Suppose 0 = 10762*l - 10668*l - 188. Let 12/7*b**l + 12/7*b + 4/7*b**3 + 4/7 = 0. Calculate b.
-1
Let c be -1 - 10 - 329/(-28). Let m(u) = u + 14. Let o be m(-11). Factor 0*q**2 + 0 - 1/2*q**o + 0*q + c*q**4.
q**3*(3*q - 2)/4
Let o = -46 - -43. Let g be 3 + 8/12 + o. Let 4/3*r - g*r**2 - 2/3 = 0. What is r?
1
Let l = 28 - 20. Let p(m) be the second derivative of 4*m**3 + l*m**2 - 1/3*m**4 - 2/5*m**6 - 1/21*m**7 + 4*m + 0 - 11/10*m**5. Factor p(w).
-2*(w - 1)*(w + 1)*(w + 2)**3
Let q(h) be the first derivative of h**8/280 - h**7/210 - h**6/45 + h**5/30 + h**4/12 + 31*h**3/3 - 25. Let k(y) be the third derivative of q(y). Factor k(m).
2*(m - 1)**2*(m + 1)*(3*m + 1)
Let r = 49 + -6. Let j = 69 - r. Factor 32 + 4*t + 6*t**3 - j*t**3 - 33*t + 88*t**2 - 83*t.
-4*(t - 2)**2*(5*t - 2)
Let v(m) be the third derivative of -m**7/147 - m**6/420 + 2*m**5/105 + 2*m**2 - 2*m. Determine g so that v(g) = 0.
-1, 0, 4/5
Let y = -18 - -21. Suppose y*a - 7 = 5. Suppose -a*b**2 - 4*b + 5*b + 4*b**2 - b**3 = 0. What is b?
-1, 0, 1
Let y(w) = -2*w**4 + 18*w**3 + 8*w**2 + 6*w - 12. Let r(s) = -2*s**4 + 17*s**3 + 9*s**2 + 5*s - 10. Let c(l) = -6*r(l) + 5*y(l). Factor c(q).
2*q**2*(q - 7)*(q + 1)
Let d = 837 + -1206. Let q = 1851/5 + d. Factor 2/5*u**2 - q*u + 4/5.
2*(u - 2)*(u - 1)/5
Let s = 3861 - 11582/3. Determine j so that -s*j**2 + 5/3 - 4/3*j = 0.
-5, 1
Suppose -z = -2*a - 6, -3 = 3*z - 5*z + a. Suppose -q + 15 = -4*p, z = -3*q - 2*q + 3*p + 24. Determine h so that 4*h - 3 + 2*h**q + 8 - 1 - 10*h = 0.
-2, 1
Let a(k) = 5*k**2 - 1. Let x = -8 + 9. Let w be a(x). Factor d**2 - 1 + 6*d**2 - 3*d - w*d**2 + 3*d**3 - 2.
3*(d - 1)*(d + 1)**2
Let z(k) = -7*k**3 - 285*k**2 - 6321*k + 21611. Let t(s) = 2*s**3 - 1. Let p(m) = 2*t(m) + z(m). Factor p(r).
-3*(r - 3)*(r + 49)**2
Determine c, given that -8 - 206*c**2 - 206*c**2 + 619*c**2 - 4*c - 205*c**2 + c**3 = 0.
-2, 2
Suppose k - 5*d - 3 = 0, 0 = -3*k - 5*d + 90 - 21. Let z = -16 + k. Factor 24*y - 3*y**3 + 2*y**4 - 5*y**3 + 10*y**z - 14*y**2 + 25 - 7.
2*(y - 3)**2*(y + 1)**2
Let i(k) = 2*k - 25. Let z be i(15). Suppose z*a = 11 + 14. Let 0*u - 9/2*u**2 + 0 - 1/6*u**a - 3/2*u**4 - 9/2*u**3 = 0. Calculate u.
-3, 0
Let m(x) = -25*x**4 + 128*x**3 - 231*x**2 + 156*x - 34. Suppose -23*w + 20*w - 9 = 0. Let s(y) = y**3 + y**2 - 1. Let o(t) = w*m(t) - 6*s(t). Factor o(f).
3*(f - 2)**2*(5*f - 3)**2
Let p be (-11)/(-2) + 21/(-42). Suppose 0*a - 3*a = -90. Factor -10*h**2 + 7*h**3 - 7*h**3 - p*h**3 + 20*h**4 - a*h**3.
5*h**2*(h - 2)*(4*h + 1)
Let x(n) be the third derivative of -13*n**8/392 + 163*n**7/735 - 13*n**6/30 + 2*n**5/21 + 2*n**4/21 + 2*n**2 - 82*n. What is l in x(l) = 0?
-2/13, 0, 1/3, 2
Let t(j) be the third derivative of 30*j**2 - 7/48*j**4 + 0*j + 1/120*j**5 + 0 + j**3. Suppose t(k) = 0. What is k?
3, 4
Let t(a) = -a**3 - 16*a**2 + 18*a + 22. Let w be t(-17). Factor g**3 - g**w - 3*g**4 + g**2 + 2*g**4 + 19*g - 19*g.
-g**2*(g - 1)*(g + 1)**2
Suppose -5*l + 2*p + 60 = 70, 2*p - 10 = 0. Find s, given that 1/3*s**2 + l*s + 0 = 0.
0
Suppose 0*c = -3*c + 9. Factor -6 + 10 + 3*r**4 - r**2 + 5*r**c - 6 - 5*r.
(r - 1)*(r + 1)**2*(3*r + 2)
Let b(s) be the first derivative of 0*s**3 + 0*s**4 + 1/15*s**6 + 0*s - 10 + 0*s**2 + 2/25*s**5. Find k, given that b(k) = 0.
-1, 0
Suppose -4*l - 5*u - 7 = 0, 0*u + 12 = -4*u. Let t(n) be the first derivative of -n**l - 4/11*n - 6/11*n**3 - 5. Determine d so that t(d) = 0.
-1, -2/9
Suppose 0 = -5*b + 5*m - 102 + 142, 4*m + 20 = 