**2. Solve d(c) = 0.
0
Factor -5*x**2 - 167*x - 194*x - 530*x + 11*x - 4275.
-5*(x + 5)*(x + 171)
Factor 18*m + 1610 + 2*m + 38*m - 34*m - 2*m**2.
-2*(m - 35)*(m + 23)
Let w(t) be the first derivative of -t**5/160 + 5*t**4/32 - 25*t**3/16 + 21*t**2 + 7. Let c(v) be the second derivative of w(v). Factor c(m).
-3*(m - 5)**2/8
Let f(q) = -3*q**2 + q - 1. Let m(b) = 49*b**2 + 7*b - 92. Let i(x) = -80*f(x) - 5*m(x). Factor i(v).
-5*(v - 4)*(v + 27)
Let c = 31282/55 - 6252/11. Let m(j) be the first derivative of -2/25*j**5 - 21 + 4/5*j + c*j**3 - 1/10*j**4 + j**2. Factor m(r).
-2*(r - 2)*(r + 1)**3/5
Let b(o) = -16*o**2 - 37664*o - 8060432. Let h(a) = 3*a**2 + 6848*a + 1465532. Let z(x) = 5*b(x) + 28*h(x). Factor z(k).
4*(k + 428)**2
Let b(a) be the second derivative of -a**5/240 + 7*a**4/72 - 17*a**3/24 + 9*a**2/4 - 2*a - 1119. Find o, given that b(o) = 0.
2, 3, 9
Let p(y) be the third derivative of y**6/15 + 25*y**5/2 - 47*y**4/6 - 942*y**2. Factor p(c).
2*c*(c + 94)*(4*c - 1)
Let n(q) = -36*q - 317. Let o(l) = -17*l - 158. Let p(h) = 6*n(h) - 13*o(h). Let d be p(-30). Find z, given that 2/19*z**d + 28/19*z + 98/19 = 0.
-7
Let y(j) = 15*j**3 + 47*j**2 + 71*j - 100. Let t(d) = -8*d**3 - 24*d**2 - 36*d + 50. Let n(f) = -11*t(f) - 6*y(f). Solve n(p) = 0.
-5, 1
Suppose -2*j = 3*j + 3*v - 198, 0 = 3*v + 12. Factor -4 - 78*x - 5*x**2 + 44*x + x**3 + j*x.
(x - 2)**2*(x - 1)
Let n(s) be the second derivative of -s**6/6 - 2*s**5 - 95*s**4/12 - 10*s**3 - 8*s - 2. Let n(d) = 0. What is d?
-4, -3, -1, 0
Let o(q) be the third derivative of q**5/120 - 367*q**4/48 - 92*q**3/3 + 2*q**2 + 663. Find f, given that o(f) = 0.
-1, 368
Suppose 0 = -2*a + 4*v - 392, -4*a + a + 3*v = 576. Let i = a - -190. Factor -32/17*o**5 + 144/17*o**4 + 230/17*o**i - 258/17*o**3 + 18/17 - 6*o.
-2*(o - 1)**3*(4*o - 3)**2/17
Suppose 0 = -2*f + 5 + 3. Let o = -227509 + 227512. Factor -f - 9*q**2 - 1/2*q**4 - 10*q - 7/2*q**o.
-(q + 1)*(q + 2)**3/2
Let z be ((-4947)/18)/(-17) - 3/(2 + (-35)/21). Factor 1/6*y**4 + 6 + 23/2*y + z*y**2 + 11/6*y**3.
(y + 1)*(y + 3)**2*(y + 4)/6
Let c = -1908 + 1910. Let b be -7 + (685/55 - 4). Factor -2/11*q**4 - b*q + 0*q**3 + 12/11*q**c + 6/11.
-2*(q - 1)**3*(q + 3)/11
Suppose 11 = -3*i + 17. Let -7 + 9*g**3 + 7*g**i + g + 18*g**3 - 28*g**3 = 0. What is g?
-1, 1, 7
Let m = -255 - -309. Let v be m/20 + 198/(-165). Find n such that -3/2*n + 3/8*n**3 + 3/8*n**2 - v = 0.
-2, -1, 2
What is v in 0 + 27/5*v**3 + 0*v + 12/5*v**2 + 3/5*v**5 + 18/5*v**4 = 0?
-4, -1, 0
Let f(k) be the first derivative of -k**4/48 + 5*k**3/24 + 3*k**2/4 - 101*k - 73. Let i(a) be the first derivative of f(a). Suppose i(p) = 0. What is p?
-1, 6
Let s be (-1)/(20/(-12684)) - 4/5. Let x = s + -631. What is a in -8*a**2 + 2/5*a**5 + 4/5*a**4 - 12/5 - x*a**3 - 38/5*a = 0?
-2, -1, 3
Factor 3/2*l**5 + 33*l**3 + 12*l**4 + 6 + 51/2*l + 42*l**2.
3*(l + 1)**4*(l + 4)/2
Let z(r) = r**2 - 16761*r - 100582. Let p be z(-6). Find q, given that 5*q**4 - 35/2*q + 5*q**2 - 5/2*q**5 - 10 + p*q**3 = 0.
-1, 1, 4
Let u(a) be the third derivative of -2*a**7/245 - 31*a**6/210 - 73*a**5/105 - a**4/2 - 5*a**2 - 339*a + 1. Find j such that u(j) = 0.
-7, -3, -1/3, 0
Let a(i) be the first derivative of -1/6*i**3 + 0*i + 1/12*i**4 + 5*i**2 - 1/60*i**5 + 15. Let f(p) be the second derivative of a(p). Factor f(r).
-(r - 1)**2
Let o(t) be the second derivative of 6 - 9/4*t**4 - 7/20*t**5 + 1/30*t**6 - 3*t - 29/6*t**3 - 5*t**2. Factor o(i).
(i - 10)*(i + 1)**3
Let q(t) be the third derivative of t**5/15 + 83*t**4/6 + 644*t**3 + 47*t**2 + 28. Find b, given that q(b) = 0.
-69, -14
Suppose -45*h - 51*h = 0. Let z(r) be the first derivative of 1/30*r**6 + 0*r**3 + h*r**2 + 1/25*r**5 + 11 + 0*r + 0*r**4. Factor z(t).
t**4*(t + 1)/5
Suppose 1469/3*b**4 - 538754/3*b**3 - 1/3*b**5 + 180075 + 179585*b - 541694/3*b**2 = 0. What is b?
-1, 1, 735
Solve -11008*u**2 + 9050*u**2 + 2705*u**3 - 746364*u - 77336*u**2 + u**5 + 5921*u**3 - 234*u**4 - 1102736 + u**5 = 0.
-4, -2, 41
Let i(h) = 10*h**2 - 112*h + 374. Let d(f) = -3*f**2 + 37*f - 119. Let r(q) = -16*d(q) - 5*i(q). Factor r(g).
-2*(g - 1)*(g + 17)
Let n(z) = z**2 + z. Let h(g) = -43*g**2 - 17*g**3 - 7*g + 14*g**3 + 51*g**2. Let a(d) = h(d) + n(d). Factor a(p).
-3*p*(p - 2)*(p - 1)
Find l such that -275/4*l**2 + 0 + 1/4*l**3 + 137/2*l = 0.
0, 1, 274
Suppose 3*x + 24 = 6. Let p be 2/8*(2 - x). Let 0*r - 2/7*r**3 + 0 + 4/7*r**p = 0. What is r?
0, 2
Let z be 840/2100*(-1)/(-4)*2100/9. Factor 54 + 96*m - z*m**2 + 4/3*m**3.
2*(m - 9)**2*(2*m + 1)/3
Let i(w) be the third derivative of -w**7/70 - w**6/20 + 3*w**5/20 + w**4/2 - 2*w**3 + 6*w**2 - 59*w. Factor i(q).
-3*(q - 1)**2*(q + 2)**2
Determine m so that -4/3*m**2 - 1036 - 472/3*m = 0.
-111, -7
Suppose 25 = 9*g + 7. Factor 200*a + 21*a**2 + 240 + 0*a**2 + 0*a**2 + 34*a**g + 5*a**3.
5*(a + 3)*(a + 4)**2
Let p(d) be the first derivative of d**6/9 - 19*d**5/5 - 91*d**4/12 + 3*d**3 + 89*d**2/6 + 10*d + 1710. Suppose p(x) = 0. What is x?
-1, -1/2, 1, 30
Solve -3332/3 - 32*r**2 - 350*r - 2/3*r**3 = 0.
-34, -7
Suppose 0 = -4*w + 3*k + 21, 5*w - 15 - 6 = 2*k. Find j such that -48*j + 46*j**2 - 407*j**w - 72 + 18*j**4 + 865*j**3 + 2*j**5 - 404*j**3 = 0.
-3, -2, 1
Let x = 31/869 - -745/3476. Factor 5/2*l**2 + 2 + 17/4*l + x*l**3.
(l + 1)**2*(l + 8)/4
Let o(c) = 2*c**3 - 189*c**2 - 5973*c + 55. Let k be o(-25). Factor -4/11*b**3 + 0 - 2/11*b**k - 6/11*b**4 + 0*b + 0*b**2.
-2*b**3*(b + 1)*(b + 2)/11
Let m be (-52)/(-6) + 24552/(-3069). Factor 0 - m*r + 13*r**2.
r*(39*r - 2)/3
Let t be 642/(-1177) + 431/770. Let r(d) be the second derivative of 0*d**3 - t*d**5 - d - 4/7*d**2 + 1/14*d**4 + 0. Determine f, given that r(f) = 0.
-1, 2
Let j(w) be the third derivative of 0 - 19/36*w**4 + 0*w**3 - 36*w**2 - w - 1/90*w**5. Factor j(g).
-2*g*(g + 19)/3
Suppose -4*d = 2*l + 12, -2*l + 3*l = -5*d - 15. Suppose t + l*q - q - 32 = 0, 0 = 2*t - q - 66. Factor -t*b + 40*b - 3*b**2 + 5*b**2.
2*b*(b + 3)
Solve 71/2*v - 134 - 1/2*v**2 = 0.
4, 67
Let f(i) be the first derivative of i**4/22 - 4*i**3 + 480*i**2/11 - 1856*i/11 - 6207. Factor f(z).
2*(z - 58)*(z - 4)**2/11
Suppose -1385 = 16*q - 8121. Let y = -417 + q. What is c in -1/2*c**y + 1/2*c - 3/2*c**2 + 0 + 3/2*c**3 = 0?
0, 1
Suppose 0 = -4*d - 8. Let k be -4 + 8830/(-5)*d. Factor 12 - k*h + 3533*h - 2 - 5*h**2.
-5*(h - 2)*(h + 1)
Let 8*j**3 + 40*j - 29*j**3 - 105*j**2 - j**3 + 201 - 18*j**3 + 5*j**4 - 101 = 0. Calculate j.
-2, -1, 1, 10
Let o(v) be the first derivative of -7*v**5/10 - 8*v**4 + 145*v**3/6 + 11*v**2/2 - 10. Find m, given that o(m) = 0.
-11, -1/7, 0, 2
Let v(i) be the second derivative of -25*i**4/18 + 490*i**3/9 - 2401*i**2/3 - 1197*i. Factor v(n).
-2*(5*n - 49)**2/3
Let j be ((-6)/18)/((-3)/108). Let g be (6 - j) + 3 + 6. Find m such that 0 + 2/5*m**2 + 4/15*m + 2/15*m**g = 0.
-2, -1, 0
Suppose -x + 12*n - 14*n = -230, n = -2*x + 463. Let i be 46 + -41 + x/(-22) - -7. Solve -8/11*c + 2/11*c**3 + i - 4/11*c**2 = 0.
-2, 2
Let i(k) be the third derivative of k**7/1260 + k**6/120 - k**5/15 - 3*k**4/8 + 2*k**2 + 14*k. Let a(x) be the second derivative of i(x). Factor a(c).
2*(c - 1)*(c + 4)
Let i(m) be the third derivative of -m**7/105 - 3*m**6/20 - 4*m**5/15 + 5*m**2 + 29*m. Factor i(j).
-2*j**2*(j + 1)*(j + 8)
Factor -28013 - 1830964*w**3 + 630*w**2 + 1830962*w**3 - 123673 - 48654*w.
-2*(w - 159)**2*(w + 3)
Let t(w) be the second derivative of 3*w**5/40 + 179*w**4/24 + 76*w**3 - 81*w**2 + 1791*w + 2. Factor t(b).
(b + 6)*(b + 54)*(3*b - 1)/2
Let v(n) be the third derivative of n**8/168 + 9*n**7/35 + 44*n**6/15 - 515*n**2. What is p in v(p) = 0?
-16, -11, 0
Let p(v) be the second derivative of 1/42*v**7 + 19/2*v**5 + 5/6*v**6 - 69*v + 729/2*v**2 + 2 - 405/2*v**3 + 45/2*v**4. Let p(a) = 0. What is a?
-9, 1
Let h(u) = -u**3 + 2*u**2 + 3. Let l be h(3). Let b be 12/(-180) - l/15. Find p, given that -2/3 - 1/3*p**3 + b*p + 2/3*p**2 = 0.
-1, 1, 2
Let u = -5128775/7 - -732683. Let u*c**5 + 24/7*c**2 + 0 + 0*c + 12/7*c**4 - 6*c**3 = 0. What is c?
-4, 0, 1
Suppose 20/3*m**2 + 2/3*m**3 - 2/3*m**4 + 16/3*m + 0 = 0. What is m?
-2, -1, 0, 4
Let c(f) = -9*f**2 + 267*f - 2426. Let i(a) = 35*a**2 - 1080*a + 9705. Let s(r) = -15*c(r) - 4*i(r). Find p such that s(p) = 0.
9, 54
Let l(y) = y**3 + y**2 - y - 3. L