 15. Let c(l) = 14*l**4 + 76*l**3 - 224*l**2 + 248*l + 40. Let d(r) = -3*c(r) + 8*y(r). Factor d(w).
-2*w*(w - 2)**2*(w + 10)
Suppose 0 = 5*a - 4*u - 1235 - 3107, -4*a = -u - 3478. Let c = -868 + a. Determine o so that -15/2*o + 5/2*o**c + 5 = 0.
1, 2
Let i(t) = -3*t - 1. Let u be i(-1). Suppose -143*v = -68*v. Let v*l**2 + 20 - 3*l**2 + 11*l**2 - 3*l**u - 20*l = 0. What is l?
2
Suppose -45*m = -27*m - 90. Factor -5*t**2 + 13*t**2 + m*t - 10*t**2 - 23*t.
-2*t*(t + 9)
Let m(v) be the second derivative of -v**6/105 + v**5/5 - 6*v**4/7 + 34*v**3/21 - 11*v**2/7 - 2628*v. Solve m(q) = 0 for q.
1, 11
Let q(r) = 2*r**3 + 84*r**2 + 81*r - 39. Let w be q(-41). Factor 24 - 4*z**2 - 18*z**4 + 15*z**4 - 12*z**3 + 7*z**4 - 8*z**w + 28*z.
4*(z - 3)*(z - 2)*(z + 1)**2
Let v be 14/(-20)*(-3)/(75/25). Factor -1/5*i**3 - 1/5*i**4 + 4/5*i**2 + 1/10*i**5 - v*i + 1/5.
(i - 1)**4*(i + 2)/10
Let o(l) = 163*l + 1144. Let w be o(-7). Let a(m) be the first derivative of -4*m - 4/3*m**w + 4*m**2 + 16. Solve a(c) = 0.
1
Let g(w) = -2*w**3 - w**2 - 1. Let o(m) = m**3 + 63*m**2 - 225*m + 267. Let t(a) = 3. Let q(r) = o(r) + 2*t(r). Let c(u) = 3*g(u) + q(u). Factor c(z).
-5*(z - 6)*(z - 3)**2
Let q(m) be the third derivative of 1/20*m**5 + 1/4*m**4 + 1/112*m**8 - 71*m**2 + 0*m**3 + 0 - 3/40*m**6 + 0*m - 1/70*m**7. Determine r, given that q(r) = 0.
-1, 0, 1, 2
Let q(u) = 11*u**2 + 192*u - 2430. Let w(l) = -3*l**2 - 63*l + 810. Let d(o) = 2*q(o) + 7*w(o). Suppose d(z) = 0. What is z?
27, 30
Let v(o) = 33*o + 24. Let x be v(-1). Let p be (-39)/(-18) - x - 6/9. Find i such that -p + 3/2*i**3 - 15/2*i**2 - 39/2*i = 0.
-1, 7
Let l be 20*1 - (-410)/(-41). Suppose -3*h + 6*f - l*f = -13, f + 5 = 2*h. What is i in 6/19*i**2 + 0*i + 2/19*i**h - 8/19 = 0?
-2, 1
Suppose 158*z**4 + 49*z**5 - 128*z**4 - 44*z**5 - 60*z + 45*z**3 - 20*z**2 = 0. Calculate z.
-3, -2, 0, 1
Let t(p) = 3*p + 22. Let v be t(-6). Determine z, given that -13*z**3 + 6*z**2 + 21*z - 5*z**3 - 38*z**4 - 35*z**v + 8 + 58*z**4 + 1 - 3*z**5 = 0.
-3, -1, 1
Let z be -3 + 4/(8/18). Let h(u) = -u**3 - u - 1. Let t(i) = -9*i**3 - 23*i**2 + 29*i - 15. Let x(v) = z*h(v) - t(v). Solve x(w) = 0 for w.
-9, 1/3, 1
Let a(m) be the first derivative of -2*m**3/15 + 2298*m**2/5 - 2640402*m/5 - 5806. Solve a(b) = 0 for b.
1149
Let l(c) be the second derivative of 9*c - 1/10*c**5 + c**4 - 3*c**3 + 0 + 0*c**2. Factor l(j).
-2*j*(j - 3)**2
Let f(g) be the second derivative of -7/3*g**4 + 44/3*g**3 + 1/10*g**5 + 2*g + 6 - 40*g**2. Factor f(o).
2*(o - 10)*(o - 2)**2
Let t(o) = 25*o - 82. Let z be t(5). Let x = z + -40. Factor -1/3*l**x - l**2 + 0 - 2/3*l.
-l*(l + 1)*(l + 2)/3
Let h(x) be the first derivative of 5*x**3/6 + 215*x**2/4 + 105*x - 951. Factor h(a).
5*(a + 1)*(a + 42)/2
Let w = -414986/19 + 21842. Suppose 18/19*a**2 + 0 + 2/19*a**4 + 0*a - w*a**3 = 0. Calculate a.
0, 3
Let u(s) = 6*s**2 - 4*s + 2. Let w be u(1). Let -56*c**2 + 57*c**2 - w*c - 14 + 10*c + 7*c = 0. What is c?
-14, 1
Let a(c) be the first derivative of 124 - 15/2*c**2 + 18*c - c**3. Solve a(l) = 0.
-6, 1
Factor 241*h**2 + 39 - 46*h**2 + 393*h + 389 - h**3 - 231.
-(h - 197)*(h + 1)**2
Let p(i) = i**2 + 54*i + 658. Let v be p(-19). Let n be (-70)/v - 222/24. Solve -n*u**2 - 9/4 + 3*u = 0 for u.
1, 3
Solve -1113/2*z**4 - 114 + 3405/2*z**3 + 27/2*z**5 - 3807/2*z**2 + 858*z = 0.
2/9, 1, 38
Let d(n) be the third derivative of -n**6/270 + 80*n**5/9 - 80000*n**4/9 + 128000000*n**3/27 - 5*n**2. Factor d(j).
-4*(j - 400)**3/9
Suppose 4*n + 2*f - 5 + 3 = 0, -2*n + 2 = 2*f. What is w in -22*w + n*w + w**2 - 3*w**2 + 0*w = 0?
-11, 0
Factor 14133*b - 13935*b - 61 - 15*b**2 - 155.
-3*(b - 12)*(5*b - 6)
Let r(m) = 237*m**2 + 241*m + 109. Let g(w) = 119*w**2 + 121*w + 44. Let c(d) = -5*g(d) + 2*r(d). Solve c(b) = 0 for b.
-1, -2/121
Factor 23328 - 6912*n + 368*n**2 + 2/9*n**4 + 64/3*n**3.
2*(n - 6)**2*(n + 54)**2/9
Let d(c) be the third derivative of 2*c**7/315 - 31*c**6/90 - c**5/15 + 95*c**4/18 - 124*c**3/9 - 126*c**2 + 6. Suppose d(o) = 0. Calculate o.
-2, 1, 31
Let v(j) = -8*j**3 + 73*j**2 - 286*j + 248. Let p(q) = -2*q**3 + q**2 - 10*q. Let x(m) = -6*p(m) + 2*v(m). Factor x(d).
-4*(d - 31)*(d - 2)**2
Factor -3*t**5 - 3729*t**4 + 4044*t**4 - 1383840*t + 203205*t**2 + 4254*t**3 + 3217428 - 16359*t**3.
-3*(t - 31)**3*(t - 6)**2
Factor 1/4*d**5 + 2*d + 0 - 2*d**4 - 11/2*d**2 + 21/4*d**3.
d*(d - 4)*(d - 2)*(d - 1)**2/4
Let z(f) be the first derivative of -f**6/2 + 3*f**5/5 + 57*f**4/4 - 25*f**3 - 99*f**2 + 216*f + 178. Solve z(l) = 0 for l.
-4, -2, 1, 3
Let r(f) be the third derivative of 238*f**2 + 0*f + 11/27*f**4 + 4/45*f**6 + 0 + 0*f**3 - 2/945*f**7 - 1/3*f**5. Factor r(o).
-4*o*(o - 22)*(o - 1)**2/9
Factor -40/3*f**3 + 0 - 1/3*f**4 - 14*f + 83/3*f**2.
-f*(f - 1)**2*(f + 42)/3
Let y = 61 + -54. Suppose 2 = -6*n + y*n. Determine c so that -23*c - 7*c**n + 12 + c**4 - 24 + 3*c + 2*c**3 = 0.
-2, -1, 3
Let m(l) = l**3 + 5*l**2 + 5*l + 6. Let p be m(-5). Let t be p/(-7) - (-2)/7. Solve 0*v**2 - 5*v**2 - 2*v**4 - t*v**2 + 9*v**3 - v**3 = 0.
0, 2
Let r = -9 - -7. Let b(f) = -4*f + 14. Let u be b(r). Determine z so that -18*z**2 - 7*z**2 + 20*z - 25*z**3 - 8 - u + 5*z**5 + 50 + 5*z**4 = 0.
-2, -1, 1, 2
Let h(c) be the third derivative of c**6/360 + 259*c**5/180 + 5633*c**4/24 + 1849*c**3/2 - 5*c**2 + 28*c. Factor h(j).
(j + 1)*(j + 129)**2/3
Let r(x) be the third derivative of 42*x**2 + 4/15*x**5 + 0*x + 1/2*x**4 + 1/30*x**6 + 0 + 0*x**3. Factor r(m).
4*m*(m + 1)*(m + 3)
Let w = 55 + -57. Let j be w/(-5) + -2*20/(-25). Factor j*x + 5*x**5 - 10*x**3 - 3*x**2 + 5 + 2*x**2 + 5*x**4 - 9*x**2 + 3*x.
5*(x - 1)**2*(x + 1)**3
Let k = -394/265 - -18658/1855. Find g, given that 2/7*g**3 + k*g**2 + 2000/7 + 600/7*g = 0.
-10
Let d(t) be the third derivative of -2/3*t**4 + 1/90*t**6 + 0*t + 0*t**3 + t**2 + 60 + 1/45*t**5. What is y in d(y) = 0?
-4, 0, 3
Let p = -4582 + 4584. Suppose 0 = -3*o + 86 - 32. Factor -6*h - o - 1/2*h**p.
-(h + 6)**2/2
Let m(b) be the third derivative of -b**6/660 + 11*b**5/10 + 122*b**4/11 + 1468*b**3/33 - 637*b**2 - 2*b + 4. Suppose m(s) = 0. What is s?
-2, 367
Let k(t) = -8*t. Let y(m) = -14*m - 198. Let u(a) = 4*k(a) - y(a). Let z be u(11). Factor 0 + s**2 + 1/3*s**3 + z*s.
s**2*(s + 3)/3
Let p(l) = -5*l**2 - 203*l - 2056. Let m be p(-21). Factor 7/6*g + 7/6*g**m + 1/3*g**3 + 1/3.
(g + 1)*(g + 2)*(2*g + 1)/6
Let m(s) be the third derivative of -s**5/15 - 20*s**4/3 - 96*s**3 - s**2 + 1098. Solve m(r) = 0 for r.
-36, -4
Let b(t) = -t**2 + 11*t - 12. Let s be b(1). Let r(w) = -w**3 - 3*w**2 - 8*w - 12. Let q be r(s). Factor q*v + 0 + 1/5*v**2.
v**2/5
Let a(y) = 70*y**2 - 10410*y - 2978. Let g(q) = 91*q**2 - 10411*q - 2979. Let t(w) = 3*a(w) - 2*g(w). Let t(s) = 0. What is s?
-2/7, 372
Let f(p) be the first derivative of 2*p**3/9 + 69*p**2 + 820*p/3 + 11165. Factor f(s).
2*(s + 2)*(s + 205)/3
Let d be (18/120*5)/((-55)/(-40) - 1). Determine h, given that 10/7 + 12/7*h + 2/7*h**d = 0.
-5, -1
Let q(s) = s**3 + s**2. Let j(t) = -21*t**3. Suppose 123 = 3*b + 3*a + 21, -176 = -5*b - 2*a. Let m = 35 - b. Let n(z) = m*j(z) - 6*q(z). Factor n(r).
3*r**2*(5*r - 2)
Suppose 0 = -5*u + 5*o + 795, 5*u - 755 = o - 6*o. Let t = 155 - u. Determine c, given that 1/9*c + t - 1/9*c**2 = 0.
0, 1
Let k(y) be the first derivative of 16*y - 100 - 5*y**3 - 2*y**4 - 1/5*y**5 + 4*y**2. Factor k(t).
-(t - 1)*(t + 1)*(t + 4)**2
Let i = 1150 - 176. Let r = i - 971. Factor -12/11*a**2 + 12/11 - 6/11*a**r + 6/11*a.
-6*(a - 1)*(a + 1)*(a + 2)/11
Let q(h) = 15*h**2 - 5500*h + 756235. Let j(b) = -23*b**2 + 8250*b - 1134351. Let a(d) = 5*j(d) + 8*q(d). Factor a(m).
5*(m - 275)**2
Let j(p) be the second derivative of -p**4/8 - 22*p**3/3 + 15*p**2 + 4445*p. Factor j(o).
-(o + 30)*(3*o - 2)/2
Let o(u) = 5*u**3 - 45*u**2 + 217*u + 210. Let l(c) = -c**3 + c**2 - 17*c. Let j(v) = 6*l(v) + 2*o(v). Factor j(g).
4*(g - 15)*(g - 7)*(g + 1)
Let d = 92353 + -92349. Suppose -3/4*g + 0 - 3/4*g**d - 9/4*g**2 - 9/4*g**3 = 0. What is g?
-1, 0
Determine o, given that -88*o**3 - 18*o**5 + 43*o**4 + 9*o**4 + 54*o**5 - 22*o**5 - 18*o**5 = 0.
0, 2, 11
Let p(d) be the first derivative of d**4/48 + d**3/24 - 3*d**2/2 - 72*d - 13. Let y(u) be the first derivative of p(u). Let y(i) = 0. Calculate i.
-4, 3
Let j(t) be the third der