17*v**2 - 27*v + 1. Factor r(j).
-(j + 1375)**2/6
Let v(b) = -330*b**3 - b**2 - 4*b - 3. Let x(l) = l**3 + 8*l**2 - 4*l - 33. Let f be x(-8). Let t be v(f). Factor -380/3*i + 40/3 + t*i**2 - 135*i**3.
-5*(i - 2)*(9*i - 2)**2/3
Determine x so that 192/5*x**3 + 0 + 72*x + 4/5*x**4 + 548/5*x**2 = 0.
-45, -2, -1, 0
Solve 0 + 36/5*t**3 - 51/5*t**2 + 3*t = 0.
0, 5/12, 1
Let v(m) = -2*m**2 + 48*m - 294. Let j(p) = 2*p**2 - 48*p + 296. Let t(g) = g**2 + 12*g + 17. Let r be t(-2). Let y(q) = r*j(q) - 4*v(q). Solve y(k) = 0 for k.
12
Let h be -248 - 11/(99/18). Let l be h/225*12/(-8). Factor l + 5/3*u - 5/3*u**3 - 5/3*u**2.
-5*(u - 1)*(u + 1)**2/3
Factor 27*x**3 - 3/2*x**4 + 108*x - 267/2*x**2 + 0.
-3*x*(x - 9)*(x - 8)*(x - 1)/2
Suppose 2*x - 2 = -4*t, -2*t + 3*x - 51 = -72. Let n(z) be the first derivative of 0*z**t + 0*z**5 - 23 + 1/6*z**2 + 0*z - 1/6*z**4 + 1/18*z**6. Factor n(p).
p*(p - 1)**2*(p + 1)**2/3
Let a(q) be the first derivative of -189 - 4*q - q**2 + 2*q**3 + 1/2*q**4 - 2/5*q**5. Determine o so that a(o) = 0.
-1, 1, 2
Factor 272 + 1910*r - 51*r**2 - 73*r**2 + 127*r**2 - 2510 + 325*r.
3*(r - 1)*(r + 746)
Let l(a) = 60*a**3 - 21725*a**2 + 43389*a - 21979. Let q(j) = -21*j**3 + 7242*j**2 - 14463*j + 7332. Let t(c) = -6*l(c) - 17*q(c). Factor t(s).
-3*(s - 2410)*(s - 1)**2
Let n(j) = -15*j**2 - 68*j - 8. Let i = 64 + -28. Let d(o) = i + 34 - 65 + 45*o + 10*o**2. Let q(r) = -8*d(r) - 5*n(r). Factor q(a).
-5*a*(a + 4)
Let n(c) be the first derivative of -c**5/20 + 7*c**4/8 + 5*c**3/4 + 1201. Solve n(v) = 0.
-1, 0, 15
Let q(u) be the third derivative of u**5/450 + u**4 - 185*u**3/9 - 3*u**2 + 105*u + 1. Let q(a) = 0. What is a?
-185, 5
Suppose 2/3*t**2 - 16*t - 434/3 = 0. Calculate t.
-7, 31
Let p(i) be the second derivative of -i**5/10 + 13*i**4/2 + 46*i. Factor p(t).
-2*t**2*(t - 39)
Let m be 1435/861*18/(-5) + (10 - 2). Factor -1/2*r**4 + 7/2*r**m + 5*r - 2*r**3 + 0.
-r*(r - 2)*(r + 1)*(r + 5)/2
Factor 1/6*d**3 + 441/2*d + 661/6 + 221/2*d**2.
(d + 1)**2*(d + 661)/6
Let v(f) be the first derivative of 5*f**6 + 3154*f**5/15 + 14605*f**4/6 + 27302*f**3/9 + 578*f**2/3 - 4418. Suppose v(z) = 0. What is z?
-17, -1, -2/45, 0
Let v = -578 - -631. Let s = v - 50. Let -3/2*a**5 + 0*a**3 + 0 + s*a**2 - 3*a**4 + 3/2*a = 0. What is a?
-1, 0, 1
Suppose -74 = -2*c - 24. Let k(h) = 3*h**2 - c*h + 68 - 28 - 18*h. Let b(f) = -20*f**2 + 280*f - 260. Let p(r) = -5*b(r) - 32*k(r). Factor p(x).
4*(x - 5)*(x - 1)
Factor -8639427/4 - 3/4*l**2 + 5091/2*l.
-3*(l - 1697)**2/4
Let w(n) be the first derivative of -9*n**2 + 0*n**4 + 1/180*n**5 - 16 + 0*n**3 - 1/720*n**6 + 0*n. Let q(c) be the second derivative of w(c). Factor q(j).
-j**2*(j - 2)/6
Suppose 4*v + 867*y - 872*y + 27 = 0, 5*v - 5*y + 25 = 0. What is z in -8/7 + 64/7*z - 16/7*z**3 + 32/7*z**4 - 18*z**v = 0?
-2, 1/4, 2
Let z(v) = -v**2 + 66*v - 5. Let g(m) = 330*m - 24. Let n be 61 - 56 - 8*1. Let j(f) = n*g(f) + 16*z(f). Factor j(d).
-2*(d - 4)*(8*d - 1)
Let y(z) be the first derivative of z**4/12 + 97*z**3/9 - 401*z**2/6 + 101*z + 2333. Factor y(x).
(x - 3)*(x - 1)*(x + 101)/3
Let d be (-6264)/126 - ((-4)/(-14) - 0). Let q be 4/d*(-7)/14*10. Factor 1/5*p**2 + q*p + 1/5.
(p + 1)**2/5
Suppose 3*n + 2526*j - 2523*j = 42, 7*n - 4*j - 21 = 0. Factor 1/4*i**2 + 27/4 + n*i.
(i + 1)*(i + 27)/4
Let n(k) = k**3 + 5*k**2 + 8*k + 42. Let j be n(-5). Suppose -4*v - 4*i = -6*i - j, 4*v + i = 11. Factor -4/5*d**3 + 0*d + 0 + 2/5*d**v + 2/5*d**4.
2*d**2*(d - 1)**2/5
Let w(r) be the first derivative of 3/10*r**4 - 12/25*r**5 - 243 + 0*r + 1/15*r**6 - 24/5*r**2 + 52/15*r**3. Let w(h) = 0. Calculate h.
-2, 0, 1, 3, 4
Factor 7/2*a**4 + 29/2*a**3 + 16 - 96*a**2 + 98*a.
(a - 2)**2*(a + 8)*(7*a + 1)/2
Let o(c) = -c**5 - c**4 + c**3 - 2*c**2 - c. Let m(i) = -2*i**5 + 31*i**4 + 161*i**3 + 296*i**2 + 268*i + 90. Let q(b) = -m(b) + 5*o(b). What is l in q(l) = 0?
-5, -3, -2, -1
Suppose -3*h + 102 = 9*x, -3*h = 6*x + 461 - 527. Factor 3/2*o**2 + x*o - 27/2.
3*(o - 1)*(o + 9)/2
Let v(a) be the first derivative of -1/20*a**5 - 1/2*a**3 - 1/4*a**4 - 10 + 0*a - 3*a**2. Let m(s) be the second derivative of v(s). Factor m(w).
-3*(w + 1)**2
Let z(i) be the second derivative of i**6/180 - i**5/45 + i**4/36 - 23*i**2 + 3*i. Let l(d) be the first derivative of z(d). Factor l(x).
2*x*(x - 1)**2/3
Let g(a) be the second derivative of -a**5/130 - 34*a**4/13 - 3535*a**3/13 - 20402*a**2/13 - 298*a. Suppose g(h) = 0. Calculate h.
-101, -2
Let i = 600 - -275/2. Let r = i + -737. Factor r*m**3 - 1/2*m + 0 + 0*m**2.
m*(m - 1)*(m + 1)/2
Let c(g) be the second derivative of g**5/15 - 407*g**4/3 + 331298*g**3/3 - 134838286*g**2/3 + g + 934. Factor c(d).
4*(d - 407)**3/3
Let b(z) be the second derivative of z**4/36 + 217*z**3/18 - 442*z**2/3 + 6659*z. Find m, given that b(m) = 0.
-221, 4
Let r(t) be the third derivative of -1/18*t**5 - 2*t**2 + 4*t**3 + 1/6*t**4 + 0*t + 1/360*t**6 - 6. Factor r(z).
(z - 6)**2*(z + 2)/3
Solve 68252*d**2 + 60*d - 68236*d**2 - 3*d - d**3 = 0 for d.
-3, 0, 19
Let g(v) be the first derivative of v**5/60 + 7*v**4/4 + 147*v**3/2 - 169*v**2/2 + 115. Let m(z) be the second derivative of g(z). Let m(b) = 0. Calculate b.
-21
Suppose 4 + 17 = 2*n - 3*x, 5*n + 2*x = 100. Let r be (-38)/(-12) - 3 - (-51)/n. Factor 9*y**3 - 23*y**2 - 24 - 3*y**4 + 60*y - 3*y**3 - 31*y**2 + 15*y**r.
-3*(y - 2)**3*(y - 1)
Let p(z) be the second derivative of z**5/120 - 35*z**4/6 + 4853*z**3/4 + 44521*z**2/6 - 1066*z. Factor p(o).
(o - 211)**2*(o + 2)/6
Let v be -5 - 2938*3*(-6)/16362. Let j = 1/101 - v. Factor -j*c + 2/9*c**2 + 14/9.
2*(c - 7)*(c - 1)/9
Let j be 2 + 32/(-18) - (-728)/126. Suppose j*r + 0 = 48. Factor -4*z**2 + r*z**2 + 8*z**2 - 2*z**3 - 2*z**2.
-2*z**2*(z - 5)
Let w(z) be the second derivative of 63*z + 29/15*z**3 + 2 + 1/60*z**4 + 841/10*z**2. Factor w(k).
(k + 29)**2/5
Suppose 10 = 5*x - 2*y, y - 4*y = -15. Solve 16 - 36 - 85*d - 5*d**5 - 110*d**3 - 40*d**x - 51957*d**2 + 51817*d**2 = 0 for d.
-4, -1
Let k(n) be the second derivative of n**5/20 - 55*n**4/2 - n**3/6 + 165*n**2 + 951*n + 1. What is o in k(o) = 0?
-1, 1, 330
Let p(r) be the third derivative of r**6/150 - 151*r**5/75 + 293*r**4/10 - 174*r**3 + 1963*r**2. Determine h, given that p(h) = 0.
3, 145
Let g = -18/355 - -809081/710. Let p = g + -1139. Determine v so that -p*v**2 - 81/8 + 9/2*v = 0.
9/2
Let x(j) = -j**2 + 2*j + 35. Let l be x(7). Let c = 231 + -1613/7. Factor 2/7 + 2/7*p**4 + l*p**3 - c*p**2 + 0*p.
2*(p - 1)**2*(p + 1)**2/7
Let p(q) = q**2 + 10*q + 88. Let k be p(-17). Determine r so that -174*r + k*r**2 - 204*r**2 - 20 + 2543 = 0.
29
Determine g so that 24*g**3 - 234*g**2 - 56 - 146*g - 8*g**3 - 136*g - 24*g**3 = 0.
-28, -1, -1/4
Let v(x) be the second derivative of -5/42*x**7 - 1/4*x**5 + 0*x**2 + 0 + 1/2*x**6 - 5/4*x**4 + 5/3*x**3 + 103*x. Determine s, given that v(s) = 0.
-1, 0, 1, 2
Let w(m) be the third derivative of 5/24*m**4 + 1/60*m**5 + 20*m**2 + 0 + 0*m + 1/6*m**3. Let o(t) = -t**2. Let f(j) = 21*o(j) + 3*w(j). Solve f(r) = 0 for r.
-1/6, 1
Let q(c) = 5*c**3 + 20*c**2 + 98*c + 408. Let v be q(-4). Factor -v*t**3 + 52/5*t**2 - 8/5*t + 0 + 36/5*t**4.
4*t*(t - 1)**2*(9*t - 2)/5
Let w = 67 - 33. Let t = w - 30. Let 8*m**t + 8*m**3 - 4*m**2 - 4*m**5 - 4 + 4 + 6*m**5 - 10*m - 4 = 0. What is m?
-2, -1, 1
Let g(a) be the second derivative of -a**7/7560 - a**6/360 + a**4/12 - 5*a**3/3 - 49*a. Let t(z) be the third derivative of g(z). Solve t(v) = 0.
-6, 0
Let n = 7 - 4. Suppose 3*d = -c + 19, -d = -57*c - 32 + 83. Factor -1/3*b**n - c + 5/3*b - 1/3*b**2.
-(b - 1)**2*(b + 3)/3
Solve -232 + 96*z**3 + 572*z + 379*z**3 + 16*z**4 + 33*z**3 + 1296*z**2 = 0 for z.
-29, -2, -1, 1/4
Suppose 161*t = 308*t - 588. Find m such that 0 + 0*m**3 + 4/5*m - 2/5*m**t + 6/5*m**2 = 0.
-1, 0, 2
Let u(s) be the third derivative of s**8/672 + s**7/420 - s**6/240 - s**5/120 - 8011*s**2. Factor u(w).
w**2*(w - 1)*(w + 1)**2/2
Let p(i) = i**2 + 2*i + 4. Let l be p(-1). Let r(o) be the third derivative of 0*o + 0 - 1/12*o**4 + 1/150*o**5 - 4*o**2 + 4/15*o**l. Factor r(a).
2*(a - 4)*(a - 1)/5
Suppose 4/9*t**3 + 244/9*t**2 - 3844/9 + 3596/9*t = 0. What is t?
-31, 1
Let p = -345 - -429. Factor 2*m**2 + 3*m**2 - p - 3*m**2 + 47*m - 25*m.
2*(m - 3)*(m + 14)
Suppose 5*p + 23*m + 45 = 20*m, 6*m + 90