- 23)**2/7
Let g(x) = -37839*x**2 - 864*x - 65. Let v(m) = m**2 + m - 10. Let u(p) = -g(p) + 6*v(p). Factor u(t).
5*(87*t + 1)**2
Let i(o) = -o**3 - 3 - 4*o**2 - 3*o + 5*o - 8. Let x be i(-5). Factor 50*k**5 - 110*k**5 + 61*k**5 - 5*k**3 - x*k**4.
k**3*(k - 5)*(k + 1)
Let c(h) = 260*h - 8056. Let y be c(31). Let f = 91/570 + -1/38. Factor 0*b + 2/5*b**3 + 0 + 2/15*b**5 + f*b**2 + 2/5*b**y.
2*b**2*(b + 1)**3/15
Factor 218/11*a - 8 - 127/11*a**2 - 3/11*a**3.
-(a - 1)*(a + 44)*(3*a - 2)/11
Let u(d) be the third derivative of d**6/420 - 187*d**5/210 - 14*d**2 - 42*d + 3. Determine n, given that u(n) = 0.
0, 187
Factor -26364 + 25266*q**2 + 4*q**4 + 1954*q - 23706*q**2 + 750*q + 0*q**4 + 144*q**3.
4*(q - 3)*(q + 13)**3
Let w(d) be the second derivative of 2/15*d**4 + 35*d - 2/5*d**2 - 2/75*d**6 + 3/50*d**5 + 0 - 1/5*d**3. Suppose w(p) = 0. Calculate p.
-1, -1/2, 1, 2
Let h = -68/133 - -106/133. Factor 0*d - 4/7*d**2 + h*d**4 - 2/7*d**3 + 0.
2*d**2*(d - 2)*(d + 1)/7
Factor 0 + 2024/5*x**3 - 3584/5*x**4 + 98/5*x**5 - 288/5*x**2 + 0*x.
2*x**2*(x - 36)*(7*x - 2)**2/5
Factor 78*m + 73*m + 5*m**2 - 9*m**2 + 92*m + 109*m.
-4*m*(m - 88)
Let v be 312/(-4680) + ((-124)/(-90))/(6/9). Determine r, given that -40/17*r**v + 0 - 18/17*r**4 + 32/17*r - 64/17*r**3 = 0.
-2, 0, 4/9
Let r(w) be the second derivative of 0*w**2 + 248*w + 0 + 2/75*w**6 - 4/25*w**5 + 1/3*w**4 - 4/15*w**3. Suppose r(q) = 0. What is q?
0, 1, 2
Let v(t) be the third derivative of t**5/60 - t**4/24 - 2*t**2 + 12*t. Let s(a) = -18*a**2. Let k(u) = s(u) + 3*v(u). Factor k(w).
-3*w*(5*w + 1)
Find m such that -1251/2*m + 513 + 519/2*m**2 + 3/2*m**4 - 81/2*m**3 = 0.
2, 3, 19
Suppose 8 = 4*y, 0 = -27*w + 28*w - y - 20. Solve -2*q**5 - 30*q**3 + 301*q + q**5 - 11*q**4 + w*q**2 - 206*q - 75 = 0.
-5, -3, 1
Let w = -521/44 + 11381/924. Find c, given that -w*c**2 - 2/3*c**3 + 2/3*c - 2/21*c**4 + 4/7 = 0.
-6, -1, 1
Let f(j) = -j**2 - 8*j + 16. Let t be f(-8). Let c = 136 - t. Determine b, given that 80*b + 16 + 110*b**2 + 36*b**4 - 17*b**2 + 55*b**2 + c*b**3 = 0.
-1, -2/3
Suppose -5*r + 12 = 2*x, -116*r + 2*x - 10 = -120*r. Let 312/5*p**r + 64/5*p + 4/5 + 448/5*p**3 + 196/5*p**4 = 0. What is p?
-1, -1/7
Let s be -7 - -16 - 192/(-160)*-5. Let -8/5*z + 0 + 4*z**s - 12/5*z**2 = 0. Calculate z.
-2/5, 0, 1
Let u(z) = -z**2 + 2*z - 1. Let j(i) = -8 - 5*i**2 + 0*i**2 + 10 + 0*i**2 - 3 - 10*i. Let v(n) = -j(n) + u(n). Suppose v(q) = 0. Calculate q.
-3, 0
Let w(c) be the third derivative of -c**8/1848 - 4*c**7/385 - 43*c**6/660 - 2*c**5/11 - 7*c**4/33 + 2701*c**2. Let w(n) = 0. What is n?
-7, -2, -1, 0
Suppose -3*j = -5*j + 5*u - 4473, 4*j - 3*u + 8967 = 0. Let h = j - -2246. Factor -h*g**2 - 6*g + 10/3*g**3 + 0 - 2/3*g**4.
-2*g*(g - 3)**2*(g + 1)/3
Let q = -611492 + 611495. Factor 0 + 4/7*j**5 - 8*j**4 + 256/7*j + 132/7*j**q + 64*j**2.
4*j*(j - 8)**2*(j + 1)**2/7
Suppose 92 + 1108 = 12*d. Determine p so that 85*p**3 + 40 - 11*p**2 - 81*p**2 + 80*p**4 - 78*p**2 - d*p - 35*p**5 = 0.
-1, 2/7, 2
Let d(a) = -a**3 + 13*a**2 - 36*a + 2. Let x be d(9). Factor 20*y + 2*y**x + y**2 + 21*y - 6*y - 8*y.
3*y*(y + 9)
Let u(x) be the second derivative of -4/135*x**6 + 37/90*x**5 - 16/9*x**2 + 0 + 88/27*x**3 - 35/18*x**4 - 75*x. What is k in u(k) = 0?
1/4, 1, 4
Let r = 598 + -603. Let b(z) = -3*z**3 - 10*z**2 + 17*z + 10. Let m(c) = -2*c**3 - 10*c**2 + 16*c + 8. Let f(q) = r*m(q) + 4*b(q). Factor f(k).
-2*k*(k - 3)*(k - 2)
Let c(m) be the first derivative of 11/5*m**2 + 121/5*m + 1/15*m**3 + 47. Determine j so that c(j) = 0.
-11
Suppose -8698*k - 69 = -8721*k. What is v in 0*v**3 + 7/3*v**2 - k*v**4 + 0 - 2/3*v = 0?
-1, 0, 1/3, 2/3
Let t(q) = 3*q + 5. Let v be t(-3). Let p(m) = -113*m + 24. Let j be p(v). Suppose 18*h**2 + 10*h**3 + j + 2*h**4 + 9*h - 472 + 5*h = 0. Calculate h.
-2, -1
Let b(n) be the second derivative of n**6/1620 + n**5/54 + 7*n**4/36 - 23*n**3/3 - n**2 - 11*n + 8. Let t(q) be the second derivative of b(q). Factor t(f).
2*(f + 3)*(f + 7)/9
Let f(b) = -3*b**3 - b - 1. Let w(o) = -10*o**4 + 48*o**3 + 114*o**2 - 56*o - 82. Let z(k) = 20*f(k) - 2*w(k). Factor z(c).
4*(c - 9)*(c + 1)**2*(5*c - 4)
Factor -4334*p + 39*p**2 - 36*p**2 + 4196*p.
3*p*(p - 46)
Let c(i) = 2*i**5 + 36*i**4 + 228*i**3 + 354*i**2 - 216*i - 460. Let r(j) = -j**3 + 3*j**2 + 2. Let w(s) = c(s) + 14*r(s). Let w(g) = 0. Calculate g.
-6, -1, 1
Let z = 308 - 303. Suppose 3*f - z*t = 0, -2*f - 47*t + 46*t + 13 = 0. Factor 0 + 0*u**2 + 0*u - 8/7*u**4 + 0*u**3 - 12/7*u**f.
-4*u**4*(3*u + 2)/7
Let m(f) be the first derivative of -f**5/120 - 7*f**4/24 - 49*f**3/12 + 65*f**2/2 - 57. Let g(h) be the second derivative of m(h). Factor g(b).
-(b + 7)**2/2
Suppose 6625/2*s**2 + 330 - 49/2*s**4 - 1288*s**3 + 2206*s = 0. What is s?
-55, -2/7, 3
Suppose 4*w = 4 + 1 + 11. Let m(l) be the second derivative of 7*l - 2/5*l**2 + 0 + 1/15*l**w + 1/25*l**5 - 2/15*l**3. Determine a, given that m(a) = 0.
-1, 1
Let f(v) = 4*v**2 - 1262*v + 1243. Let k(h) = 7*h**2 - 1895*h + 1864. Let u(w) = -8*f(w) + 5*k(w). Find d, given that u(d) = 0.
-208, 1
Let b(z) be the second derivative of -1/4*z**4 + 0 + 3*z**3 - 27/2*z**2 - 255*z. Solve b(f) = 0 for f.
3
Suppose -2*a = 4*g + 16, -369*g + 374*g + 41 = -4*a. Let 2/17*j**g + 0 + 2/17*j + 4/17*j**2 = 0. Calculate j.
-1, 0
Let b be (468/(-169))/((-12882)/11752). Factor -2/19*r**3 - b*r - 22/19*r**2 + 72/19.
-2*(r - 1)*(r + 6)**2/19
Let l(v) be the third derivative of v**5/20 - 2*v**4 + 53*v**3/2 - v**2. Let z(i) = 6*i**2 - 97*i + 320. Let c(n) = -13*l(n) + 6*z(n). Solve c(k) = 0 for k.
7
Let d(y) be the third derivative of y**5/30 + 33*y**4 - 796*y**3/3 + 10*y**2 - 6*y - 2. Factor d(h).
2*(h - 2)*(h + 398)
Let n be 4/14 + -4 + 268/(-7). Let c = n + 62. Factor -c*t**3 + 8*t**2 + 14*t**2 - 8*t**2 + 18*t**2 + 4*t**4 - 16*t.
4*t*(t - 2)**2*(t - 1)
Suppose 66 = 5*l - 4*z, z - 34 = -3*l + 2*z. Let v be ((-6)/45)/((-4)/l). Factor -5/3*g + 2 + v*g**2.
(g - 3)*(g - 2)/3
Let a(j) be the second derivative of 1/18*j**4 + 25/9*j**3 - 18*j**2 + 143*j + 0. Let a(c) = 0. Calculate c.
-27, 2
Find r, given that 70*r - 14*r - 40*r - 13*r**2 + 84 = 0.
-2, 42/13
Let f(z) be the first derivative of 0*z**4 + 0*z**3 - 157 + 0*z**2 + 1/15*z**6 - 16/25*z**5 + 0*z. Factor f(c).
2*c**4*(c - 8)/5
Let t(i) be the second derivative of i**4/3 + 43*i**3/30 + 7*i**2/5 - 1665*i. Factor t(h).
(4*h + 7)*(5*h + 2)/5
Let u(l) be the second derivative of -3/20*l**5 + 4/3*l**3 + 1/30*l**6 - 1/2*l**4 + 0*l**2 + 7*l - 4. Factor u(m).
m*(m - 4)*(m - 1)*(m + 2)
Suppose 15*f - 45 = -0*f. Determine c, given that 20 - 11*c**2 + 8*c - 210*c**3 + 103*c**f + 108*c**3 = 0.
-1, 2, 10
Let w = -586054/9 - -586096/9. Factor w + 2/3*q**2 - 16/3*q.
2*(q - 7)*(q - 1)/3
Let i(l) be the second derivative of -l**4/12 - 181*l**3/6 - 67*l. Factor i(f).
-f*(f + 181)
Suppose 77*u + 840 = 85*u. Let a be 203/u + 2/(-6). Factor -2/5*c**2 - 6/5 - a*c.
-2*(c + 1)*(c + 3)/5
Let h(m) be the second derivative of -m**6/12 + 4*m**5/3 - 205*m**4/24 + 505*m**3/18 - 50*m**2 + 304*m - 5. What is c in h(c) = 0?
5/3, 2, 3, 4
Let i(h) = -19*h**2 + h + 2. Let s(m) = -344*m**2 + 2380*m + 2400. Let c(k) = -18*i(k) + s(k). Suppose c(d) = 0. Calculate d.
-1, 1182
Suppose 5*g = 5*o + 120, 5*o - 7*o - 25 = -g. Let w be ((-3)/(-12))/(25 - g). Determine c so that -1/4*c + w + 1/8*c**2 = 0.
1
Suppose 8*v = 2*v + 17*v - 44. Let c(d) be the first derivative of -16 + 0*d - 4*d**2 - 1/8*d**v - 4/3*d**3. Factor c(s).
-s*(s + 4)**2/2
Suppose -204 = -109*j + 123. Determine t, given that -57*t**2 - 12*t**4 + 3/2*t**5 + 75/2*t**j + 42*t - 12 = 0.
1, 2
Let g(v) be the first derivative of -2/3*v**2 + 1/9*v**3 + 1/3*v**4 - 1/3*v - 63. Determine x, given that g(x) = 0.
-1, -1/4, 1
Let i = 202691/9 - 22521. Factor -14/9*w**2 - i*w**3 - 2 - 10/3*w.
-2*(w + 1)*(w + 3)**2/9
Let m(w) = -53*w - 197. Let j be m(-4). Suppose -j = 20*i - 95. Factor 2/5*c**2 - 2/15*c**i + 2/15*c**3 + 4/15 - 2/3*c.
-2*(c - 1)**3*(c + 2)/15
Let r = -1 - -18. Factor 2*k - r*k - 5*k**2 + 1435 - 1415.
-5*(k - 1)*(k + 4)
Suppose 350 = 8*j + 310. Let w(t) be the first derivative of 2/27*t**3 - 1/45*t**j - 1/54*t**6 + 29 + 1/18*t**4 - 1/18*t**2 - 1/9*t. What is m in w(m) = 0?
-1, 1
Suppose -23*b + 248 = -18*b + 26*b. Let w(h) be the second derivative of -1/48*h**4 + 