- 2896. Factor 722*y**3 - m*y**3 + 2*y**2 - 4*y**2.
-2*y**2*(y + 1)
Suppose 46458*r + 376 = 46646*r. Solve -3/8*q**r + 3/8*q + 9/4 = 0.
-2, 3
Let v(b) = 14808*b + 592335. Let k be v(-40). Factor -69*w + 27/4*w**2 + k.
3*(w - 10)*(9*w - 2)/4
Let p(j) = -15*j**2 + 3*j + 4. Let x be p(-1). Let o(n) = n**2 + 15*n + 16. Let d be o(x). Factor 10/3*y - 8/3 - 2/3*y**d.
-2*(y - 4)*(y - 1)/3
Let v(d) = d**3 - 16*d**2 - 4*d + 44. Let x be v(8). Let j = x - -506. Solve 0 - 3/2*c**4 - j*c + 6*c**2 + 3/2*c**3 = 0 for c.
-2, 0, 1, 2
Let c be (110/88)/((-1)/(-129)). Let p = c - 159. Solve 5*y + p*y**2 + 1 = 0 for y.
-2, -2/9
Factor -2/13*c**3 + 0 - 116/13*c**2 + 240/13*c.
-2*c*(c - 2)*(c + 60)/13
Let t(f) be the third derivative of f**5/80 - 501*f**4/16 + 251001*f**3/8 - 10504*f**2. Let t(b) = 0. What is b?
501
Let w(r) be the first derivative of -r**4/26 - 20*r**3/13 + 72*r**2/13 + 512*r/13 - 2702. Factor w(t).
-2*(t - 4)*(t + 2)*(t + 32)/13
Let 3185288/7 + 2/7*n**2 + 5048/7*n = 0. What is n?
-1262
Let k(q) be the third derivative of q**6/2880 - q**4/192 - 25*q**3 - 204*q**2. Let y(o) be the first derivative of k(o). Factor y(a).
(a - 1)*(a + 1)/8
Let o be 4/(4/599) - (-5 - -9). Determine w, given that -1914*w**3 + 2178*w**4 - 16 - 4612*w**2 - o*w - 77*w + 136*w = 0.
-1, -2/33, 2
Factor 1/3 + 7*q**2 - 22/3*q.
(q - 1)*(21*q - 1)/3
Suppose 0 = 4*c + n - 7, -3*c - 1401*n + 1406*n - 35 = 0. What is p in c + 3/4*p**2 - 27/4*p = 0?
0, 9
Determine n, given that -18/5 + 2/5*n**2 - 18/5*n + 2/5*n**3 = 0.
-3, -1, 3
Suppose -1194*c = -1187*c - 35. Let h(d) be the first derivative of -1/4*d**3 - 3/8*d**4 + 3/20*d**c - 10 + 3/4*d**2 + 0*d. Factor h(i).
3*i*(i - 2)*(i - 1)*(i + 1)/4
Let o(m) be the third derivative of -m**5/540 + 23*m**4/54 - 1058*m**3/27 - 34*m**2 + 23. Suppose o(d) = 0. What is d?
46
Let u(c) be the second derivative of c**7/147 + 29*c**6/105 - 47*c**5/35 + 32*c**4/21 + 3*c + 5017. Find o, given that u(o) = 0.
-32, 0, 1, 2
Let o(p) be the second derivative of 0*p**2 - 2*p - 69 - 16/9*p**3 - 1/9*p**4. Find k, given that o(k) = 0.
-8, 0
Let d = -12849 + 12851. Let f(y) be the first derivative of 2/15*y + 2/45*y**3 + 22 - 2/15*y**d. Let f(q) = 0. Calculate q.
1
Let q be (-13 - (-259)/21)/((-4)/30). Let l(z) be the third derivative of 0*z**4 + q*z**2 + 0 + 1/120*z**6 + 0*z**3 + 0*z - 1/15*z**5. Factor l(k).
k**2*(k - 4)
Solve 22/9*w**2 - 2/9*w**3 - 76/9*w + 80/9 = 0.
2, 4, 5
Let o(a) be the first derivative of -a**4/2 - 32*a**3/3 + 148*a**2 + 704*a - 5182. Determine p so that o(p) = 0.
-22, -2, 8
Suppose -12*b + 83 = -r + 12, b + 5*r = 11. Let k = 6/43 - -117/86. What is p in 0*p + b - k*p**2 = 0?
-2, 2
Suppose 0 = -4*f - 1 + 9. Let y be 8/(3 - 2) + f/(-1). Solve -38*w**3 + 48*w**3 + 0*w**2 + y*w**4 - 4*w**2 = 0.
-2, 0, 1/3
Let i(q) be the second derivative of 5*q**4/6 + 48*q**3 - 29*q**2 - 8*q + 222. Let i(m) = 0. What is m?
-29, 1/5
Let z be (3/9*130)/(4/6). Determine w so that -3*w + 37 - 9*w**2 + 34 - z = 0.
-1, 2/3
Let i(v) be the third derivative of v**9/756 + v**8/210 - v**7/70 + 8*v**3/3 - 42*v**2. Let s(f) be the first derivative of i(f). Factor s(t).
4*t**3*(t - 1)*(t + 3)
Let z(g) be the second derivative of -1/120*g**6 + 0*g**2 - 1/80*g**5 + 2*g + 1/24*g**4 + 19 + 0*g**3. Determine b so that z(b) = 0.
-2, 0, 1
Let s = 6225/2 - 3112. Let v(y) be the first derivative of 1/16*y**4 - 1/4*y**3 + s*y + 1/20*y**5 + 7 - 1/8*y**2. Determine n so that v(n) = 0.
-2, -1, 1
Suppose 7 = -2*j - k, -k - 6 = -5*j - 13. Let a be 2/(5/((-30)/24)) - j. Find r, given that -a*r + 3/2*r**3 - 3/4*r**4 + 0*r**2 + 3/4 = 0.
-1, 1
Let p(h) be the first derivative of h**5/10 + 23*h**4/8 + 10*h**3 - 217*h**2 + 392*h - 1786. Factor p(d).
(d - 4)*(d - 1)*(d + 14)**2/2
Let c(y) = -39*y - 1167. Let g be c(-30). Let h(x) be the second derivative of -g*x**3 + 2/3*x**4 + 0 + 2*x**2 + 8*x. What is v in h(v) = 0?
1/4, 2
Factor -1551 + 10*x**2 - 2816*x - 8679*x - 4402 + 203.
5*(x - 1150)*(2*x + 1)
Let q(t) = -3*t**2 - 481*t + 1504. Let s(c) = -23*c**2 - 3846*c + 12034. Let y(l) = -17*q(l) + 2*s(l). Suppose y(x) = 0. Calculate x.
-100, 3
Let o(g) be the second derivative of 2*g**7/147 - 18*g**6/35 + 116*g**5/35 - 44*g**4/7 + 5170*g. Suppose o(z) = 0. Calculate z.
0, 2, 3, 22
Suppose 0 = 13*x - 15*x - 6, x = -o - 33. Let k be (3 - 1) + 25/o*-20. Find a, given that 32/3*a + 104/9*a**3 + 16/9 + k*a**2 + 7/3*a**4 = 0.
-2, -2/3, -2/7
Find s, given that -5*s**2 - 18*s**2 + 22*s**2 + 316 + 52*s**2 + 105*s - 310 = 0.
-2, -1/17
Solve -40*a - 48 + 256*a**2 + 98*a**3 + 188*a**4 + 12*a**5 + 272*a**3 - 36*a**2 + 18*a**5 = 0.
-3, -2, -1, -2/3, 2/5
Let k(s) be the first derivative of s**6/200 - s**5/50 - s**4/10 + 4*s**3/5 + 23*s**2 + 49. Let f(o) be the second derivative of k(o). Factor f(j).
3*(j - 2)**2*(j + 2)/5
What is t in t**4 + 19*t**3 + 81*t - 36773 + 51*t**2 + 36773 + 48*t**2 = 0?
-9, -1, 0
Let m(i) be the first derivative of -i**4/4 - 2*i + 19. Let h(c) = -6*c**3 - 6*c**2 - 16*c + 4. Let v(l) = h(l) - 10*m(l). Factor v(j).
2*(j - 2)*(j + 2)*(2*j - 3)
Let v(p) = -13*p**2 - 4304*p - 4596. Let b be v(-330). Determine q so that -b - 3/2*q**2 - 51/2*q = 0.
-16, -1
Let d be (30 - 30) + (475 - 1). Let c = d + -464. Solve 5/2 + c*s + 15/2*s**2 = 0 for s.
-1, -1/3
Let b(o) = 6*o + 8. Suppose -579*p = -574*p - 70. Let v(l) = l**2 - 17*l - 25. Let j be 2/(-4)*(-6 + -2). Let i(x) = j*v(x) + p*b(x). Factor i(g).
4*(g + 1)*(g + 3)
Determine h so that 23266*h - 23266*h + 268*h**4 + 4*h**5 + 776*h**3 + 512*h**2 = 0.
-64, -2, -1, 0
Suppose -3*j + 24 = -3*d, -12 = -2*j + 5*d + 4. Suppose -5*r + 294 = v, 3*r + 302 = j*r + 3*v. Factor -8 + 16*w + 14*w**2 + 12*w + 84*w**2 + r*w**2.
4*(3*w + 1)*(13*w - 2)
Suppose -190*q - 30 = -193*q. Suppose h + 3*m - 15 = 0, -5*h + m - q = -7*h. Factor -2/5*a**h - 6/5*a**2 - 6/5*a - 2/5.
-2*(a + 1)**3/5
Let f be (1 - (-39)/(-9))/(14/252). Let l be ((-3)/4)/(f/140). Suppose l*b**4 + 0 - b + 5*b**2 - 23/4*b**3 = 0. What is b?
0, 2/7, 1, 2
Let -304/7 - 15700/7*w**2 + 256/7*w**5 - 6080/7*w**4 + 3740/7*w + 23920/7*w**3 = 0. Calculate w.
1/4, 4, 19
Suppose 0 = -7*a + a - 48, 3*p + 5*a - 33 = 95. Let -p*k + 4/5*k**2 - 284/5 = 0. What is k?
-1, 71
Let a = -31 + 37. Suppose a*g - 106 = 686. Solve y**4 + 132*y**3 - g*y**3 + 0*y**4 = 0.
0
Let b(k) be the second derivative of -k**4/48 - 15*k**3/8 - 11*k**2/2 + 380*k + 5. Solve b(z) = 0 for z.
-44, -1
Let t(n) be the third derivative of 0*n - 43 + 1/360*n**6 - 1/2016*n**8 - 1/36*n**3 - 2*n**2 + 1/180*n**5 - 1/1260*n**7 - 1/144*n**4. Let t(i) = 0. What is i?
-1, 1
Let t(f) = 6*f + 15. Let x be t(8). Let v = x + -60. Suppose 4*z - v + 5*z**2 + z + 3 = 0. What is z?
-1, 0
Let f(d) be the third derivative of -d**6/1140 - 11*d**5/570 + 17*d**4/114 + 104*d**3/57 + 2*d**2 - 67*d. Let f(p) = 0. Calculate p.
-13, -2, 4
Let k be ((-60)/45)/(1088/(-48) - -22). Factor -8 - 74/9*g - 2/9*g**k.
-2*(g + 1)*(g + 36)/9
Let f(j) be the first derivative of -31*j**3/33 - 64*j**2/11 - 16*j/11 - 1011. Find w, given that f(w) = 0.
-4, -4/31
Factor -11/2*n - 1/2*n**2 - 9.
-(n + 2)*(n + 9)/2
Factor 19/2*u - 105/4 - 1/4*u**2.
-(u - 35)*(u - 3)/4
Let i(l) be the second derivative of -l**5/10 + 23*l**4/3 + 31*l**3/3 - 30*l**2 - 2*l + 4. Let z(j) be the first derivative of i(j). Factor z(q).
-2*(q - 31)*(3*q + 1)
Suppose -4/7*g**2 + 2/7*g**5 - 44/7*g**3 - 2/7*g**4 + 138/7*g - 90/7 = 0. What is g?
-3, 1, 5
Let p(z) be the first derivative of 53 + 196/17*z + 1/34*z**4 + 32/51*z**3 + 77/17*z**2. Factor p(l).
2*(l + 2)*(l + 7)**2/17
Suppose -2*r + 0 = -6*y + 6, 0 = r - 4*y. Let j be 24/(-20) + r/(-10). Factor -4/7*t**2 - 6/7*t**3 + j*t + 0 - 2/7*t**4.
-2*t**2*(t + 1)*(t + 2)/7
Let h be (3 - 1)/(11*(-2)/(-88)). Let g(t) = 4*t**3 + 3*t**2 - 3*t - 3. Let p(o) = 11*o**3 + 11*o**2 - 8*o - 8. Let j(z) = h*g(z) - 3*p(z). Factor j(c).
-c**2*(c + 9)
Let r be (-12)/((-109)/52 + (972/(-234) - -4)). Determine b, given that 6*b - 2/3*b**2 - r = 0.
1, 8
Let o = -155 - -1149/7. Let a = -1954/119 - -318/17. Factor -4/7 - 100/7*g**3 - o*g**4 - 4*g - a*g**5 - 76/7*g**2.
-4*(g + 1)**3*(2*g + 1)**2/7
Let s be (8/(-111 - 1))/(134/(-3384)). Let u = s + -6/67. Determine r, given that u*r**2 - 24/7*r - 2/7*r**3 + 16/7 = 0.
2
Let i(b) be the first derivative of 32/15*b**5 - 80/9*b**3 - 2/9*b