hird derivative of -w**6/540 - 47*w**5/270 + 97*w**4/108 - 49*w**3/27 - 527*w**2. Factor c(l).
-2*(l - 1)**2*(l + 49)/9
Let n = 13393771/20 - 669444. Let l = -1219/5 + n. Factor -9/4 - 3/4*k**3 + 9/4*k**2 + l*k.
-3*(k - 3)*(k - 1)*(k + 1)/4
Let a(w) = -w**2 - 18*w - 29. Let r be a(-16). Suppose 19 = 3*g + 3*n - 7*n, -r*g + 2*n = -29. Factor g*k + 3*k**2 + 0*k**2 - 4*k**2 - 9*k.
-k*(k - 4)
Suppose 88 = 8*i - 80. Determine n so that 6*n**4 + i*n**3 - 81*n**3 + 25*n**4 - 4*n**2 = 0.
-2/31, 0, 2
Let k(u) be the second derivative of u**7/840 - u**6/80 + 3*u**5/80 - 11*u**2/2 - u - 16. Let t(o) be the first derivative of k(o). Factor t(v).
v**2*(v - 3)**2/4
Let g = 12226 - 61129/5. Let y(k) be the first derivative of 3 - 4/15*k**3 - g*k**2 + 0*k - 1/10*k**4. Let y(i) = 0. Calculate i.
-1, 0
Let 46*u**2 + 371/2*u - 1/8*u**3 + 186 = 0. Calculate u.
-2, 372
Let h be 4/(9648/(-585)) - 1/(-4). Let y = h + 199/268. Suppose 3/4*n**3 + 0 + 0*n - y*n**2 = 0. Calculate n.
0, 1
Suppose y = -3 + 15. Let j(d) = 0*d**2 - 3*d - 14 + d**2 + y. Let r(l) = 4*l**2 - 8*l - 5. Let a(g) = -7*j(g) + 2*r(g). Factor a(w).
(w + 1)*(w + 4)
Let c = -7352 - -36976/5. Let s = c - 849/20. Solve -3/4*k**5 + s*k**3 + 1/2*k**4 - 1/2*k**2 + 0 + 0*k = 0 for k.
-1, 0, 2/3, 1
Suppose -12168 + 1341*n - 263*n**2 + 403*n - n**3 + 269*n**2 - 379*n - 2*n**3 = 0. What is n?
-24, 13
Factor 693*z**2 + 300 - 1110*z + 1323/2*z**3.
3*(z + 2)*(21*z - 10)**2/2
Let x(f) be the first derivative of 5*f**4/108 + 17*f**3/27 - 7*f**2/18 + 47*f + 11. Let c(d) be the first derivative of x(d). Find j, given that c(j) = 0.
-7, 1/5
Let r be -10 + -4 - (-322)/23. Find t such that 1/3*t**2 + 2*t + 1/3*t**5 - 7/3*t**3 + r - 1/3*t**4 = 0.
-2, -1, 0, 1, 3
Let d be 1/(-5 + 78/15). Suppose -2*l**2 + 4*l**4 - 13*l + 3*l**4 + l - d*l**4 + 12*l**3 = 0. Calculate l.
-6, -1, 0, 1
Let l(s) be the third derivative of -s**6/24 - 117*s**5/20 + 95*s**4/8 + 71*s**3/6 - 207*s**2 + 7. Factor l(x).
-(x - 1)*(x + 71)*(5*x + 1)
Solve -944*r**3 + 728 + 64*r**4 - 7705*r**5 + 2408*r**2 + 15464*r**5 - 2260*r - 7755*r**5 = 0.
-26, 1, 7
Let a(i) be the first derivative of -4*i**3/3 + 76*i**2 - 768*i + 720. Solve a(w) = 0 for w.
6, 32
Let v(x) be the second derivative of -x**8/10080 + x**7/2520 + x**6/270 + x**3/6 - x**2/2 + 215*x. Let q(z) be the second derivative of v(z). Factor q(k).
-k**2*(k - 4)*(k + 2)/6
Suppose -17915*r - 1046 = -18438*r. Factor 0 + 38/15*a + 12/5*a**r - 2/15*a**3.
-2*a*(a - 19)*(a + 1)/15
Find v, given that -112 - 76/3*v - 4/3*v**2 = 0.
-12, -7
Let a(i) = i + 27. Let k be a(0). Suppose 5 + k = 16*j. Factor -12*c + 4/3 + 27*c**j.
(9*c - 2)**2/3
Let r(k) be the first derivative of k**6/6 + 6*k**5/5 - 25*k**4/4 + 6*k**3 - 4106. Factor r(s).
s**2*(s - 2)*(s - 1)*(s + 9)
Let b(q) be the second derivative of q**6/60 - 23*q**5/4 + 500*q**4 + 12000*q**3 + 521*q - 3. Suppose b(c) = 0. Calculate c.
-10, 0, 120
Let z(d) be the first derivative of -41 + 15/4*d**4 + 0*d**3 + 0*d - d**5 - 10*d**2. Let z(y) = 0. What is y?
-1, 0, 2
Let s be ((1664/720)/52)/(0 - (-2)/42). Suppose -34/15*z - 4/15 - s*z**3 - 44/15*z**2 = 0. Calculate z.
-2, -1, -1/7
Let a be (1 - -26) + (405/180)/(9/(-48)). Factor a + 40/3*t - 5/3*t**2.
-5*(t - 9)*(t + 1)/3
Let w(d) = 10*d**2 + d - 2. Let v be w(1). Suppose -3*f - 26 = -c - 4*c, 4*f = -8. Factor -v*q - 2*q**4 - 2*q**5 + 3*q + 4*q**2 - 2 + c*q + 4*q**3.
-2*(q - 1)**2*(q + 1)**3
Suppose -17*y - 152 = -526. Factor -y - 75*z + 3 + 0 - 69*z**2 + 6 + 7.
-3*(z + 1)*(23*z + 2)
Let g(y) = 15*y**2 + 7*y - 18. Let m(o) = -2*o**2 - o + 2. Let q(i) = 3*g(i) + 21*m(i). Suppose q(x) = 0. Calculate x.
-2, 2
Let f(x) be the first derivative of x**6/21 + 12*x**5/35 + 4*x**4/7 - 4*x**3/7 - 9*x**2/7 + 382. Find a, given that f(a) = 0.
-3, -1, 0, 1
Determine w so that -51/2*w**2 + 0 + 18*w**3 - 135*w - 3/2*w**4 = 0.
-2, 0, 5, 9
Let l(d) be the third derivative of d**5/210 - 239*d**4/84 + 158*d**3/7 - 2*d**2 + 4*d + 232. Factor l(m).
2*(m - 237)*(m - 2)/7
Let b be (1/12)/(207/8832). Let n(j) be the second derivative of -13*j + 0 - b*j**2 - 1/27*j**4 + 16/27*j**3. Factor n(y).
-4*(y - 4)**2/9
Factor 1252*l - 3182914 + 504*l + 777313 + 1346*l - l**2.
-(l - 1551)**2
Let t(m) = m**3 + 2*m**2 - 7*m + 30. Let y be t(-5). Let x be 10/(y/(-3)) - 3. Factor 0 + 1/11*o**4 + 0*o**2 - 1/11*o**3 + x*o.
o**3*(o - 1)/11
Let c(x) = 8*x**3 - 5*x**2 - 4*x + 3. Let i(w) = -7*w**3 + 5*w**2 + 6*w - 2. Let q(h) = -2*c(h) - 3*i(h). Suppose q(v) = 0. What is v?
-1, 0, 2
Let r be (16 + -1)*20/50. Let a(h) = h**2 - 8*h - 7. Let z be a(9). What is q in -66 - 9*q + 130 - 64 + r*q**z = 0?
0, 3/2
Let q(z) be the third derivative of z**5/30 + 4*z**4/3 + 13*z**3 + 9*z**2 - 19*z - 9. Factor q(g).
2*(g + 3)*(g + 13)
Let h be ((-39)/26)/((-4)/8). Let j(s) be the first derivative of -29 + 98/9*s**h - 13/2*s**4 + 8/3*s - 8*s**2 + 4/3*s**5. Let j(z) = 0. What is z?
2/5, 1/2, 1, 2
Solve -202*o - 1803 - 546*o + 333 + 721 + o**2 = 0 for o.
-1, 749
Let y be -7*6/(-210) + ((-2)/(-25))/(54/2265). Factor 0 - y*l**2 + 64/3*l - 20/9*l**3 + 4/9*l**4.
4*l*(l - 4)**2*(l + 3)/9
Let q(c) = -3*c**3 + c**2 + 12*c + 2. Let r(o) = -13*o**3 + 4*o**2 + 49*o + 5. Let p(u) = 9*q(u) - 2*r(u). Solve p(s) = 0.
-2, -1, 4
Suppose -240/13 + 164/13*y**4 - 596/13*y**2 - 174/13*y**3 - 10/13*y**5 + 856/13*y = 0. What is y?
-2, 2/5, 1, 2, 15
Let h(g) be the first derivative of -2/25*g**5 + 204*g**2 - 314/15*g**3 + 168 - 2312/5*g - 3*g**4. Let h(u) = 0. Calculate u.
-17, 2
Let c(j) = -5*j**3 - 15*j**2 - 15*j + 5. Let a(z) = 8*z**3 + 23*z**2 + 22*z - 7. Suppose 0 = 62*u - 65*u - 21. Let g(w) = u*c(w) - 5*a(w). Factor g(m).
-5*m*(m + 1)**2
What is o in 24 + 2/5*o**2 + 38/5*o = 0?
-15, -4
Let l(k) be the first derivative of -1/9*k**3 - 278 - 4*k**2 - 21*k. Factor l(n).
-(n + 3)*(n + 21)/3
Let h(q) be the first derivative of q**4/9 - 616*q**3/27 - 2*q**2/9 + 616*q/9 - 212. Factor h(l).
4*(l - 154)*(l - 1)*(l + 1)/9
Let v = 31483 + -31483. Let y(t) be the third derivative of 25*t**2 + 1/48*t**4 + v*t - 1/120*t**5 + 0*t**3 + 0. Factor y(q).
-q*(q - 1)/2
Let a = -77620 - -77621. Factor -3/2*j**3 - 1/2*j**2 - 1/2*j**4 + 3/2*j + a.
-(j - 1)*(j + 1)**2*(j + 2)/2
Let o(u) be the third derivative of u**6/15 - 51*u**5/5 + 494*u**4 - 2888*u**3/3 - 179*u**2 + 3*u. Factor o(c).
4*(c - 38)**2*(2*c - 1)
Let o(i) be the third derivative of 0*i + 1/8*i**3 + 1/16*i**5 + 1/8*i**4 + 1/80*i**6 - 8*i**2 - 2. Find q such that o(q) = 0.
-1, -1/2
Let p(q) = 2*q - 8. Let t be p(6). Let m be (4/(-6))/((-24)/(-9) + -3). Suppose -y**2 - 5*y - 4*y**2 + t*y**m + 3*y = 0. What is y?
-2, 0
Let q(h) be the third derivative of -1/20*h**6 - 3*h + 0 - 3/4*h**5 + 0*h**3 + 0*h**4 - 1/1050*h**7 - 57*h**2. Factor q(r).
-r**2*(r + 15)**2/5
Suppose -6*b = -16 - 2. Suppose -b*x + 88 = 4*s, 25 = 4*s - 2*x - 83. Factor -12*a + 3*a**4 - 22*a**3 - 9*a**2 - 6 - 3*a + s*a**3.
3*(a - 2)*(a + 1)**3
Let 101*u**2 - 4*u - 34*u**2 - 25*u**2 - 8 - 34*u**2 + 4*u**3 = 0. Calculate u.
-2, -1, 1
Find c such that 2472*c + 915*c**2 - 4588*c**2 - 1331*c**2 + 2512*c**3 + 20 = 0.
-5/628, 1
Let v(o) = -o**2 + 26*o + 37. Let n be v(27). Suppose -25*i**2 - 16 - 475*i**3 + 470*i**3 - 9 - n*i**2 - 55*i = 0. What is i?
-5, -1
Let b(p) be the first derivative of 20*p**2 + 56/5*p - 198 + 14/15*p**3. Determine u, given that b(u) = 0.
-14, -2/7
Let c = 77574 + -531794/7. Let b = c - 1600. Determine i, given that -36/7 - b*i - 4/7*i**2 = 0.
-3
Let y(s) be the first derivative of 12*s - 25*s**2 - 25/2*s**4 + 12/5*s**5 + 76/3*s**3 + 19. Suppose y(p) = 0. What is p?
2/3, 1, 3/2
Let i(f) = -6*f**2 + 10*f - 4. Let h be i(1). Let u(y) be the second derivative of y + 1/30*y**6 + 0*y**2 + 0*y**5 + 0*y**4 + h + 0*y**3. Factor u(n).
n**4
Let q(z) = 259*z - 512. Let p be q(2). Let n(y) be the third derivative of 0 + 0*y + 0*y**5 + 0*y**4 + 1/40*y**p - 4*y**2 + 0*y**3. Find j, given that n(j) = 0.
0
Let g(h) = 2*h**2 - 6*h + 5. Let z be g(18). Let v = z + -542. Factor 2/7*k**5 - 2/7*k**v + 0 + 0*k + 0*k**2 + 0*k**4.
2*k**3*(k - 1)*(k + 1)/7
Let h be -7 + 0 + 9488/80 + 6. Let v = 4126/35 - h. Factor -2/7*j**2 + 4/7 - v*j.
-2*(j - 1)*(j + 2)/7
Let v = -52993 + 52996. Factor -2/3*h**v + 8/3*h**2 - 2/3*h**4 - 7/3*h + 2/3 + 1/3*h**5.
(h - 1)**4*(h + 2)/3
Let r = 1718/609 + 510/203. 