be the third derivative of 3/26*w**5 - 5/156*w**6 + 0 - 2/13*w**4 + 4/39*w**3 - w**2 + 10*w. Factor h(d).
-2*(d - 1)*(5*d - 2)**2/13
Let g(x) be the first derivative of x**5/15 - 18*x**4 - 73*x**3/3 + 217*x**2/3 - 2519. Factor g(y).
y*(y - 217)*(y - 1)*(y + 2)/3
Suppose 2/9*i**2 + 490/9*i + 0 = 0. What is i?
-245, 0
Let b(k) be the first derivative of -40/11*k**2 + 82/33*k**3 - 3 - 1/22*k**4 + 0*k. Factor b(l).
-2*l*(l - 40)*(l - 1)/11
Suppose 9*g = 3*m + 4*g - 1, 4*g = 4. Suppose -146*y**m + 273*y**2 - 3*y**3 - 133*y**2 = 0. Calculate y.
-2, 0
Factor -546 - 92*f + 1395*f**2 - 1396*f**2 - 93*f.
-(f + 3)*(f + 182)
Let f(u) = 76*u**2 - 60*u - 238. Let o be f(-4). Suppose -1223*d = -o*d. Factor d*b + 2/5*b**3 + 6/5*b**2 - 8/5.
2*(b - 1)*(b + 2)**2/5
Let v(n) be the third derivative of n**8/2520 - 106*n**7/1575 + 728*n**6/225 - 2704*n**5/225 + 1038*n**2. Factor v(t).
2*t**2*(t - 52)**2*(t - 2)/15
Determine q, given that 200 + 55781*q**4 - 446*q - 66*q**2 - 4*q**3 + 102*q**3 + 54*q - 55777*q**4 = 0.
-25, -2, 1/2, 2
Let d = 20257/15258 + 29/5086. Factor -4/9*v + d*v**2 + 7/9*v**3 + 0.
v*(v + 2)*(7*v - 2)/9
Factor 68*i**2 - 1536*i**4 + 66*i**3 - 1561*i**4 + 3095*i**4.
-2*i**2*(i - 34)*(i + 1)
Let m be 483/(-115) - (-312)/65. Find h, given that 37/5*h - 26/5 + m*h**2 = 0.
-13, 2/3
Let p = -303082/3 + 606173/6. Determine b, given that 75/2 - p*b**2 + 36*b = 0.
-1, 25
Factor -99/8*t - 1/8*t**3 + 65/4 - 15/4*t**2.
-(t - 1)*(t + 5)*(t + 26)/8
Suppose 2*k**3 - 15*k**3 + 45*k**2 + 96*k + 7*k**3 + 9*k**3 - 396 = 0. What is k?
-11, -6, 2
Let w(c) be the second derivative of -4 - 5/3*c**3 + 41/4*c**5 + 0*c**2 - 2*c + 7/5*c**6 - 9/4*c**4. Factor w(q).
q*(q + 5)*(6*q + 1)*(7*q - 2)
Let z(s) be the first derivative of 1/21*s**4 - 44*s - 8/3*s**3 + 38 + 56*s**2. Let o(u) be the first derivative of z(u). Solve o(x) = 0.
14
Let r(d) = -112*d - 156. Let j be r(-15). Let p = -4571/3 + j. Factor z + 0 - p*z**2.
-z*(z - 3)/3
Suppose 342*x = 322*x + 80. Let r(g) be the first derivative of 0*g + 0*g**2 + 2/9*g**3 - 40 - 1/30*g**5 + 0*g**x. Factor r(p).
-p**2*(p - 2)*(p + 2)/6
Let b(p) be the first derivative of 0*p + 9/16*p**2 - 13/8*p**3 + 3/8*p**4 + 38. Factor b(y).
3*y*(y - 3)*(4*y - 1)/8
Let g(i) be the second derivative of -16/9*i**2 - 35*i - 8/9*i**3 + 5/18*i**4 - 3 - 1/45*i**5. Let g(q) = 0. Calculate q.
-1/2, 4
Let z(p) be the third derivative of -p**7/420 + 479*p**6/240 + 481*p**5/120 - 479*p**4/48 - 40*p**3 - 9*p**2 + 34. Determine h so that z(h) = 0.
-1, 1, 480
Let f(t) = -18*t**2 - 642*t - 11484. Let z(l) = -28*l**2 - 964*l - 17232. Let b(v) = -8*f(v) + 5*z(v). What is q in b(q) = 0?
-51, -28
Let k(a) = -880*a**2 + 341*a + 105. Let j(s) = 660*s**2 - 255*s - 79. Let y(n) = 9*j(n) + 7*k(n). Factor y(z).
-4*(5*z - 3)*(11*z + 2)
Let t(n) be the third derivative of -n**7/525 + 17*n**6/300 - 46*n**5/75 + 49*n**4/15 - 48*n**3/5 + 606*n**2. Let t(m) = 0. Calculate m.
2, 4, 9
Let y(l) = -2*l**2 - l + 43. Let c(s) = 5*s**2 + 2393*s + 2304. Let n(t) = -3*c(t) - 6*y(t). Determine h so that n(h) = 0.
-2390, -1
Let l(t) = 35*t**3 + 4520*t**2 + 4320*t - 165. Let b(s) = -2*s**3 - 251*s**2 - 240*s + 9. Let r(f) = -55*b(f) - 3*l(f). Factor r(h).
5*h*(h + 1)*(h + 48)
Let b(m) be the third derivative of -m**5/15 + 72*m**4 + 870*m**3 - 9833*m**2. Factor b(i).
-4*(i - 435)*(i + 3)
Let y(b) be the third derivative of 0 - 13/6*b**6 + 0*b + 2/7*b**7 - 43*b**2 + 0*b**3 - 40/3*b**4 + 8*b**5 - 5/336*b**8. Determine u, given that y(u) = 0.
0, 2, 4
Let p(r) be the first derivative of r**8/560 - r**7/280 - r**6/120 + r**5/40 + 14*r**3 - 68. Let g(f) be the third derivative of p(f). Let g(m) = 0. What is m?
-1, 0, 1
Let h(p) be the first derivative of 95*p + 65 - 45/4*p**4 + 565/2*p**2 + 275*p**3. Find x, given that h(x) = 0.
-1/3, 19
Factor 9641*m**3 - 51582 - 9644*m**3 - 231*m**2 - 5445*m + 15645.
-3*(m + 11)*(m + 33)**2
Suppose 4*z - 2*n = 2*z + 3326, 0 = z + 2*n - 1654. Suppose -6*t + z*t**2 + 34*t - 1664*t**2 = 0. What is t?
0, 7
Let p(h) be the second derivative of -h**7/70 - h**6/50 + 39*h**5/100 + 13*h**4/20 - 18*h**3/5 - 54*h**2/5 - 762*h - 1. Suppose p(z) = 0. What is z?
-3, -2, -1, 2, 3
Let q be 1*((-36)/108)/((-1)/6). What is r in 2*r**2 - 233 + 36*r + 272 + 0*r**q - 5*r**2 = 0?
-1, 13
Let p be (-4 - (65/(-10) - -3))*891/(-198). Factor 3/8*q**3 + p - 15/8*q - 3/4*q**2.
3*(q - 3)*(q - 1)*(q + 2)/8
Suppose 192 - 216 = -6*p. Factor -14 - p*d - 24*d - 8*d**2 - 3*d + 9 - 17 + d**3.
(d - 11)*(d + 1)*(d + 2)
Let h(u) be the third derivative of -u**7/420 + 3*u**6/40 - 17*u**5/24 + 3*u**4/2 + 44*u**3/3 + 1032*u**2. Factor h(c).
-(c - 11)*(c - 4)**2*(c + 1)/2
Determine c, given that -79 - 736*c**2 + 735*c**2 - 18*c + 2 = 0.
-11, -7
What is d in 605/2 + 300*d - 5/2*d**2 = 0?
-1, 121
Let h = -261904 + 261904. Determine b, given that -48/5*b**2 + 0*b + h - 3/5*b**5 + 0*b**4 + 36/5*b**3 = 0.
-4, 0, 2
Let k = 45 + -20. Suppose -a = -4*h + k, 3*h - 8 = 5*a + 15. Determine w so that -272 + 64*w - 10*w**2 + h*w**2 - 36 + 52 = 0.
8
Suppose -1 + 0*l**2 - 30*l**2 - 36*l**4 + 1 - 12960*l**5 + 63*l**3 + 12963*l**5 = 0. What is l?
0, 1, 10
Let y(l) be the third derivative of l**8/420 - l**7/70 - l**6/6 - 17*l**5/30 - l**4 + 5*l**3/3 - 12*l**2. Let z(k) be the first derivative of y(k). Factor z(a).
4*(a - 6)*(a + 1)**3
Let l(w) be the second derivative of w**4/4 + 560*w**3 + 470400*w**2 + 463*w - 1. Determine k, given that l(k) = 0.
-560
Let u(c) = -2*c**5 - c**4 - 2*c**3 - 2*c**2 + 2*c + 1. Let n(a) = -56*a**5 + 276*a**4 + 1287*a**3 - 324*a**2 + 13*a - 4. Let p(d) = -n(d) - 4*u(d). Factor p(t).
t*(t - 7)*(t + 3)*(8*t - 1)**2
Let z(w) = -w**3 + 14*w**2 + 2108*w - 29510. Let j be z(14). Determine o so that -3698/7 - 2/7*o**j + 172/7*o = 0.
43
Factor 85 + 43*v + 30*v - 680*v**2 + 667*v**2 - v**3.
-(v - 5)*(v + 1)*(v + 17)
Let i(k) be the third derivative of -k**8/1680 + 6*k**3 - k**2 - k. Let r(m) be the first derivative of i(m). Factor r(l).
-l**4
Factor 112/11*n + 2/11*n**2 + 600/11.
2*(n + 6)*(n + 50)/11
Let l(s) = s**3 - 5*s**2 - 9*s + 20. Let b be l(6). What is y in 43*y**4 - 11*y**b - 2*y**2 - 44*y**3 + 6*y + 20*y**5 - 12*y**3 = 0?
-3, -2/5, 0, 1/4, 1
Suppose 0 = -4*r - c + 243, 0 = 5*r - 4*c - 329 + 41. Let u = r - 56. Suppose -3*q**u - q**4 - q**4 = 0. What is q?
0
Suppose 1/4*t**5 + 328*t - 17/4*t**3 - 185 - 593/4*t**2 + 37/4*t**4 = 0. What is t?
-37, -5, 1, 2
Let d(w) be the second derivative of 1/35*w**6 + 1/147*w**7 + 0*w**4 - 15*w + 1/35*w**5 + 0*w**3 - 5 + 0*w**2. Factor d(j).
2*j**3*(j + 1)*(j + 2)/7
Let m(n) be the second derivative of 5*n**7/56 + 146*n**6/5 + 2091*n**5/80 - 233*n**4/8 + 1127*n. Find c, given that m(c) = 0.
-233, -1, 0, 2/5
Let x be (150/(-425))/((-416)/884). Factor -x + 3/4*l**2 + 0*l.
3*(l - 1)*(l + 1)/4
Suppose -49 = -10*z + 2641. Let b = z - 266. Determine o so that 14/5*o - 28/5*o**4 + 2/5*o**b + 26/5*o**2 + 2/5 - 16/5*o**5 = 0.
-1, -1/2, -1/4, 1
Let v = -7534/5 - -23852/15. Let g(l) be the first derivative of -6*l**5 + 1/3*l**6 + 0*l**2 + 0*l + 75/2*l**4 - v*l**3 - 26. Factor g(k).
2*k**2*(k - 5)**3
Let q(v) = -8*v**4 - 482*v**3 - 1290*v**2 - 1192*v - 366. Let o(k) = -6*k**4 - 484*k**3 - 1290*k**2 - 1191*k - 364. Let r(w) = 4*o(w) - 6*q(w). Solve r(d) = 0.
-37, -1, -5/6
Let y = 10 + -22. Let f be (y/(-15))/(2/5). Factor 152*i**2 + 3*i + 146*i**f + i**3 - 4*i - 2 - 296*i**2.
(i - 1)*(i + 1)*(i + 2)
Let y(i) be the second derivative of -5*i**6/19 - 979*i**5/19 + 7234*i**4/57 - 6856*i**3/57 + 1056*i**2/19 - 5*i + 94. Suppose y(z) = 0. What is z?
-132, 2/5, 2/3
Factor -97/7*t + 1/7*t**2 + 96/7.
(t - 96)*(t - 1)/7
Let y be (((-3)/18)/((-6)/(-4)))/(8357/(-626775)). Find x, given that 10*x**2 - 40/3 - 20/3*x + y*x**3 + 5/3*x**4 = 0.
-2, 1
Let l(j) = -78*j**3 - 27*j**2 + 60*j - 46. Let b(q) = -67*q**3 - 26*q**2 + 61*q - 46. Let x(h) = 7*b(h) - 6*l(h). Let x(t) = 0. What is t?
-23, 1, 2
Let s(l) be the second derivative of -l**4/4 - 20*l**3 - 693*l**2/2 - 3211*l. Factor s(x).
-3*(x + 7)*(x + 33)
Suppose -3*i + 17 = -5*c - 14, -2*i - 1 = c. Suppose -t + 46*q - 43*q = -84, 140 = -6*t - 5*q. Factor t*f**2 + 1/2*f**4 + 0 + 0*f + 0*f**3 - i*f**5.
-f**4*(4*f - 1)/2
Let w(q) be the third derivative of -q**5/360 + 125*q**4/72 + 253*q**3/12 - 2*q**2 - 485. Factor w(i).
-(i - 253)*