96/3 - -283478/21. Find d such that 12/7 + v*d**2 - 2*d = 0.
1, 6
Let a(b) = -b**3 + 25*b**2 + 174*b - 4750. Let w be a(24). Let s(q) be the second derivative of 1/2*q**w + 0 + 2/3*q**3 + 37*q + 1/4*q**4. Factor s(k).
(k + 1)*(3*k + 1)
Let x(f) be the third derivative of 11*f**8/2352 - 3*f**7/49 + 41*f**6/420 + 107*f**5/105 + 65*f**4/56 - 25*f**3/21 + f**2 + 639*f. Find o, given that x(o) = 0.
-1, 2/11, 5
Factor 6*m**4 - 31*m**4 - 3287*m - 3296*m**2 + m**5 + 599*m - 634*m**3.
m*(m - 42)*(m + 1)*(m + 8)**2
Factor -400 + 45*u - 28*u**2 - u**4 + 7*u**3 + 220*u + 52*u**2 + 59*u**2 + 46*u**2.
-(u - 16)*(u - 1)*(u + 5)**2
Factor 6*f - 144/7*f**2 - 51/7*f**4 + 150/7*f**3 + 3/7.
-3*(f - 1)**3*(17*f + 1)/7
Let k(o) be the second derivative of -87/2*o**4 + 5046*o**3 + 126*o + 0 - 292668*o**2 + 3/20*o**5. Factor k(t).
3*(t - 58)**3
Let k(f) = -367*f + 2202. Let j be k(6). Let w(p) be the third derivative of 0*p**3 + j*p**4 + 0 - 8*p**2 + 0*p - 1/120*p**6 + 1/60*p**5. Factor w(i).
-i**2*(i - 1)
Let b(a) be the third derivative of 13*a**7/735 - a**6/210 - 13*a**5/30 - 16*a**4/21 + 4*a**3/7 - 1259*a**2. Determine w so that b(w) = 0.
-2, -1, 2/13, 3
Let u(r) = -r**2 + 8*r + 43. Let f be u(9). Factor 558*w**2 + 101*w**3 + 1809*w - 1245*w + 21*w**4 + 60*w**3 + 120 + f*w**3.
3*(w + 2)**2*(w + 5)*(7*w + 2)
Let l(r) = 8*r + 7. Let k be l(0). Factor -s - 3*s**2 - 13*s + 19 - k*s + 5.
-3*(s - 1)*(s + 8)
Let t(d) be the third derivative of 7*d**2 + 1/60*d**6 + 0*d**3 + 23 + 2*d**5 + 0*d + 75*d**4. Find z such that t(z) = 0.
-30, 0
Let y(f) be the third derivative of f**6/240 - 31*f**5/120 - 217*f**4/48 - 185*f**3/12 + 2*f**2 - 503. Factor y(n).
(n - 37)*(n + 1)*(n + 5)/2
Let m be (-1)/(-4)*52/585. Let p(n) be the second derivative of 0*n**3 + 0*n**2 + 0 - m*n**6 - 1/18*n**4 - 12*n - 1/15*n**5. Factor p(j).
-2*j**2*(j + 1)**2/3
Let p(w) = -42*w**3 - 54*w**2 - 7*w. Let k(j) = -21*j**3 - 27*j**2 - 3*j. Let o be 13/52 + (-26)/8. Let b(y) = o*p(y) + 5*k(y). Factor b(f).
3*f*(f + 1)*(7*f + 2)
Let b(c) be the second derivative of c**5/110 + 175*c**4/66 - 353*c**3/33 + 177*c**2/11 + 54*c + 43. Factor b(t).
2*(t - 1)**2*(t + 177)/11
Let v(m) = -3*m - 42. Let k be v(-14). Let r be 12/3 - 2 - k. What is p in p**2 + 17 - 5*p**r - 21 + 8*p = 0?
1
Let h(z) = 2*z**3 - 10*z**2 + 8*z - 5. Let b be h(4). Let x be 48 - 49 - (-1 + 1 + b). Let 1/5*n + 3/5*n**x - 3/5*n**2 - 1/5*n**3 + 0 = 0. What is n?
-1, 0, 1/3, 1
Let s = -304 + 306. Let h(p) be the first derivative of -7 + 0*p + 3*p**3 - 6*p**s + 3/4*p**4. Determine q, given that h(q) = 0.
-4, 0, 1
Suppose 9*v - 35 = 1. Let 53 + 28 + v - 15 - 105*l + 5*l**2 + 30 = 0. Calculate l.
1, 20
Let i(y) be the second derivative of y**5/34 + 13*y**4/102 - 26*y**3/51 + 8*y**2/17 + 2*y - 3641. Factor i(h).
2*(h - 1)*(h + 4)*(5*h - 2)/17
Let a(t) be the second derivative of 0*t**2 - 22/3*t**3 - 12/5*t**5 + 0 - 15/2*t**4 - 1/15*t**6 + 70*t. Determine w so that a(w) = 0.
-22, -1, 0
Let g = -242 - -245. Let p = 747 - 6713/9. Let 2/3*q**2 + 0 - p*q**g + 4/9*q = 0. What is q?
-2/5, 0, 1
Let d be -11*(-6)/(-132)*((-6)/(-3))/(-2). Let r(y) be the first derivative of 0*y + 1/6*y**3 - d*y**2 + 4. Factor r(c).
c*(c - 2)/2
Let s(f) be the third derivative of f**5/60 - 119*f**4/24 - 20*f**3 - 2875*f**2. Factor s(g).
(g - 120)*(g + 1)
Let x(m) be the second derivative of 75*m + 0*m**2 + 0*m**3 + 0 + 3/140*m**5 + 1/2*m**4. Factor x(h).
3*h**2*(h + 14)/7
Let k(t) = -24*t**4 - 33*t**3 + 195*t**2 + 139*t + 47. Let j(p) = -8*p**4 - 12*p**3 + 66*p**2 + 46*p + 16. Let g(u) = 22*j(u) - 8*k(u). Factor g(a).
4*(a - 3)*(a + 2)*(2*a + 1)**2
Suppose 9*t = 543 - 1066 + 541. Find b, given that 4/3*b**5 - 28/3 + 56/3*b**t - 8/3*b**3 + 4/3*b - 28/3*b**4 = 0.
-1, 1, 7
Let h(q) be the third derivative of q**6/60 + 13*q**5/30 - 65*q**4/12 + 17*q**3 - 2*q**2 - 449. Factor h(y).
2*(y - 3)*(y - 1)*(y + 17)
Let p(j) be the first derivative of -2/3*j**3 + 0*j**2 + 16 + 1/42*j**4 + 0*j - 1/210*j**5 + 1/2520*j**6. Let i(t) be the third derivative of p(t). Factor i(u).
(u - 2)**2/7
Let n(v) be the second derivative of v**8/2352 - 157*v**2/2 - 177*v. Let g(y) be the first derivative of n(y). Determine d, given that g(d) = 0.
0
Let b(o) = -27*o**5 - 168*o**4 + 183*o**3 + 12*o**2 - 24. Let r(a) = 25*a**5 + 168*a**4 - 182*a**3 - 11*a**2 + 22. Let j(s) = -11*b(s) - 12*r(s). Factor j(t).
-3*t**3*(t - 1)*(t + 57)
Let a(v) be the third derivative of 0 - 8/35*v**7 + 9/4*v**4 + 9/5*v**6 - 85*v**2 - 61/20*v**5 + 0*v - 7/8*v**3. Solve a(f) = 0 for f.
1/4, 1/2, 7/2
Let g(u) = u. Let t be g(5). Suppose -5*c + 2*p = -0*c - 15, 2*p + t = 3*c. Let 29*m**2 - 64*m**2 + 30*m**2 + 10 + c*m = 0. Calculate m.
-1, 2
Let h(n) = 8631*n**2 + 34524*n + 6. Let y be h(-4). Factor -y*q**2 - 5/2 - 7*q - q**3 + 1/2*q**4.
(q - 5)*(q + 1)**3/2
Let s(j) be the first derivative of j**6/900 + j**5/20 + 7*j**4/30 + 8*j**3 + 2*j - 21. Let p(k) be the third derivative of s(k). Suppose p(d) = 0. Calculate d.
-14, -1
Let n be 13639/6 - 11000/(-1320). Solve -117/2*w + n + 3/8*w**2 = 0.
78
Let n(y) = 9*y + 30. Let u be n(-5). Let f be 17/6 - ((-80)/u - 4). Factor 3/4*m**4 - f*m**3 + 0 + 0*m - 9/4*m**2.
3*m**2*(m - 3)*(m + 1)/4
Let w(t) be the second derivative of -47*t**4/4 + 29*t**3/6 + 3*t**2 - 1799*t. Factor w(z).
-(3*z - 1)*(47*z + 6)
Let o(z) = -8127*z + 235685. Let l be o(29). Solve 98 - 27/2*t**l + 1/2*t**3 + 84*t = 0.
-1, 14
Determine z so that 81*z**2 + 129*z + 357*z**3 - 199*z**3 - 218*z**3 + 4*z**4 - 517*z + 195*z**2 + 168 = 0.
1, 6, 7
Suppose 3*c + 407 = 434. Let w(g) be the third derivative of 1/240*g**6 + 5/144*g**4 + 0*g - 2/45*g**5 - c*g**2 + 0 + 0*g**3. Factor w(o).
o*(o - 5)*(3*o - 1)/6
Let c(b) be the second derivative of -47*b + 1/2*b**2 - 2 + 1/12*b**4 + 1/3*b**3. Factor c(l).
(l + 1)**2
Let c(k) = -90*k + 85. Suppose 3*i - 28 = -5*d, -8*d + 10*d - 9 = i. Let q(v) = v**2 - v - 1. Let x(g) = d*q(g) - c(g). Let x(z) = 0. What is z?
-18, 1
Let q be ((-312)/130)/((-240)/50). Factor 128*a + 128 + 8*a**3 + 48*a**2 + q*a**4.
(a + 4)**4/2
Let u(i) be the second derivative of i**4/84 + 79*i**3/42 - 30*i**2 - 8752*i. Find w, given that u(w) = 0.
-84, 5
Let w(v) be the third derivative of v**7/165 - v**6/60 + v**5/330 + v**4/44 - 2*v**2 + 908*v. Suppose w(b) = 0. Calculate b.
-3/7, 0, 1
Factor 0*o + 2/13*o**3 - 186/13*o**2 + 0.
2*o**2*(o - 93)/13
Let l(f) be the second derivative of -f**5/70 - 257*f**4/42 + f**3/21 + 257*f**2/7 - 2852*f. Find b, given that l(b) = 0.
-257, -1, 1
Let j be (-4)/7 - -1 - (-372)/(-1260). Let m(h) be the first derivative of -2/5*h**2 - 2/5*h + 3 - j*h**3. Solve m(y) = 0 for y.
-1
Let f = 3084086/15 - 205604. Factor 42/5 - 34/5*r - 2/15*r**3 + f*r**2.
-2*(r - 7)*(r - 3)**2/15
Let x(s) be the third derivative of -s**7/350 + 94*s**6/25 + 1507*s**5/100 + 377*s**4/20 + 11*s**2 + 27*s. Suppose x(q) = 0. Calculate q.
-1, 0, 754
Let w be (-2750)/7500 - ((-4)/10 - 0). Let f(t) be the first derivative of -1/6*t**3 + 0*t**4 - 1/6*t**2 - 18 + w*t**5 + 0*t. Factor f(a).
a*(a - 2)*(a + 1)**2/6
Let j(q) be the first derivative of -q**5/60 + 5*q**4/18 - 25*q**3/18 - 74*q - 6. Let g(x) be the first derivative of j(x). Factor g(s).
-s*(s - 5)**2/3
Factor -331*g + 60 + 11/2*g**2.
(g - 60)*(11*g - 2)/2
Let a(o) be the second derivative of o**6/50 + 231*o**5/100 + 55*o**4 + 2432*o**3/5 + 1152*o**2 - o + 1758. Determine r, given that a(r) = 0.
-60, -8, -1
Let q(s) = -s**2. Let d(o) = 16*o**2 - 4. Suppose -r = 2*r + 2*w + 1, -3*r - 7 = -4*w. Let v(x) = r*d(x) - 12*q(x). Factor v(j).
-4*(j - 1)*(j + 1)
Factor -153/4*y + 3/4*y**2 + 405/2.
3*(y - 45)*(y - 6)/4
Let q be 18/30*-1*-5. Find v such that -5*v**q - 6*v**2 - 4 + 12 + 8*v**3 - v**3 = 0.
-1, 2
Factor 27/2*m**2 - 3/4*m**3 - 177/4*m + 63/2.
-3*(m - 14)*(m - 3)*(m - 1)/4
Suppose 5*p + 3*c = 251 + 73, c + 68 = p. Suppose -27 = 7*v - 48. Factor v - 2*f - f + 69*f**2 - 3*f - p*f**2.
3*(f - 1)**2
Let q be (-4)/(-21)*-3*(11 - 12). Let o be 1 - -3*7/(147/14). Factor 1/7*a**4 + 2/7*a**2 - q*a**o + 4/7*a - 3/7.
(a - 3)*(a - 1)**2*(a + 1)/7
Factor -41*t**3 - 251*t**3 + 5172*t**2 + 6068*t + 10909 - 21861 + 4*t**4.
4*(t - 37)**2*(t - 1)*(t + 2)
Factor 17205125 + f**2 + 20042*f + 11*f**2 - 704*f - 788*f - 7*f**2.
5*(f + 1855)**2
Suppose 0 = 264*w - 241*w + 483. Let z be w/