 o(v) be the second derivative of 7 - 1/50*v**5 + 4/15*v**3 + 4/5*v**2 - 2*v - 1/30*v**4. Factor o(x).
-2*(x - 2)*(x + 1)*(x + 2)/5
Suppose -988 = -38*f + f - 210*f. Let m(j) be the first derivative of -215/3*j**3 - 7*j**5 + 18 - 60*j**2 - 75/2*j**f - 20*j. Determine l, given that m(l) = 0.
-2, -1, -2/7
Let x(q) be the third derivative of 11*q**7/210 - 8*q**6/15 - q**5/5 - 1353*q**2. Factor x(i).
i**2*(i - 6)*(11*i + 2)
Let v(j) = 2*j**2 - 47*j + 254. Let s be v(5). Suppose s + 235 = 38*u. Let u*d + 32 + 1/2*d**2 = 0. What is d?
-8
Suppose 325*f**3 - 160 + 520*f - 1245/2*f**2 - 125/2*f**4 = 0. What is f?
1, 8/5
Let f = -451 + 448. Let w be (-12)/(-63)*(f - -2)/(-2). Determine v, given that 2/7*v**2 + 0 + w*v**3 - 8/21*v = 0.
-4, 0, 1
Let y(b) be the second derivative of b**6/10 - 33*b**5/20 + 9*b**4/4 + 11*b**3/2 - 15*b**2 + 3830*b. Determine i, given that y(i) = 0.
-1, 1, 10
Let a(j) = j**3 + 21*j**2 - 25*j - 41. Let z be a(-22). Suppose 8*d - 25964*d**3 + 0*d**2 + 25929*d**3 + 2*d**2 + z*d**4 = 0. Calculate d.
-2/5, 0, 4/5, 1
Suppose 0 = 3*o + 10*o - 169. What is d in 189*d**4 - 20 + 135*d**4 - 208*d**3 + 204*d**2 - 284*d**4 - 34*d + 5*d**5 + o*d**5 = 0?
-5, -2/9, 1
Solve 9189/5*c**3 - 399*c**4 + 1392*c - 15801/5*c**2 - 180 + 147/5*c**5 = 0 for c.
2/7, 3, 5
Let v be 17 - 35*14/30. Suppose 5*f + 2*w - 2 = 0, 5*f - 4*f = -4*w + 4. Find d such that -v*d - 2/3*d**2 + f = 0.
-1, 0
Suppose 3551 - 829 + 3419 + 378 = 2173*l. Suppose -51/4*i**2 + 156*i + 169 + 1/4*i**l = 0. What is i?
-1, 26
Let f be 1211/1213 - (36/27)/(-4). Let c = 2/1213 + f. Factor -4/3*v**2 + c + 0*v.
-4*(v - 1)*(v + 1)/3
Determine n so that -16/7*n + 12/7*n**2 + 16/7*n**3 - 2 + 2/7*n**4 = 0.
-7, -1, 1
Factor 1/2*t**2 - 64 + 4*t.
(t - 8)*(t + 16)/2
Let t(g) be the third derivative of g**6/30 + 11*g**5/5 + 41*g**4 + 736*g**3/3 - 6115*g**2. Find p, given that t(p) = 0.
-23, -8, -2
Let 480*w - 320 - 100*w**2 + 169*w**5 - 174*w**5 + 23*w**3 - 76*w**3 - 47*w**3 + 45*w**4 = 0. What is w?
-2, 1, 2, 4
Let k = 651 + -595. Let l be (-350)/k*(-5)/25. Determine c so that 7/4*c**2 + l*c**4 - 1/4*c**5 - 9/4*c**3 + 0 - 1/2*c = 0.
0, 1, 2
Let d = 3564725/11 + -324065. Let 28/11 + d*v - 2/11*v**2 = 0. What is v?
-2, 7
Let i(y) = -13*y**2 - 3*y - 14. Let n(b) = -5*b**2 - b - 6. Let l(z) = -3*i(z) + 7*n(z). Let v be l(-1). Factor -1 + v*k - 1/2*k**3 + 1/4*k**4 - 3/4*k**2.
(k - 2)*(k - 1)**2*(k + 2)/4
Find v, given that -658807*v**2 - 9070*v**3 + 4*v**4 + v**4 + 1409750*v**2 + 907585*v**2 + 2454717*v**2 = 0.
0, 907
Let c(s) = s**3 + 2*s**2 - 5*s + 2. Let u(f) = 7*f**2 + 32*f - 12. Let o(l) = -4*c(l) - u(l). Factor o(v).
-(v + 2)**2*(4*v - 1)
Suppose -24*w - 13 = -25*w + y, -5*w - 3*y = -33. Let b be w/((-36)/(-7)) + (-3)/(-12). Factor 0 + 0*p**b - 2/3*p**3 + 2/3*p.
-2*p*(p - 1)*(p + 1)/3
Suppose -623*u - 439 = -834*u - 17. Factor 64 + 60/7*d**u - 288/7*d - 4/7*d**3.
-4*(d - 7)*(d - 4)**2/7
Let c be ((-3)/20)/(56 - (88 - 46) - 149/10). Factor -5/3*w + 0 - c*w**3 + 11/6*w**2.
-w*(w - 10)*(w - 1)/6
Let i(m) = 21*m**2 + 23*m - 84. Let w be i(4). Let v = w - 341. Determine s, given that 0 - 3*s**2 - 3/5*s**v + 0*s = 0.
-5, 0
Let d(a) = -6*a**2 + 2*a + 979. Let j(i) = -5*i**2 + 50*i + 980. Let g(z) = 8*d(z) - 10*j(z). What is n in g(n) = 0?
-4, 246
Let y be ((-12)/(-100))/((-3543)/(-59050)). Factor y*z + 24/13 + 2/13*z**2.
2*(z + 1)*(z + 12)/13
Let h(t) = 274*t - 61101. Let r be h(223). Factor -1/3*c + c**2 - r + 1/3*c**3.
(c - 1)*(c + 1)*(c + 3)/3
Let j = -903 - -1970. Factor -l + 1063*l**2 - 3*l + 48 - j*l**2.
-4*(l - 3)*(l + 4)
Let c(r) = -9*r**3 - 72*r**2 + 615*r. Let n(b) = 4*b**3 + 38*b**2 - 308*b. Let x(i) = 7*c(i) + 15*n(i). Factor x(f).
-3*f*(f - 15)*(f - 7)
Let i(a) be the third derivative of a**8/1344 - a**7/105 - a**6/80 + 7*a**5/30 - 67*a**4/96 + a**3 + a**2 + 944. Factor i(z).
(z - 8)*(z - 1)**3*(z + 3)/4
Let o = -30687/14 + 2196. Let b = -485/126 + o. Solve 4/9 - 2/9*h**2 + b*h = 0.
-1, 2
Let u be 4/(-40) + 0 + 8*316/320 + -3. Solve 4/5*i**3 + 8/5 + u*i + 18/5*i**2 = 0 for i.
-2, -1/2
Let p = -107 - -151. Let c = 61 - p. Let -65*g**2 + 7*g**5 - 4*g**5 + 11*g**2 + 46*g**3 - 24*g**4 + c*g**3 = 0. What is g?
0, 2, 3
Factor 6134*r - 2*r**2 + 402 - 2778*r - 2956*r.
-2*(r - 201)*(r + 1)
Let d(g) = -15*g**2 + 25*g. Let t(l) = -7*l**2 + 13*l. Suppose i + 11 = 4*u - 14, 0 = 4*u - 20. Let h(k) = i*t(k) + 2*d(k). Factor h(j).
5*j*(j - 3)
Let q(v) be the second derivative of 1/12*v**3 + 0 + 1/24*v**4 + 0*v**2 - 90*v. Factor q(c).
c*(c + 1)/2
Let k(w) = 545*w**3 + 2416*w**2 + 59*w - 5. Let m(h) = -1368*h**3 - 6040*h**2 - 148*h + 12. Let t(z) = -12*k(z) - 5*m(z). Solve t(l) = 0.
-4, -2/75, 0
Let d be ((-8)/(-3))/((-36)/54) + 6. Let w(s) = 2*s**2 + 5*s - 16. Let o be w(d). Factor -2*g - 819*g**o - 2 - 2 + 818*g**2 - 2*g.
-(g + 2)**2
Let 8*f**3 - 428*f**2 - f**4 - 3001*f + 37*f**3 + 1081*f + 204 + 2100 = 0. Calculate f.
-4, 1, 24
Let b = -265 + 490. Determine k so that 4*k**3 - 21*k**2 - 112 + b - 19*k - 107 = 0.
-1, 1/4, 6
Suppose -19*s - 108 = -46*s. Let -2*m + 44*m**s - 74 - 112*m**2 - 8*m**3 + 4*m**5 + 118 + 24*m**2 + 6*m = 0. Calculate m.
-11, -1, 1
Let w be 10/((-4 - (-75)/20)*-5). Let t be 4/(-10) - 44/(-10). Let 8 + 3*o**2 + 25*o**3 + 28*o + 35*o**2 + 296*o**5 - 295*o**5 + w*o**t = 0. What is o?
-2, -1
Let v be (-788)/(-198) - (-2316)/114642. Suppose -6/19*r**4 + 44/19*r**3 - 98/19*r**2 + v*r - 16/19 = 0. What is r?
1/3, 1, 2, 4
Let d(c) be the first derivative of -c**4/8 + 38*c**3/3 - 11498. Let d(n) = 0. Calculate n.
0, 76
Let q(s) = -s**2 - s. Let l(t) = t**2 + t + 2. Let j(f) = -40*f**2 - 30*f - 60. Let w(p) = -j(p) - 30*l(p). Let x(d) = 5*q(d) + w(d). Factor x(k).
5*k*(k - 1)
Factor -57/7*s**2 - 17/7*s**3 - 1/7*s**4 - 67/7*s - 26/7.
-(s + 1)**2*(s + 2)*(s + 13)/7
Let i(d) = 14*d**2 - 5898*d - 5928. Let p(l) = -19*l**2 + 7864*l + 7905. Let n(o) = 22*i(o) + 16*p(o). Factor n(a).
4*(a - 984)*(a + 1)
Let z(a) be the second derivative of 0 - 1/2*a**5 - 61*a + 1/21*a**7 - 4/15*a**6 + 0*a**4 + 0*a**2 + 0*a**3. Let z(m) = 0. Calculate m.
-1, 0, 5
Let 4/5*x**2 + 0 + 2/5*x - 4/5*x**4 + 0*x**3 - 2/5*x**5 = 0. Calculate x.
-1, 0, 1
Suppose -x + 28 = -2*f + 10, -3*x - 2*f + 22 = 0. Suppose -y - 4*r - x = -24, -r - 5 = -4*y. Find h, given that -5*h**y + 46*h - 125 + 16*h - 12*h = 0.
5
Let g(n) be the first derivative of 142 + 115*n**3 + n**5 + 125/4*n**4 + 335/2*n**2 + 110*n. Suppose g(t) = 0. Calculate t.
-22, -1
Suppose g = 5*q + 22, -2*g - 2*g = q - 4. Suppose 0 = 3*r - g*l - 10, -5*l = 5*r - l - 24. Solve -3/2*i**r + 3 - 3/2*i**2 + 9/2*i**3 - 9/2*i = 0.
-1, 1, 2
Let i = -50 - -71. Suppose -41 - i = -2*g. Factor 9*o + g*o + 4*o**2 + 120 - 20.
4*(o + 5)**2
Let c(x) be the third derivative of 71*x**5/30 + x**4/15 + 2458*x**2 - 2*x. Factor c(k).
2*k*(355*k + 4)/5
Let p(d) = 103*d**3 + 476*d**2 - 645*d + 90. Let l(q) = 208*q**3 + 956*q**2 - 1290*q + 180. Let g(u) = -4*l(u) + 9*p(u). Let g(s) = 0. Calculate s.
-6, 3/19, 1
Suppose -117 = 4*d - 6*d - 37*d. Let x(v) be the first derivative of 2/3*v**d - 2/15*v**5 - 25 + 0*v**4 - 2/3*v**2 + 0*v. Factor x(t).
-2*t*(t - 1)**2*(t + 2)/3
Let z = -265 + 373. Let l = z - 105. Let 3*a**2 + a**3 + l*a + 4*a - 5*a = 0. Calculate a.
-2, -1, 0
Suppose -252 = 5*u + 1153. Let k = 281 + u. Factor 2/9*i + k*i**3 - 2/9*i**5 - 4/9*i**4 + 4/9*i**2 + 0.
-2*i*(i - 1)*(i + 1)**3/9
Let b = 67978/3 + -271909/12. Factor -1/2*o + 3/4 - b*o**2.
-(o - 1)*(o + 3)/4
Find p such that 18*p**2 - 53*p - 3*p**4 - 15*p + 7*p**3 + 40*p - 24 = 0.
-2, -2/3, 2, 3
Let m(n) = 2*n**2 + 3*n. Let d(k) = 18*k**2 + 1082*k - 138338. Let f(q) = 2*d(q) - 20*m(q). Determine i so that f(i) = 0.
263
Let z(b) be the third derivative of b**9/241920 - b**8/23040 + b**6/640 - b**5/30 - 3*b**3/2 + 61*b**2. Let w(o) be the third derivative of z(o). Factor w(m).
(m - 3)*(m + 1)*(2*m - 3)/8
Solve -288 - 3/7*t**3 - 1002/7*t + 1011/7*t**2 = 0 for t.
-1, 2, 336
Let q(j) = j**3 - 14*j**2 - j - 27. Let z be q(7). Let x = z + 1511/4. Factor -3/4*h**2 + x - 2*h.
-(h + 3)*(3*h - 1)/4
Let o(m) be the second derivative of -m**3 - 1/50*m**5 + 3/10*m**4 + 81*m + 0 + 7/5*m**2. Factor o(x).
-2*(x - 7)*(x - 1)**2/5
Let w(i) be the first derivative of i**8/1680 - i**6/360 + 2*i**3/3 + 134. Let f(z) be the third derivative of w(z). 