 Let w(o) = o**5 - o**4 - 2*o**3 + o**2 - o + 1. Let j(s) = n(s) - 6*w(s). Factor j(i).
3*(i - 9)**3*(i - 5)*(i + 1)
Let o(t) be the second derivative of t**7/21 - 9*t**6/20 + 37*t**5/40 + 13*t**4/8 - 41*t**3/12 - 3*t**2 - 14*t - 37. Solve o(x) = 0 for x.
-1, -1/4, 1, 3, 4
Let b = -39634 + 39638. Factor -2/11*d**5 + 0*d**2 - 2/11*d**3 + 0 + 0*d + 4/11*d**b.
-2*d**3*(d - 1)**2/11
Determine g so that -14253*g**3 + 128*g**2 + 560*g + 14249*g**3 + 134 + 442 = 0.
-2, 36
What is w in 598/3*w + 592 + 2/3*w**2 = 0?
-296, -3
Let i = 95355743/87926 - -2/43963. Let m = i - 1075. Find f, given that 9/2 - 15/4*f**5 - 3/4*f - m*f**3 + 37/2*f**4 - 37*f**2 = 0.
-1, -2/5, 1/3, 3
Let q(s) = 8*s**2 - 2*s - 1. Let t(d) = -46*d**2 - 5128*d + 3302456. Let j(v) = 6*q(v) + t(v). Factor j(o).
2*(o - 1285)**2
Factor 3/2*i**2 - 13 - 1/2*i**4 - 37/2*i + 13/2*i**3.
-(i - 13)*(i - 2)*(i + 1)**2/2
Let n = -2/31101 + 155513/124404. Determine p, given that -n*p**5 - 18 - 51*p + 59/4*p**3 + 2*p**4 - 19/2*p**2 = 0.
-2, -2/5, 3
Let p(d) be the third derivative of d**7/630 - 413*d**6/360 + 3151*d**5/10 - 71415*d**4/2 - 146004*d**3 - d**2 + 30*d. Factor p(n).
(n - 138)**3*(n + 1)/3
Let o(i) be the first derivative of -3/16*i**4 - 1/20*i**5 + 22 + 1/3*i**3 + 0*i + 0*i**2. Determine u so that o(u) = 0.
-4, 0, 1
Factor -88/7 - 40/7*n + 2/7*n**2.
2*(n - 22)*(n + 2)/7
Factor 9*z**3 - 380*z + 61*z**2 - 7*z**3 + 39*z**2 + 55*z**2 - 137*z**2.
2*z*(z - 10)*(z + 19)
Let s = -6/54085 - -130507171/594935. Let y = s + -219. Factor -4/11*j**2 - y*j**3 + 2/11*j**5 + 2/11*j + 2/11 + 2/11*j**4.
2*(j - 1)**2*(j + 1)**3/11
Let w = -66047 + 66050. Let -w - 1/2*n**2 - 7/2*n = 0. What is n?
-6, -1
Solve 718/3*u + 178 + 2/3*u**3 + 62*u**2 = 0 for u.
-89, -3, -1
Suppose -4*f - 4*l = 484, 815 = -5*f + l + 192. Let i = f + 993/8. Solve 0*j + i*j**5 + 0*j**2 + 0*j**3 - 1/4*j**4 + 0 = 0.
0, 2
Factor 488/9 + 4/9*r**2 - 28*r.
4*(r - 61)*(r - 2)/9
Let q(d) be the first derivative of 4*d**5/45 - 29*d**4/3 + 680*d**3/27 - 748. Find v, given that q(v) = 0.
0, 2, 85
Let m(f) be the second derivative of f**6/75 + 3*f**5/50 + f**4/30 - f**3/5 - 2*f**2/5 - 35*f - 4. Factor m(i).
2*(i - 1)*(i + 1)**2*(i + 2)/5
Let f(s) be the third derivative of -s**6/720 + 59*s**5/180 - 51*s**4/16 + 19*s**3/2 - 2*s**2 - 800. Let f(i) = 0. Calculate i.
1, 3, 114
Let d(l) = -19*l - 114. Let n be d(-6). Let c(h) be the third derivative of 1/300*h**6 + 0 + n*h**4 + 0*h + 4/15*h**3 - 1/50*h**5 - 12*h**2. Factor c(o).
2*(o - 2)**2*(o + 1)/5
Factor 15*n**2 + 4496406 - n**2 + 54824398 - 5*n**2 - 5*n**2 + 30808*n.
4*(n + 3851)**2
Let -176/7*i + 1/7*i**2 + 0 = 0. What is i?
0, 176
Let u(f) be the third derivative of -f**8/1344 - f**7/840 + f**6/480 + f**5/240 - 5*f**2 + 199*f. Factor u(l).
-l**2*(l - 1)*(l + 1)**2/4
Determine c, given that 61/9*c**3 + 5/9*c**5 + 37/9*c**4 - 10/3*c + 0 - 1/9*c**2 = 0.
-5, -2, -1, 0, 3/5
Let a be -8*90/(-384)*12/15. Let x be 14/12 - 16/24. Factor 1/2*r**3 - 5/2*r - a*r**2 + x*r**4 - 1.
(r - 2)*(r + 1)**3/2
Let z(i) be the third derivative of i**6/40 + 42*i**5 + 29400*i**4 + 10976000*i**3 + 412*i**2 - i + 1. Determine t so that z(t) = 0.
-280
Let k = 5/3151 - -56693/15755. Factor -12/5*z**3 - 12/5*z - 3/5 - 3/5*z**4 - k*z**2.
-3*(z + 1)**4/5
Factor 321*f**2 - 40201955*f - 3*f**3 + 40201955*f.
-3*f**2*(f - 107)
Let h = 1105 - 1102. Let t(g) be the second derivative of 0*g**h + 17*g - 9/230*g**5 + 1/69*g**4 + 0*g**2 + 0. Factor t(w).
-2*w**2*(9*w - 2)/23
Let r(v) be the first derivative of 0*v - 2/65*v**5 + 0*v**3 + 4/13*v**2 - 39 - 3/26*v**4. Factor r(u).
-2*u*(u - 1)*(u + 2)**2/13
Suppose 0*l + 2*b = 2*l + 2, 2*b + 1 = 3*l. Suppose -q - 33 = -l*t, -2*q + 55 = 5*t + q. Determine a, given that -4 - 2*a**2 - 4 - a + t*a = 0.
1, 4
Let v be 2 - (182000/45)/7. Let w = v - -576. Factor w*c**2 + 0 + 2/3*c.
2*c*(c + 3)/9
Let n(u) be the first derivative of 20/3*u**3 + 16*u + 44/3*u**2 - 87 + 2/15*u**5 + 3/2*u**4. Factor n(t).
2*(t + 2)**3*(t + 3)/3
Let d = 5/8 + -39/88. Let l = -3622/25 - -41042/275. Factor -d*v**3 - 56/11*v + 20/11*v**2 + l.
-2*(v - 6)*(v - 2)**2/11
Let m(o) = 2*o**2 + 82*o + 372. Let z be m(-5). Let d(k) be the second derivative of 6*k**3 + 4*k + 0 - 3/2*k**4 + 3/20*k**5 - z*k**2. Let d(l) = 0. What is l?
2
Suppose 6*j - 8*j = v - 24, v + 86 = 8*j. Factor -2/7*k**v - 32/7 - 20/7*k.
-2*(k + 2)*(k + 8)/7
Let d(u) be the second derivative of -u**4 + 3572*u**3/3 + 2384*u**2 + 2797*u. Factor d(c).
-4*(c - 596)*(3*c + 2)
Let l(v) be the second derivative of v**4/48 + 13*v**3/4 + 1521*v**2/8 + 994*v. Factor l(o).
(o + 39)**2/4
Let g(h) be the first derivative of h**6/72 - h**5 - 125*h**4/24 + 28*h**3 + 2. Let d(l) be the third derivative of g(l). Let d(w) = 0. Calculate w.
-1, 25
Let g(q) be the third derivative of 0*q**4 + 0 + 0*q + 0*q**3 + 1/105*q**5 - 97*q**2 - 1/168*q**6 + 1/1470*q**7. What is s in g(s) = 0?
0, 1, 4
Let v(w) be the third derivative of 0*w + 11/12*w**4 - 1/30*w**5 + 75*w**2 + 0 + 4*w**3. Suppose v(b) = 0. What is b?
-1, 12
Let p be ((-45)/10 + 6)/((-3)/(-36)). Suppose p*b**3 - 15*b - 100*b - 23*b**2 - 13*b**3 - 17*b**2 + 150 = 0. Calculate b.
-3, 1, 10
Let y = -724 - -797. Factor 11*z + 21*z - y*z**2 + 256 + 40*z**2 + 34*z**2.
(z + 16)**2
Let r(a) be the first derivative of -3*a**5/5 + 39*a**4 - 1014*a**3 + 13182*a**2 - 85683*a + 522. Let r(u) = 0. What is u?
13
Suppose -175*l = 97*l - 1088. Let y(w) be the second derivative of 2/9*w**l + 0 + 1/30*w**5 + 5/9*w**3 + 20*w + 2/3*w**2. Factor y(s).
2*(s + 1)**2*(s + 2)/3
Suppose 0 = 2*w + 2*a - 106, 3*w - 160 = 2*a - 6*a. Let k be 112/w - (2 + (-48)/26). Factor 2*g**3 + 4*g**4 + 2*g**k - 6*g**4 + 4*g + 0*g - 6*g.
-2*g*(g - 1)**2*(g + 1)
Let c be -2 + (-3)/(-9)*63/6. Let d be (24/(-18))/(2 + 3 + (-632)/120). Determine v so that -5/4*v + 3/4*v**3 - 7/4*v**4 - c + 17/4*v**2 - 1/2*v**d = 0.
-3, -2, -1/2, 1
Factor -756*c**2 + 1512*c**2 - 761*c**2 + 68*c + 930 + 57*c.
-5*(c - 31)*(c + 6)
Let x be (5/(-12))/(53/(-424)). Let o(c) be the first derivative of 5/2*c**2 - 5/4*c**4 + 18 - x*c**3 + 10*c. Suppose o(f) = 0. What is f?
-2, -1, 1
Suppose 350 = 3*y - j, 0 = 8*y - 4*y + 3*j - 471. Let q be (-9)/(-1) + y/(-13). Solve 8/5*g**2 - 4/5*g**4 + q*g**3 - 4/5 + 0*g = 0 for g.
-1, 1
Let h(f) be the first derivative of f**5/100 - f**4/20 + f**3/10 - f**2/10 - 4*f - 130. Let d(l) be the first derivative of h(l). Factor d(j).
(j - 1)**3/5
Let j(h) = -h**3 + 59*h**2 - 151*h + 75. Let z(c) = 329 + 650*c**2 - 762*c - 898*c + 496 - 10*c**3. Let y(b) = 65*j(b) - 6*z(b). Solve y(t) = 0 for t.
-15, 1
Suppose -20*z + 47 + 128 - 55 = 0. Find b such that 39/2*b - z - 9/2*b**2 = 0.
1/3, 4
Let r(d) be the first derivative of 16/9*d**4 - 16/27*d**3 + 2/3*d**6 - 28/15*d**5 + 0*d**2 - 32 + 0*d. Factor r(x).
4*x**2*(x - 1)*(3*x - 2)**2/9
Let x = -494 + 1019. Let p = 527 - x. Factor -2/7*r**p + 12/7 - 2/7*r.
-2*(r - 2)*(r + 3)/7
Let n be 1/(152/16) - (-110)/38. Factor 7*g + 12 + 33 + 556*g**n + 88*g - 551*g**3 + 55*g**2.
5*(g + 1)**2*(g + 9)
Factor 3250*x + 34*x**4 + 1482*x**2 + 1654*x**2 - 8758 + 364*x**2 - 2*x**4 + 1258 + 720*x**3 - 2*x**5.
-2*(x - 30)*(x - 1)*(x + 5)**3
Suppose 71*w**3 + 9*w**3 - 300*w**5 - 14*w**3 + 30*w**4 + 9*w**2 + 298*w**5 + 25*w**2 = 0. What is w?
-1, 0, 17
Factor 11040/7*p + 4/7*p**3 + 396/7*p**2 + 8464.
4*(p + 7)*(p + 46)**2/7
Suppose 44 = 4*b - 4*s, -19*b + 17*b + 18 = 2*s. Suppose -b = o - 4*o - q, -2 = 3*o - 2*q. Let -9/7*k**3 - 9/7*k**o - 3/7*k**4 - 3/7*k + 0 = 0. Calculate k.
-1, 0
Determine p so that 93*p**2 + 142*p**2 + 5*p + 117*p**2 - 287*p**2 = 0.
-1/13, 0
Let y(r) = 45*r**3 - 471*r**2 + 495*r - 69. Let u(j) = -11*j**3 + 118*j**2 - 124*j + 17. Let x(k) = 13*u(k) + 3*y(k). Let x(d) = 0. What is d?
1/8, 1, 14
Let t(s) be the first derivative of -3/4*s**3 - 63/4*s + 24*s**2 + 5. Factor t(y).
-3*(y - 21)*(3*y - 1)/4
Let t(w) be the third derivative of 5*w**8/672 + 7*w**7/60 - 7*w**6/24 - 19*w**5/60 + 65*w**4/48 - 11*w**3/12 - 183*w**2 + 4. Determine p, given that t(p) = 0.
-11, -1, 1/5, 1
Let q be (-1911)/(-6370)*4/3. Factor 28/5 + q*u**2 + 18/5*u.
2*(u + 2)*(u + 7)/5
Let a(n) = -n + 9. Let f be a(14). Let y(q) = -q**2 + 17*q + 44. Let g(w) = -w**2 - 3*w + 1. Let b(x) = f*y(x) + 10*g(x). Factor b(i).
-5*(i + 2)*(i + 21)
Let r(f) be the sec