i) = i**2 - 34*i + 147. Let n be p(u). Factor 1/4*k**n + 1/2*k - 3/4.
(k - 1)*(k + 3)/4
Let h be ((-1089)/117 - -9)*(1479/(-18) - -2). Factor -1369/6*f**2 + h*f - 2/3.
-(37*f - 2)**2/6
Let y(u) be the second derivative of u**6/10 + 3*u**5/20 - 1407*u. Factor y(h).
3*h**3*(h + 1)
Let y(q) = q**3 - 65*q**2 + 429*q - 1332. Let h be y(58). Find k such that 1/2*k**2 + 3/2 - h*k = 0.
1, 3
Let a be (27/(-297) + 62/(-44))*(-10)/18. Let i(h) be the first derivative of -18 + a*h**2 + 1/18*h**3 + 25/6*h. Suppose i(l) = 0. What is l?
-5
Let t(r) be the third derivative of 12*r**2 + 0*r + 0 + 1/20*r**5 + 9/2*r**3 + 3/4*r**4. Let t(j) = 0. Calculate j.
-3
Factor 0 - 5/4*y**4 + 235/2*y**2 + 0*y + 225/4*y**3.
-5*y**2*(y - 47)*(y + 2)/4
Let j be (-6)/96*(797 - 981). Factor -1/2*g**3 + 15/2*g**2 + 5 - j*g - 1/2*g**4.
-(g - 2)*(g - 1)**2*(g + 5)/2
Determine s, given that -32/17*s**2 - 12/17 - 50/17*s + 30/17*s**3 = 0.
-3/5, -1/3, 2
Factor -238572/7 + 8460/7*u - 75/7*u**2.
-3*(5*u - 282)**2/7
Let n(q) be the third derivative of q**6/840 - q**5/42 - 50*q**4/7 - 11232*q**2. Factor n(g).
g*(g - 40)*(g + 30)/7
Let c be -2*1 + (-60)/(-12). Let h = 15 - 10. Factor -h*y - 10*y**2 - 2*y**3 + 5*y + 5*y**4 - c*y**3.
5*y**2*(y - 2)*(y + 1)
Solve 80 - 86*r**2 - 208*r**4 + 392*r - 32*r**5 + 30*r**3 + 906*r**2 - 32 = 0 for r.
-6, -2, -1/4, 2
Let y(k) = -5*k**3 - 47*k**2 + 130*k - 87. Let t(a) = 22*a**3 + 234*a**2 - 648*a + 434. Suppose 0 = 4*s - 26 - 30. Let u(p) = s*y(p) + 3*t(p). Factor u(f).
-4*(f - 7)*(f - 3)*(f - 1)
Find i, given that 12*i + 432/5 + 2/5*i**2 = 0.
-18, -12
Suppose -153*g = -162*g - 72. Let n be (g/80*5)/((-3)/18). Factor -3/5*m**2 + 0*m + 0 + 1/5*m**4 - 2/5*m**n.
m**2*(m - 3)*(m + 1)/5
Factor -2/7*p**2 - 33800/7 - 520/7*p.
-2*(p + 130)**2/7
Let f(w) = 2*w + 28. Let x = -60 + 51. Let k be f(x). Determine g, given that k*g**4 - 9*g**3 - 103*g**5 + 2*g**4 + 100*g**5 = 0.
0, 1, 3
Suppose -5/4*u**2 - 9/2 - 47/4*u = 0. Calculate u.
-9, -2/5
Suppose 0 = 9*c + 55 - 109. Factor 3*k**5 + 36*k**4 - 6*k - k**5 - c*k**3 - 40*k**4 + 6*k.
2*k**3*(k - 3)*(k + 1)
Let u(s) = -7*s**2 - 231*s + 849. Let m(i) = -12*i**2 - 478*i + 1697. Let f(w) = 3*m(w) - 5*u(w). Suppose f(h) = 0. Calculate h.
-282, 3
Let f = 8963 - 349555/39. Let o(q) be the first derivative of -8 + 2/13*q - f*q**3 + 0*q**2. Determine w, given that o(w) = 0.
-1, 1
Let x(a) be the first derivative of -a**5/20 + 9*a**4 - 4879*a**3/12 - 5661*a**2/2 + 6845*a - 1183. Factor x(u).
-(u - 74)**2*(u - 1)*(u + 5)/4
Let o be ((-3400)/153)/50 + 46/9. Solve 100/3*a**3 + o*a**5 + 20*a**4 + 10*a + 4/3 + 80/3*a**2 = 0 for a.
-1, -2/7
Let s = -465797/10275 - 1/3425. Let p = 979/21 + s. Factor 3/7*i**2 + 0 + 6/7*i - p*i**3.
-3*i*(i - 1)*(3*i + 2)/7
Factor -2/13*b + 0 - 2222/13*b**2.
-2*b*(1111*b + 1)/13
Let a(y) be the second derivative of -55*y + 0*y**2 - 1/21*y**3 + 2 + 11/126*y**4 + 2/105*y**5. Factor a(n).
2*n*(n + 3)*(4*n - 1)/21
Let n be ((10 + -16)/(-36))/(1 + (-6)/9). Let i(o) be the first derivative of 6*o**2 + 6 - 12*o**3 + 0*o + n*o**6 - 18/5*o**5 + 39/4*o**4. Factor i(w).
3*w*(w - 2)**2*(w - 1)**2
Suppose 23*f - 123 = -18*f. Let -93/5*b**f + 198*b**2 + 600 - 780*b + 3/5*b**4 = 0. Calculate b.
1, 10
Let d(s) = s**3 + 18*s**2 + 79*s + 6. Let g be d(-8). Let i(n) be the first derivative of 5/9*n**3 + g + 5/12*n**2 + 0*n + 5/24*n**4. Let i(t) = 0. Calculate t.
-1, 0
Suppose -a - 4*s - 9*s - 441 = 4*s, 97 = -7*a - 4*s. Let g(r) = r**2 - 4*r - 3. Let p be g(5). Find o, given that -a + 1/4*o**p + 0*o = 0.
-2, 2
Let b(v) be the first derivative of 3*v**4/4 + 8*v**3 + 6*v**2 - 144*v - 524. Find n such that b(n) = 0.
-6, -4, 2
Let t(u) be the first derivative of u**4/6 - 142*u**3/9 + 1147*u**2/3 + 2738*u - 899. Factor t(l).
2*(l - 37)**2*(l + 3)/3
Let n(s) be the third derivative of 1/480*s**6 + 1/12*s**4 - 50*s**2 - 1/40*s**5 + 0*s**3 + 0 + 0*s. Factor n(p).
p*(p - 4)*(p - 2)/4
Let d(o) be the second derivative of o**4/4 - 7*o**3/2 - 180*o**2 - 859*o. Determine c, given that d(c) = 0.
-8, 15
Let v = 31210 - 31201. Factor -v*h**3 - 15/2 + 3/2*h**4 + 9*h + 6*h**2.
3*(h - 5)*(h - 1)**2*(h + 1)/2
Let a be (-60)/40 + 146/4*-1. Let i be (-2)/(-19) - a/(-361). Determine g, given that -4/5*g**2 - 6/5*g**3 + 0 - 2/5*g**4 + i*g = 0.
-2, -1, 0
Suppose 43*r - 43*r + 2*r - 8 = 0. Factor 1/2*k - 7/6*k**2 + 5/6*k**3 - 1/6*k**r + 0.
-k*(k - 3)*(k - 1)**2/6
Let r(x) be the first derivative of -x**4/4 + 11*x**3/3 - 7*x**2 + 10*x + 77. Let u(i) = i**2 - i + 1. Let z(o) = r(o) - 6*u(o). Let z(l) = 0. Calculate l.
1, 2
Let s(v) = -38*v + 1713. Let i be s(45). Let -18/5*r**2 + 0*r + 2/5*r**4 + 0 + 0*r**i = 0. Calculate r.
-3, 0, 3
Suppose -63 - 7 = 5*q. Let w be (-14)/49 - 18/q. Factor -2*a**4 + 6*a**2 - 7 - 16*a**3 + 13*a**3 - w + 7*a**3 - 8*a.
-2*(a - 2)**2*(a + 1)**2
Let p(n) be the first derivative of 3/2*n + 3/16*n**2 + 31 - 3/32*n**4 - 1/2*n**3. Let p(h) = 0. What is h?
-4, -1, 1
Let m(z) be the second derivative of z**6/30 - z**4/6 + 87*z**2/2 - 40*z - 2. Let n(p) be the first derivative of m(p). Factor n(d).
4*d*(d - 1)*(d + 1)
Let d(r) = -2*r**3 - 2*r**2 + 3*r + 6. Let g be d(-4). Let q = g + -87. Factor 1547 + 10*z**2 - 1547 + 2*z + 8*z**4 + 16*z**q.
2*z*(z + 1)*(2*z + 1)**2
Suppose 147/4 + 193/4*r + 45/4*r**2 - 1/4*r**3 = 0. What is r?
-3, -1, 49
Let -7574 - 2876*d - 1726395 + 186236 - d**2 - 520111 = 0. What is d?
-1438
Suppose 0 = 4*v - v + 282. Let k = v + 96. Factor 57 + 3*x**4 + 830*x - x**3 + 55*x**3 + 291*x**k - 398*x + 135.
3*(x + 1)**2*(x + 8)**2
Let x(m) be the second derivative of -7*m**6/450 - 83*m**5/75 + 8*m**4/5 + 271*m**3/6 - 12*m + 3. Let q(l) be the second derivative of x(l). Solve q(v) = 0.
-24, 2/7
Let h be (153/(-27))/17*6 - 26/(-12). Solve -h*t**2 + 0*t + 1/6*t**5 - 1/2*t**4 + 0 + 1/2*t**3 = 0 for t.
0, 1
Let v be 5/(0 - (-30)/42). Factor 1057*n**2 + 1064*n**2 - n**4 - 2103*n**2 - v*n**3.
-n**2*(n - 2)*(n + 9)
Let h(l) = -27*l**2 + 80*l - 392. Let x(j) = -30*j**2 + 81*j - 393. Let b(y) = -9*h(y) + 8*x(y). Let b(z) = 0. Calculate z.
8, 16
Let k(l) be the third derivative of -l**9/5040 - l**8/1008 - l**7/630 + l**5/30 + 11*l**4/24 - 54*l**2. Let t(j) be the third derivative of k(j). Factor t(d).
-4*d*(d + 1)*(3*d + 2)
Let d(r) = 2*r**3 - 14*r**2 + 5*r + 11. Let k be d(9). Let a = k + -378. Factor 4/3*n**a + 0 + 2/3*n**3 + 0*n.
2*n**2*(n + 2)/3
Let q = 11126/3 - 3708. Let a(b) be the first derivative of 12 + 2/9*b**3 - 1/6*b**4 + 1/3*b**2 - q*b. Factor a(r).
-2*(r - 1)**2*(r + 1)/3
Factor 3 - 36*a**2 - 60*a - 12*a**3 - 8*a**2 - 4 - 7*a**2 - 11.
-3*(a + 2)**2*(4*a + 1)
Suppose 5*b + 13 = 3, -3*a + 16 = -5*b. Let k(m) = 12*m**3 - 19*m**2 + 2*m. Let p(c) = -c**3 + 2*c**2. Let o(r) = a*k(r) + 22*p(r). Solve o(v) = 0.
-2, -1, 0
Let j(o) = 21*o**2 - 21*o + 2. Let l be j(2). Suppose -35*r = -l*r + 18. Let -14/19*h**4 + 0 - 36/19*h**3 - 16/19*h - 2/19*h**5 - 40/19*h**r = 0. Calculate h.
-2, -1, 0
Factor 1/3*k**3 - 16/3*k**2 - 14/3 + 29/3*k.
(k - 14)*(k - 1)**2/3
Suppose 5/6*u**4 - 20/3*u**3 + 10/3*u - 50/3 + 25/2*u**2 = 0. What is u?
-1, 2, 5
Suppose 0*n + 3/2*n**5 + 0 - 57/2*n**3 - 3*n**4 + 30*n**2 = 0. What is n?
-4, 0, 1, 5
Let x(s) = -195*s**4 - 95*s**3 + 455*s**2 - 865*s + 470. Let n(l) = -20*l**4 - l**3 - l**2 + l - 2. Let g(d) = 10*n(d) - x(d). Suppose g(q) = 0. Calculate q.
1, 2, 7
Let k(w) be the third derivative of 5*w**7/168 - w**6/12 + w**5/40 + w**4/12 + w**3/24 - 4*w**2 + 889*w. Factor k(a).
(a - 1)**2*(5*a + 1)**2/4
Determine u so that -194*u**2 - 1936*u**4 + 292 - 4*u - 172*u**5 + 257 + 1484*u**5 - 1278*u**3 - 549 = 0.
-1/4, -1/41, 0, 2
Let f(w) be the third derivative of -w**5/20 + 183*w**4/2 - 731*w**3/2 + 2253*w**2. Factor f(y).
-3*(y - 731)*(y - 1)
Let y(p) = -p**2 - 24*p - 92. Let x be y(-19). Find n, given that -5*n**5 + 2*n**x + 2*n**2 + 3*n**5 + 3674*n**4 - 3676*n**4 = 0.
-1, 0, 1
Solve -128 - 7*c - 14637*c**2 - 23*c - 2*c + 14635*c**2 = 0 for c.
-8
Let j(f) be the third derivative of -f**6/300 + 14*f**5/75 - 9*f**4/20 + 241*f**2 + 1. Find x, given that j(x) = 0.
0, 1, 27
Suppose -29*i = 86*i + 25*i. Let n(t) be the third derivative of 0*t**3 + 0 + 1/960*t**6 - 7*t**2 - 1/192*t**4 + 0*t + i*t**5. Solve n(f) = 0.
-1, 0, 1
Solve 3438/11*a**3 + 250/11*a**4 + 594*a - 1350*a**2 + 4/11*a**5 + 0 = 0.
-