3577. Factor n(u).
-2*u*(u + 2)*(u + 159)/3
Let b = -4 + 6. Let j = 1515726/5 - 303145. Find d, given that 1 + 6/5*d + j*d**b = 0.
-5, -1
Determine c, given that -318/11*c**4 + 0 - 2/11*c**5 + 0*c**2 + 0*c + 320/11*c**3 = 0.
-160, 0, 1
Suppose 572 = -57*w + 101*w. Factor -2*s**2 - 7 - 3*s - 34*s - w*s - 24*s - 133.
-2*(s + 2)*(s + 35)
Let n = -5114/7 - -727. Let a = n - -275/28. Solve a*w**2 + 15*w + 5 = 0.
-2, -2/5
Let g(m) = 2*m**3 + m**2 - m - 1. Let l be -4 + (84/49)/(6/56). Let w(c) = 2*c**4 + 4*c**3 + 60*c**2 + 8*c - 62. Let k(z) = l*g(z) - w(z). Factor k(s).
-2*(s - 5)**2*(s - 1)*(s + 1)
Let i(s) = 4*s - 16. Let g be i(-19). Let t = g - -112. Factor 3*n**2 + 2*n**2 + 25 + 50*n - t*n + 0*n**2.
5*(n + 1)*(n + 5)
Let n(w) be the third derivative of 0 + 0*w**3 + 3*w**2 + 22*w + 1/54*w**5 + 1/54*w**4. What is x in n(x) = 0?
-2/5, 0
Let r(j) be the second derivative of -30/17*j**2 - j - 1/51*j**3 + 6 + 1/102*j**4. Factor r(x).
2*(x - 6)*(x + 5)/17
Let o = 154 + -85. Suppose 851*n + 22 = 862*n. Let 2*c**4 - o - n*c**3 - 73 + 142 + 24*c - 16*c**2 = 0. What is c?
-3, 0, 2
Let p(w) be the first derivative of 4*w**6/3 + 328*w**5/5 + 1909*w**4/2 + 3116*w**3 + 3249*w**2 + 611. Factor p(n).
2*n*(n + 19)**2*(2*n + 3)**2
Let n = 489616 - 489602. Let -11 - n*l**2 - 53/2*l + 3/2*l**3 = 0. Calculate l.
-1, -2/3, 11
Let b be (-19 + 5 + 0)/(2/(-1)). Determine q so that -16*q**5 - 9*q**4 - 3*q**4 + b*q**5 + 23*q**3 + 36*q + 54*q**2 + 8 = 0.
-1, -2/3, 2
Determine i, given that 3976 - 4*i**3 - 407*i + 2403*i + 18163700*i**2 - 18165684*i**2 = 0.
-497, -1, 2
Let v(a) = -93771*a**3 + 41292*a**2 - 5829*a + 438. Let h(u) = -9377*u**3 + 4129*u**2 - 583*u + 43. Let k(b) = -21*h(b) + 2*v(b). Factor k(s).
3*(5*s - 1)*(25*s - 3)**2
Let m(d) = d**2 - 62*d + 305. Let w be m(57). Let t(k) be the first derivative of 5/2*k**4 + k**5 - 13 - 5*k**3 + w*k - 10*k**2. Find b such that t(b) = 0.
-2, 1
Let l(b) be the second derivative of b**5/80 - b**4/16 + b**3/8 - 255*b**2/2 + 73*b + 1. Let o(u) be the first derivative of l(u). Determine w so that o(w) = 0.
1
Let y(m) be the third derivative of 260*m**2 + 0*m**5 + 1/40*m**6 + 0*m + 0 + 0*m**4 + 1/560*m**7 + 0*m**3. Solve y(k) = 0.
-8, 0
Determine r, given that -57*r + 8*r**2 + 4796 - r**2 - 12*r**2 - 4652 + 8*r**2 = 0.
3, 16
Suppose 14*l = 24 + 32. Factor 10*p**2 + 0*p**3 - 52 + p**2 - l*p + 41*p**2 + 4*p**3.
4*(p - 1)*(p + 1)*(p + 13)
Let t(u) be the first derivative of 3*u**5/20 - 7*u**4/4 - 5*u**3 + 24*u**2 + 65*u - 13. Let b(q) be the first derivative of t(q). Factor b(d).
3*(d - 8)*(d - 1)*(d + 2)
Let m = -30 + 66. Let b(a) = -a**2 - 7*a - 4. Let w be b(-6). Factor -w*p**4 - 21*p**3 + m*p**3 - 3*p**4.
-5*p**3*(p - 3)
Let r(z) be the first derivative of 5*z**4/4 + 130*z**3/3 - 455*z**2/2 - 580*z + 2295. Solve r(n) = 0 for n.
-29, -1, 4
Let q(g) be the first derivative of 2*g**6/21 + 464*g**5/35 + 228*g**4/7 - 8*g**3/21 - 458*g**2/7 - 456*g/7 + 1921. Determine r so that q(r) = 0.
-114, -1, 1
Let a(q) be the second derivative of q**5/30 - 13*q**4/18 + 32*q**3/9 - 20*q**2/3 - 809*q. Let a(s) = 0. What is s?
1, 2, 10
Let m(b) be the first derivative of b**7/525 - b**5/25 - 2*b**4/15 - b**3/5 + 5*b**2/2 + 270. Let p(r) be the second derivative of m(r). Solve p(f) = 0.
-1, 3
What is l in -143/4*l + 1/4*l**2 + 71/2 = 0?
1, 142
Let o(w) be the second derivative of 2*w**6/15 - 136*w**5/5 + 1974*w**4 - 141376*w**3/3 - 1038230*w**2 + 4276*w. Solve o(z) = 0.
-5, 47
Suppose 22 = 4*f - 2. Suppose -f*i = -i - 40. Let x(u) = 15*u**2 - 180*u + 540. Let g(s) = 5*s**2 - 60*s + 180. Let d(n) = i*g(n) - 3*x(n). Factor d(z).
-5*(z - 6)**2
Let x = -564 + 579. Factor -3*z + 51 - x + 10*z**2 - 18*z**2 + 5*z**2 + 6*z.
-3*(z - 4)*(z + 3)
Let a(m) be the first derivative of m**5/420 + m**4/24 - 22*m**3/21 - 133*m**2/2 + 49. Let h(c) be the second derivative of a(c). Find s such that h(s) = 0.
-11, 4
Suppose 0 = -3*t - f + 30, -3*t + 20 + 10 = 4*f. Suppose t*o - 5*o + 0*o = 0. What is v in 2/5*v**3 - 6/5*v**2 + 4/5*v + o = 0?
0, 1, 2
What is u in -3*u**4 - 42*u - 99/2*u**3 - 108*u**2 + 0 = 0?
-14, -2, -1/2, 0
Let 676*v - 130*v**2 + 56 + 716*v**2 + 792*v**2 + 95*v**3 = 0. Calculate v.
-14, -2/5, -2/19
Suppose -25*k + 67 + 86 = 26*k. Let o(s) be the first derivative of 10/3*s - 8 - 5/4*s**2 - 5/18*s**k. Factor o(f).
-5*(f - 1)*(f + 4)/6
Let r = -2/7277 - -7293/58216. Let a(p) be the second derivative of 0*p**3 + 0*p**2 + 1/28*p**7 - 3/40*p**5 + 1/20*p**6 - r*p**4 + 19*p + 0. Solve a(q) = 0.
-1, 0, 1
Let p(a) = -14*a**2 - 50*a + 5. Suppose m - 2*m - 5*j - 15 = 0, 5*j = 2*m - 30. Let o(v) = 8*v**2 + 26*v - 3. Let h(b) = m*o(b) + 3*p(b). Factor h(t).
-2*t*(t + 10)
Let 195 - 49*y**3 - 191/4*y**2 + 196*y - 1/4*y**4 = 0. Calculate y.
-195, -2, -1, 2
Let m = -1989/64540 + 35/922. Let y(f) be the third derivative of 23*f**2 - 1/12*f**3 + 0*f + 1/20*f**5 + 0*f**4 + m*f**7 + 1/30*f**6 + 0. Factor y(c).
(c + 1)**3*(3*c - 1)/2
Solve -13*h + 172/3 - 1/3*h**2 = 0 for h.
-43, 4
Factor -80*w**5 - 536*w**2 - 193 - 18*w**4 + 256*w**5 - 63 - 624*w - 174*w**5 - 188*w**3.
2*(w - 16)*(w + 1)*(w + 2)**3
Suppose 176/5*c - 4*c**3 + 2/5*c**4 - 96/5 - 62/5*c**2 = 0. Calculate c.
-4, 1, 12
Find g, given that -355*g**2 + 50*g**3 + 938*g**2 - 39*g**4 - 775*g + 5*g**5 - 6*g**4 - 204*g**2 + 375 + 11*g**2 = 0.
-3, 1, 5
Let m be 184/1518*(3 + (-45)/(-18)). Let r(s) = s - 2. Let k be r(4). What is u in -m + 2/3*u**k - u = 0?
-1/2, 2
Suppose 137*r - 234 - 40 = 0. Let k(a) be the first derivative of -8/7*a**r + 22/21*a**3 - 8/7*a - 2/5*a**5 + 13/14*a**4 - 5/21*a**6 + 5. Solve k(v) = 0.
-2, -1, -2/5, 1
Suppose -8/3*s**2 + 0*s - 2/9*s**4 + 0 + 14/9*s**3 = 0. Calculate s.
0, 3, 4
Let y(w) be the third derivative of 6*w**2 + 22/9*w**3 + 6 - 1/180*w**6 + 7/45*w**5 - 35/36*w**4 + 0*w. Solve y(s) = 0.
1, 2, 11
Suppose -129*u**2 + 75*u**2 + u + 70*u**2 - 5*u**4 - 3*u**4 - 2*u**3 - 8 + u**5 = 0. What is u?
-1, 1, 8
Let p(d) = 10*d**3 - 24*d**2 - 40*d - 63. Let y(s) = -s**3 + s**2 - s. Suppose -12*j + 616 = 16*j. Let i(k) = j*y(k) + 2*p(k). Suppose i(t) = 0. What is t?
-7, -3
Let w(b) be the third derivative of 3*b**6/20 - 7*b**5/30 - 17*b**4/6 + 32*b**3/3 + 2795*b**2. Factor w(f).
2*(f - 1)*(f + 2)*(9*f - 16)
Let o(j) be the first derivative of -9/5*j + 6/5*j**2 + 3/25*j**5 - 66 - 3/5*j**4 + 2/5*j**3. Factor o(g).
3*(g - 3)*(g - 1)**2*(g + 1)/5
Let s be (90/33 + -2 + -1)/((-768)/512). Factor 8/11 + s*l**2 + 8/11*l.
2*(l + 2)**2/11
Let i = 13523781804/1355 + -9980650. Let f = i - -6/271. Suppose -8/5*s**4 - 18/5*s + f + 18/5*s**3 + 4/5*s**2 = 0. What is s?
-1, 1/4, 1, 2
Find w such that -79883*w**2 + 39941*w**2 + 39944*w**2 - 2118 - 2116*w = 0.
-1, 1059
Let m be (-4)/(-24) - 114180/(-18). Let v = m + -5976. Solve 0 + 24*h - 216*h**2 - 378*h**4 - v*h**5 + 600*h**3 = 0.
-2, 0, 2/7, 2/5
What is t in 526/15*t**2 - 11616/5 + 2288*t + 2/15*t**3 = 0?
-132, 1
Let h(w) be the second derivative of w**8/448 + w**7/40 + 11*w**6/160 + w**5/16 + 83*w**2/2 - 6*w + 4. Let y(g) be the first derivative of h(g). Factor y(v).
3*v**2*(v + 1)**2*(v + 5)/4
Let u be 5 + -1 + 8/(-4) - -2. Factor -24*q**2 + 128*q + 45 + 0*q**4 + 83 - 20*q**3 + 4*q**u.
4*(q - 4)**2*(q + 1)*(q + 2)
Let d(b) be the second derivative of 0 - 11/3*b**4 - 29*b - 12*b**3 + 0*b**2. Find v such that d(v) = 0.
-18/11, 0
Let m = 41966 - 293760/7. Factor 12/7*j + 0 + 10/7*j**2 - m*j**3.
-2*j*(j - 6)*(j + 1)/7
Suppose -7*o + 2*o = -4*h + 28, -12 = 3*o. Let u be 7 - h - (-1)/(-5). Factor -u*y + 72/5 + 2/5*y**2.
2*(y - 6)**2/5
Suppose -131*g - 24 = -123*g. Let d(n) = -3*n**2 + 2*n + 8. Let o(m) = -m**2 + 2. Let x(v) = g*d(v) + 12*o(v). Factor x(u).
-3*u*(u + 2)
Let r(m) be the first derivative of 4*m**5/55 + 17*m**4/22 + 30*m**3/11 + 27*m**2/11 - 54*m/11 - 28. Suppose r(v) = 0. Calculate v.
-3, 1/2
Let p(r) = -r**2 + 17*r + 20. Let c be 9/36 - 2*(-213)/24. Let a be p(c). Find t such that -6*t**3 + t**3 - t**a + 6*t**2 = 0.
0, 1
Let a = -4/197 - -17364/1379. Let j be ((-72)/2)/(406/(-58)). Find m such that -j - 32/7*m**3 - a*m**2 - 96/7*m - 4/7*m**4 = 0.
-3, -1
Let z = -71/90 - -8/9. Let j(t) be the third derivative of -z*t**5 + 0*t**4 + 0 + 4/3*t**3 - 27*t**2 + 0*t - 1/60*t**6. Let j(w) = 0. What is w?
-2, 1
Let d(o) = 4*o**2 + o - 1. Let t(m) = 7*m**2 -