). Factor k(j).
-(j - 154)*(j + 3)*(7*j - 2)
Determine f so that 274576/3*f + 0 - 1048/3*f**2 + 1/3*f**3 = 0.
0, 524
Let s(r) be the third derivative of -1/5*r**5 + 1/35*r**7 + r**3 + 0*r + 1/672*r**8 + 0 - 109*r**2 + 1/48*r**4 - 1/120*r**6. Determine h, given that s(h) = 0.
-12, -1, 1
Let o be (-3)/12*0*(6 - 5). Factor -67*d**3 + o - 6*d + 8*d**2 + 65*d**3 + 0.
-2*d*(d - 3)*(d - 1)
Let w = 53499/959 + -7584/137. Factor w*a**2 + 18/7*a - 3.
3*(a - 1)*(a + 7)/7
Suppose -31*g + 32*g + 3 = 2*z, -5*g + 5*z = 0. Suppose -10*i + t + 1 = -9*i, -g*t - 9 = -5*i. Factor 18*x - 27/2*x**2 - 6 + 3*x**i.
3*(x - 2)**2*(2*x - 1)/2
Factor -5*i**4 - 588200*i**2 + 759*i**3 - 1795740*i - 9 + 2686*i**3 + 17 - 8.
-5*i*(i - 346)**2*(i + 3)
Let r = -3215 + 3218. Let i(w) be the second derivative of 0 + 6*w + 1/9*w**r - 1/72*w**4 - 1/3*w**2. Solve i(u) = 0 for u.
2
Let d(g) = -7*g**4 + 82*g**3 - 331*g**2 + 250*g + 2. Let n(m) = -22*m**4 + 247*m**3 - 996*m**2 + 750*m + 7. Let z(j) = -7*d(j) + 2*n(j). Factor z(i).
5*i*(i - 10)*(i - 5)*(i - 1)
Let u = 1439/524 - -5635/524. Factor -15/4*f**2 + u + 129/4*f.
-3*(f - 9)*(5*f + 2)/4
Let 22/19*u**4 + 18/19*u**2 + 2/19*u**5 + 0 + 0*u + 2*u**3 = 0. Calculate u.
-9, -1, 0
Let a = 141 - -177. What is y in -a*y**3 + 32 + 322*y**3 + 4*y**2 - 47*y + 7*y = 0?
-4, 1, 2
Let f = -939/8 - -8467/72. Let u(l) be the first derivative of f*l**3 - 21 + 0*l + l**2. Find b, given that u(b) = 0.
-3, 0
Let l(s) be the first derivative of -s**3 + 0*s + 3/2*s**2 - 157 - 9/2*s**4. Determine u, given that l(u) = 0.
-1/2, 0, 1/3
Let f(d) = d**2 - 132*d - 148. Let j(t) = -66*t - 60. Let b(r) = 3*f(r) - 5*j(r). Determine h, given that b(h) = 0.
-2, 24
Let u(t) = -t**5 + 2*t**4 + 4*t**3 - 6*t**2 - 3*t. Let h(q) = q**5 + q**4 - q**3. Let k(i) = 11*i + 29. Let z be k(-3). Let o(g) = z*h(g) - u(g). Factor o(w).
-3*w*(w - 1)*(w + 1)**3
Let g be (-18)/(-3) - (-11)/(22/8). Let -6*u + 20*u**2 + u**3 - 21*u**3 + 2 - 12*u**5 - 4*u + 10*u**5 + g*u**4 = 0. What is u?
1
Let r(w) be the second derivative of 67 + 2*w + 36*w**2 - 23/6*w**4 + 2*w**3 - 1/30*w**6 + 13/20*w**5. Factor r(h).
-(h - 6)**2*(h - 2)*(h + 1)
Let c(g) be the first derivative of -27*g**2 + 324*g - 517. Let t be c(6). Factor 0*s**3 + 1/4*s + t - 1/8*s**4 + 3/8*s**2.
-s*(s - 2)*(s + 1)**2/8
Let l(u) = -u**2 - 89*u - 718. Let w be l(-9). Let b be w/6*171/76. Find q, given that -33/4 + 15/2*q + b*q**2 = 0.
-11, 1
Suppose -8*m = 5*f + 775 - 687, 0 = -2*f + m + 11. Factor f + 1/6*n**2 + 0*n.
n**2/6
Let p(q) be the first derivative of -20*q**3/3 + 534*q**2 - 424*q - 3116. Solve p(t) = 0.
2/5, 53
Let f(z) be the first derivative of 0*z**2 + 3/4*z**4 - 2*z - z**3 - 12 + 3/4*z**5. Let a(d) be the first derivative of f(d). Factor a(y).
3*y*(y + 1)*(5*y - 2)
Find c such that 50*c - 87*c**2 + 16*c**3 - 6*c**3 - 22*c**2 - 5*c + 14*c**2 = 0.
0, 1/2, 9
Let a be (-17625)/(-275) - (2/22)/1. Let m be a/42 + (-7)/(-49). Factor -625/3 + 70/3*h**3 + 250/3*h + 100*h**2 + m*h**4.
5*(h - 1)*(h + 5)**3/3
Suppose -174*c = -181*c + 28. Let w(a) = 6*a**4 + 16*a**3 + 46*a**2 + 4*a. Let s(k) = 5*k**4 + 17*k**3 + 47*k**2 + 3*k. Let q(g) = c*s(g) - 3*w(g). Factor q(p).
2*p**2*(p + 5)**2
Let p(j) be the first derivative of j**3/3 + 4*j**2 - 180*j - 4850. Factor p(n).
(n - 10)*(n + 18)
Let l(q) be the first derivative of -2*q**3/3 - 108*q**2 + 666*q + 1292. Factor l(y).
-2*(y - 3)*(y + 111)
Let l(p) be the third derivative of 2/195*p**5 - 2*p + 1/2184*p**8 + 0*p**3 + 22*p**2 - 7/780*p**6 + 0*p**4 + 2/1365*p**7 + 0. Factor l(y).
2*y**2*(y - 1)**2*(y + 4)/13
Let 505*s**3 + 12*s**2 - 538*s**3 - 66*s - 48 + 9*s**4 + 126*s = 0. What is s?
-4/3, 1, 2
Let i(v) be the first derivative of v**5/5 + 7*v**4 + 292*v**3/3 + 672*v**2 + 2304*v - 300. Factor i(g).
(g + 6)**2*(g + 8)**2
Let v = -107 - -116. Factor -4*j + 10 - 11 - 2*j**4 + 8*j**3 - 4*j + v - 6*j**2.
-2*(j - 2)**2*(j - 1)*(j + 1)
Determine g so that 28/11*g**3 + 0 - 30/11*g + 2/11*g**5 + 16/11*g**2 - 16/11*g**4 = 0.
-1, 0, 1, 3, 5
Let o = 208435/555912 - -4/69489. What is n in 5/8*n**3 + o*n**4 - 1/2*n - 15/8*n**2 - 1/8*n**5 + 3/2 = 0?
-2, -1, 1, 2, 3
Let b(a) be the first derivative of 0*a**2 + 24 - 1/45*a**5 - 2/27*a**4 + 17*a + 2/9*a**3. Let v(d) be the first derivative of b(d). Factor v(k).
-4*k*(k - 1)*(k + 3)/9
Let m(d) be the third derivative of -1/42*d**7 + 0*d**4 + 1/3*d**5 + 0*d**3 + 0 + 27*d**2 + 0*d**6 + 0*d. Factor m(u).
-5*u**2*(u - 2)*(u + 2)
Suppose -3*j + 14 = 4*w, -w + 23 = 2*w - 4*j. Suppose -35 = -5*d + w*h, 11 = 4*d + 3*h + 18. Factor 2/19*b + 4/19*b**d + 2/19*b**3 + 0.
2*b*(b + 1)**2/19
Let p(f) be the second derivative of -f**6/30 + 47*f**5/100 - 59*f**4/30 + 4*f**3/3 + 485*f. Find n such that p(n) = 0.
0, 2/5, 4, 5
Suppose 41040*u - 17939*u**2 - 4456*u**2 - 2053 - 74400*u**4 + 2978*u**2 - 3067 - 101543*u**2 + 1125*u**5 + 155480*u**3 = 0. Calculate u.
2/5, 2/3, 64
Let c be 30 - (22 + 1740/319). Factor -2/11*v**5 + 32/11*v**2 - 18/11*v - c*v**3 + 12/11*v**4 + 4/11.
-2*(v - 2)*(v - 1)**4/11
Factor -46*d + 124*d**3 + 6*d**4 - 184*d**2 + 146*d + 0*d**4 - 276*d.
2*d*(d - 2)*(d + 22)*(3*d + 2)
Let n(c) = -c**2 - 7*c + 289. Let z be n(-20). Suppose 12*j - 4*m + 32 = 17*j, -z = -5*j - 3*m. Factor -12/5*f**2 - 2/5 + 8/5*f + 8/5*f**3 - 2/5*f**j.
-2*(f - 1)**4/5
Let t = 13431521/9 + -1492391. Find u, given that 0*u + 20/9*u**3 + t*u**4 + 0 - 16/3*u**2 = 0.
-12, 0, 2
Let i = 208 + -162. Let -i + 3*u**2 + 18*u - 3*u**3 + 5*u + 3*u + u + 19 = 0. What is u?
-3, 1, 3
Factor 3/5*s**4 + 27/5 - 24/5*s**3 - 6*s**2 + 24/5*s.
3*(s - 9)*(s - 1)*(s + 1)**2/5
Let d(z) = -13*z + 173*z**2 - 9*z**3 + 37*z - 185*z**2 + 6. Let o = 13 + 4. Let u(t) = -26*t**3 - 35*t**2 + 72*t + 17. Let k(a) = o*d(a) - 6*u(a). Factor k(n).
3*n*(n - 2)*(n + 4)
Let l = 256949 + -256945. Solve 32/7 + 80688/7*n**2 + 5651522/7*n**l - 1102736/7*n**3 - 2624/7*n = 0 for n.
2/41
Let v(b) = -19*b**2 - 4706*b + 1104500. Let u(g) = 80*g**2 + 18825*g - 4418000. Let t(m) = -6*u(m) - 25*v(m). Solve t(w) = 0 for w.
470
Factor 2045820*w**2 + 67*w - 2045834*w**2 + 206 + 1373*w.
-2*(w - 103)*(7*w + 1)
Let k(b) = 32*b**2 - 870*b + 12615. Let y(o) = -11*o**2 + 290*o - 4205. Let n(g) = 6*k(g) + 17*y(g). Suppose n(u) = 0. Calculate u.
29
Let r(o) be the first derivative of -8*o**5/35 + o**4/14 + 26*o**3/7 - 9*o**2/7 - 54*o/7 - 10264. Suppose r(z) = 0. What is z?
-3, -3/4, 1, 3
Let l(q) be the second derivative of -q**7/126 - 13*q**6/90 - 11*q**5/20 + 37*q**4/36 + 41*q**3/9 - 12*q**2 - 754*q - 1. Find u, given that l(u) = 0.
-9, -4, -2, 1
Let l be (800/7)/((-1452)/154 + 11). Determine y so that -2/11*y**3 - l - 80*y - 82/11*y**2 = 0.
-20, -1
Let h(f) be the third derivative of -f**6/840 + 61*f**5/420 - 71*f**4/42 + 16*f**3/3 + 6764*f**2. Factor h(x).
-(x - 56)*(x - 4)*(x - 1)/7
Let s(y) = -48*y - 17. Let l be s(-1). Find w, given that 18*w - 28 + l*w**2 + 771*w**3 + 2*w**4 - 789*w**3 - 5*w**2 = 0.
-1, 1, 2, 7
Let n(i) = -i**2 + 5*i - 1. Let v be n(3). Suppose v*s - 30 = 4*x, x + x + 2 = -4*s. Factor -9 + 15*p**3 + 4*p + 6 - 9 + 39*p**s + 8*p.
3*(p + 1)*(p + 2)*(5*p - 2)
Let l(c) be the first derivative of -2/15*c**3 + 2/75*c**5 + 8/15*c + 4/15*c**2 - 1/15*c**4 - 56. Factor l(t).
2*(t - 2)**2*(t + 1)**2/15
Suppose 0 = -8*s + 4*s - 4*a + 4, -5*s + 19 = -2*a. Suppose -2*j**5 + 4*j**4 - 4*j**2 + 388*j - 392*j - j**5 + 7*j**s = 0. What is j?
-1, -2/3, 0, 1, 2
Let a be ((-301)/(-99) - (-38)/209)*(-8 + 37). Factor -a - 58/9*r - 1/9*r**2.
-(r + 29)**2/9
Let p(c) be the second derivative of c**5/45 - 109*c**4/3 + 23762*c**3 - 7770174*c**2 - 77*c + 1. Determine n, given that p(n) = 0.
327
Let r = -68961/10 - -6889. Let v = 679/90 + r. Determine x so that 7*x**3 + v*x - 8/9 + 130/9*x**2 = 0.
-2, -2/7, 2/9
Let b be 7 - 1 - -2 - 8. Let k be 8*(-117)/(-520) + b. Factor 15 + 51*j + k*j**3 + 93/5*j**2.
3*(j + 5)**2*(3*j + 1)/5
Suppose 14*n = 16*n - 4. Let r be (-406)/(-1421) + (36/7)/3. Find d such that -2*d + 1/2*d**4 - n + 3/2*d**r + 2*d**3 = 0.
-2, -1, 1
Let n = 88 + -106. Let a be (0 - 3)/9 + (-1500)/n. Factor 11*y - 176*y**2 + 92*y**2 + a*y**2 - 10.
-(y - 10)*(y - 1)
Suppose 463*g - 510*g = -282. Let p(z) be the first derivative of -1/36*z**g + 0*z - 1/18*z**3 - 2 + 0*z**2 + 1/30*z**5 + 1/24*z**4. Factor p(u).
-u**2*(u - 1)**2*(u + 1)/6
Let