. Factor -z*v**3 - 22/3*v + 7*v**2 + 1/3*v**4 + 8/3.
(v - 4)*(v - 2)*(v - 1)**2/3
Factor -378*g + 71442 + 1/2*g**2.
(g - 378)**2/2
Suppose 131 = 4*t + 4*y - 69, -3*t + 4*y + 178 = 0. Let d = t - 51. Factor -2*g - 2/3*g**2 + 2/3*g**4 + 2*g**d + 0.
2*g*(g - 1)*(g + 1)*(g + 3)/3
Let k be (384/(-30))/(21/((-2520)/528)). Factor 18/11*a**2 + 148/11*a + k.
2*(a + 8)*(9*a + 2)/11
Let z(j) = -2*j**2 + 4*j - 99. Let x be z(0). Let c be (-6)/14*132/x. Let -2/7*a**2 + 0 + c*a = 0. Calculate a.
0, 2
Let x(r) be the first derivative of 0*r - 1/180*r**6 - 25/3*r**3 - 6 + 0*r**2 + 1/12*r**4 + 0*r**5. Let i(t) be the third derivative of x(t). Factor i(l).
-2*(l - 1)*(l + 1)
Let f = 7 - -4. Let d(y) = f*y**2 - y + 6*y - y + 9*y**3 + 3*y. Let c(m) = 26*m**3 + 34*m**2 + 20*m. Let h(g) = -3*c(g) + 8*d(g). Factor h(j).
-2*j*(j + 2)*(3*j + 1)
Factor 30*j**2 + j**5 - 55*j + 32*j**2 + 16 - 2*j + 2 - 24*j**3.
(j - 3)*(j - 1)**3*(j + 6)
Determine a, given that -25*a**2 + 35*a**5 - 17*a**3 + 40*a**5 + 2*a**3 - 45*a**2 - 40*a - 70*a**5 + 20*a**4 = 0.
-4, -1, 0, 2
Let a(y) = 8*y**3 + 58*y**2 - 185*y + 140. Let w(u) = 4*u**3 + 56*u**2 - 186*u + 140. Let r(q) = -2*a(q) + 3*w(q). Factor r(x).
-4*(x - 7)*(x - 5)*(x - 1)
Let f(y) be the second derivative of -y**5/80 + 151*y**4/2 - 182408*y**3 + 220348864*y**2 - 3*y + 243. Factor f(o).
-(o - 1208)**3/4
Let w(j) be the first derivative of 11/10*j**4 + 4/5*j**3 - 28 + 14/25*j**5 - 2/5*j + 1/10*j**6 - 1/10*j**2. Factor w(r).
(r + 1)**3*(r + 2)*(3*r - 1)/5
Let x = 2317797/5 + -463554. Solve -6/5 + 27/5*m**3 - x*m + 6/5*m**2 = 0 for m.
-1, -2/9, 1
Let j(y) be the third derivative of -y**6/24 - 7*y**5/2 - 175*y**4/24 + 205*y**3 - 1875*y**2 - 3. Factor j(x).
-5*(x - 2)*(x + 3)*(x + 41)
Let g(t) = -3*t**3 + 1142*t**2 - 1137*t - 66. Let l(c) = 5*c**3 - 2285*c**2 + 2275*c + 165. Let z(s) = -5*g(s) - 2*l(s). Determine r so that z(r) = 0.
0, 1, 227
Suppose -432/5*o**4 - 24/5*o**3 - 100/3 + 50/3*o + 124*o**2 = 0. What is o?
-5/6, 1/2, 10/9
Let w(m) be the third derivative of m**7/3360 + m**6/720 - m**5/120 - m**4/12 + 7*m**3/2 + 2*m**2 + 17*m. Let a(p) be the first derivative of w(p). Factor a(z).
(z - 2)*(z + 2)**2/4
Let t = -127 + 152. Suppose -9 = 8*y - t. Factor -2*d**4 + 4*d**2 - 4*d + d**2 + d**y.
-2*d*(d - 1)**2*(d + 2)
Let a(z) be the third derivative of z**6/60 + 9*z**5/5 - z**4/12 - 18*z**3 + 6*z**2 + 73*z - 1. Factor a(f).
2*(f - 1)*(f + 1)*(f + 54)
Let x(d) = 32*d + 418. Let t be x(-13). Let s = -3 - -6. Determine h, given that 24 + 88*h + 315*h**s + 81*h**4 + 92*h + 344*h**t + 46*h**2 = 0.
-2, -1, -2/3, -2/9
Let o(u) be the second derivative of 0*u**3 + 5 + 1/20*u**5 + 0*u**2 - 1/42*u**7 + 1/12*u**4 + 2*u - 1/30*u**6. Factor o(f).
-f**2*(f - 1)*(f + 1)**2
Let c(b) be the third derivative of -b**6/120 - 49*b**5/15 - 193*b**4/6 - 128*b**3 - 507*b**2. Let c(n) = 0. Calculate n.
-192, -2
Factor 2415/2*b + 3/4*b**2 + 1944075/4.
3*(b + 805)**2/4
Let z(b) be the third derivative of -1/4*b**4 - 3/20*b**5 + 62*b**2 - 2*b + 0 + 1/80*b**6 + 2*b**3 + 1/140*b**7. Factor z(j).
3*(j - 2)*(j - 1)*(j + 2)**2/2
Factor 2/9*y**2 - 4 - 34/9*y.
2*(y - 18)*(y + 1)/9
Let h(v) be the third derivative of v**7/840 + 3*v**6/40 + v**4/24 + 13*v**3/6 - 7*v**2. Let t(q) be the second derivative of h(q). Factor t(s).
3*s*(s + 18)
Let t(i) = -20*i**2 + 406*i - 3999. Let m(j) = -j - 1. Let y(v) = -6*m(v) - t(v). Let c(l) = -9*l**2 + 200*l - 2002. Let a(w) = -5*c(w) - 2*y(w). Factor a(z).
5*(z - 20)**2
Let n = 7580 + -7578. Let x(r) be the second derivative of 1/24*r**4 - 1/240*r**6 - 9*r - 1/160*r**5 + 0*r**n + 1/12*r**3 + 0. Factor x(j).
-j*(j - 2)*(j + 1)*(j + 2)/8
Let n(v) be the second derivative of -v**5/4 + 25*v**4/6 - 35*v**3/2 + 1696*v - 1. Find g such that n(g) = 0.
0, 3, 7
Let v(z) be the first derivative of -4*z**5/5 + 9*z**4 + 100*z**3/3 - 66*z**2 + 2384. Factor v(u).
-4*u*(u - 11)*(u - 1)*(u + 3)
Let a(r) be the third derivative of -r**5/240 - 1345*r**4/96 - 56*r**3 + 5647*r**2. Let a(s) = 0. What is s?
-1344, -1
Let k(q) be the first derivative of q**4/48 - 59*q**3/24 - 15*q**2/2 - 37*q + 139. Let h(v) be the first derivative of k(v). Let h(o) = 0. Calculate o.
-1, 60
Let o(x) = x + 18. Let w be o(-17). Let p(b) = 2*b**4 - 30*b**2 - 24*b. Let l(j) = -j**4 - j**2. Let k(z) = w*p(z) - 2*l(z). Factor k(v).
4*v*(v - 3)*(v + 1)*(v + 2)
What is d in 3496/5 - 4/5*d**2 - 348*d = 0?
-437, 2
Suppose -16*h + 527 = -65. Factor 87 + h*b**4 - 303 - 396*b**2 + 16*b**5 + 172*b**3 - 1249*b + 277*b + 79*b**4.
4*(b - 2)*(b + 3)**3*(4*b + 1)
Let n(a) = -6*a**3 + 47*a**2 - 90*a + 816. Let r be n(8). Determine p, given that 8*p + r + 1/2*p**2 = 0.
-8
Factor 68/7*o**3 - 2*o**4 + 1/7*o**5 + 0 - 130/7*o**2 + 75/7*o.
o*(o - 5)**2*(o - 3)*(o - 1)/7
Find b, given that -24 - 27*b**2 + 3787*b - 3692*b - 41*b**2 - 3*b**3 = 0.
-24, 1/3, 1
Determine c so that -55*c - 30 - 38*c**2 - 102334*c**3 + 8*c**2 + 102329*c**3 = 0.
-3, -2, -1
Let k(w) be the third derivative of 0*w**3 - 10 + 5*w**2 + 1/570*w**5 + 0*w + 1/38*w**4. Let k(m) = 0. Calculate m.
-6, 0
Suppose 55 = 55*k - 15 - 26 - 14. Factor -338/11 - 2/11*f**k + 52/11*f.
-2*(f - 13)**2/11
Let n(t) be the third derivative of t**5/390 + 31*t**4/39 + 41*t**3/13 + t**2 - 14*t. Suppose n(y) = 0. What is y?
-123, -1
Suppose 23 - 8 = r. Factor 5*h + 35 - 5*h**2 - r*h + 4*h + 36*h.
-5*(h - 7)*(h + 1)
Determine c, given that -220/17 - 18/17*c**2 - 134/17*c = 0.
-5, -22/9
Let p = -1445 + 1441. Let y be (-1)/p*((1 - -6) + -4). Find l, given that y*l**2 + 48 + 12*l = 0.
-8
Suppose 69*x = 267*x - 594. Factor 0 - 4/23*o**2 - 6/23*o + 2/23*o**x.
2*o*(o - 3)*(o + 1)/23
Let s(j) be the first derivative of -140/3*j**3 - 77 - 20*j - 8*j**5 + 55/2*j**4 + 85/2*j**2 + 5/6*j**6. Find u, given that s(u) = 0.
1, 4
Let n = 378 - 390. Let i be n/10 + -10*(-104)/700. Factor 0*r + i - 2/7*r**2.
-2*(r - 1)*(r + 1)/7
Factor -3/5*k**2 - 93/5*k - 504/5.
-3*(k + 7)*(k + 24)/5
Let h(k) be the second derivative of 4/45*k**5 - 2/27*k**3 + 6*k + 0 - 1/54*k**4 + 0*k**2 - 1/27*k**6. Let h(g) = 0. What is g?
-2/5, 0, 1
Suppose -4*z - r + 661 = 0, 5*r - 189 = -4*z + 3*z. Let d = -153 + z. Factor -4 - 14*a - 5/2*a**3 - d*a**2.
-(a + 2)**2*(5*a + 2)/2
Let c(t) be the first derivative of 2*t**3/33 + 8*t**2/11 - 96*t/11 + 1641. Factor c(i).
2*(i - 4)*(i + 12)/11
Let w(j) be the first derivative of -j**4/3 + 80*j**3/9 - 256*j**2/3 + 1024*j/3 - 132. Solve w(q) = 0 for q.
4, 8
Let c = 71/12 - -797/60. Find b such that -c - 32/5*b**3 - 14/5*b**4 - 256/5*b + 272/5*b**2 = 0.
-6, -2/7, 2
Suppose 2*q + 78 + 192 = -2*x, q = 5*x + 705. Let u be x/(-20)*(-14)/(-6). Factor -1/3*r**2 - 14/3*r - u.
-(r + 7)**2/3
Let j(z) = -194*z**2 - 5262*z + 186142. Let t(p) = 10*p**2 + 277*p - 9797. Let x(k) = -6*j(k) - 116*t(k). Factor x(v).
4*(v - 70)**2
Let -27823*y - 1202*y**3 - 101*y**4 - 279*y**4 - 6*y**5 + 28543*y - 108*y**2 = 0. Calculate y.
-60, -3, -1, 0, 2/3
Let y be (-8)/(-8) - 69/34. Let v = 8/17 - y. Factor -10*a**2 - v*a**4 - 7*a**3 + 0 - 4*a.
-a*(a + 2)**2*(3*a + 2)/2
Find t such that 62/5*t**2 - 63/5*t + 0 + 1/5*t**3 = 0.
-63, 0, 1
Let i = -16 - -24. Solve -12*j**2 - i - 16 + 24 + 3*j**3 + 9*j = 0 for j.
0, 1, 3
Let f(g) be the third derivative of g**8/2016 - 191*g**7/1260 + 1597*g**6/120 - 2433*g**5/20 + 2697*g**4/16 + 8649*g**3/4 - 1067*g**2. Solve f(i) = 0 for i.
-1, 3, 93
Let x(z) = 2*z**5 + 2*z**3 + z**2 - 2. Let n(q) = -30*q**5 - 132*q**4 + 206*q**3 - 69*q**2 + 10. Let p(a) = -n(a) - 5*x(a). Let p(r) = 0. What is r?
-8, 0, 2/5, 1
Let c(v) be the first derivative of -16/3*v**3 - 10*v**2 + 0*v - 2/3*v**6 + 16/5*v**5 - 65 + 6*v**4. Suppose c(g) = 0. Calculate g.
-1, 0, 1, 5
Suppose 5*v = -2*b - 20, -6*v + 121 - 145 = -5*b. Factor 0*c + b + 4/9*c**3 + 2/9*c**2 + 2/9*c**4.
2*c**2*(c + 1)**2/9
Let d(a) be the third derivative of a**6/1020 + 1259*a**5/510 - 1262*a**4/51 + 1684*a**3/17 - 9*a**2 + 625*a. Factor d(z).
2*(z - 2)**2*(z + 1263)/17
Factor -9*h + 81/7 - 3*h**2 + 3/7*h**3.
3*(h - 9)*(h - 1)*(h + 3)/7
Let x(m) = 44*m - 143. Let h be x(4). Let w be (6 + (-176)/h)/((-1)/(-3)). Factor 10/7*o + 1/7*o**w + 0.
o*(o + 10)/7
Let n = 1323422/3 + -441140. Factor n*a**3 + 0*a**2 + 0 - 2/3*a.
2*a*(a - 1)*(a + 1)/3
Let o = -280 - -396. Let -21*w**3 - 43*w**2 + 48*w + 6*w**3 - o*w**2 + 18