t a(r) be the third derivative of r**6/160 - 57*r**5/40 + 443*r**4/32 - 165*r**3/4 + 67*r**2. Factor a(x).
3*(x - 110)*(x - 3)*(x - 1)/4
Let 7640*r + 0*r**3 + 1250*r**2 + 11337 - 2*r**3 - 3*r**3 - 1097 = 0. Calculate r.
-4, -2, 256
Let u(v) be the third derivative of -v**7/630 - 2*v**6/45 - 19*v**5/45 - 4*v**4/3 + 296*v**2 + v. Solve u(r) = 0 for r.
-8, -6, -2, 0
Let t(r) be the first derivative of -40*r**2 + 2/3*r**3 + 47 + 800*r. Factor t(n).
2*(n - 20)**2
Let n(s) be the third derivative of -s**5/150 - 227*s**4/5 - 618348*s**3/5 - 3343*s**2. Factor n(y).
-2*(y + 1362)**2/5
Let k(z) be the third derivative of -z**7/1470 + 23*z**6/280 + 77*z**2 - 6. Factor k(j).
-j**3*(j - 69)/7
Suppose -312*l + 20 + 706 + 210 = 0. Factor 3/2*v**4 - 6*v - 3/2*v**2 + 6*v**l + 0.
3*v*(v - 1)*(v + 1)*(v + 4)/2
Let x(y) = -y**3 + 5*y**2 + 120*y - 740. Let z be x(7). Factor -1/4*s**z - 4 + 5/2*s.
-(s - 8)*(s - 2)/4
Let d(s) be the first derivative of s**4/18 + 20*s**3/27 + 31*s**2/9 + 20*s/3 + 269. Factor d(h).
2*(h + 2)*(h + 3)*(h + 5)/9
Let h(f) be the first derivative of f**3/33 - 211*f**2/11 + 1408. Factor h(w).
w*(w - 422)/11
Let u(c) be the third derivative of 97*c**2 - 1/1344*c**8 + 0 + 0*c**3 - 13/480*c**6 - 1/40*c**5 + 0*c - 1/105*c**7 + 0*c**4. Factor u(m).
-m**2*(m + 1)**2*(m + 6)/4
Let i(h) be the first derivative of 0*h - 205 - 6/7*h**2 + 2/35*h**5 + 3/7*h**4 - 2/21*h**3. Factor i(z).
2*z*(z - 1)*(z + 1)*(z + 6)/7
Let n(v) = -15*v**4 + v**3 + v + 1. Let w(a) = 20*a**4 + 9*a**3 - 860*a**2 + 1669*a - 826. Let j(o) = n(o) + w(o). Determine t so that j(t) = 0.
-15, 1, 11
Let z(c) be the third derivative of c**2 + 7/360*c**5 - 14*c + 0*c**3 - 1/72*c**4 + 0. Factor z(q).
q*(7*q - 2)/6
Let t(z) be the second derivative of -3/4*z**5 - 18*z**2 + 1/14*z**7 - 2 + 2*z**3 + 15/4*z**4 - z - 3/10*z**6. Let t(y) = 0. What is y?
-2, -1, 1, 2, 3
Suppose 804/5 + 6/5*q**2 + 414/5*q = 0. Calculate q.
-67, -2
Let o = -260963/36 + 7249. Let s(f) be the second derivative of 0 - 1/6*f**2 - 1/36*f**3 + 1/120*f**5 - 29*f + o*f**4. Factor s(w).
(w - 1)*(w + 1)*(w + 2)/6
Let s = -526743/5 - -105998. Let y = 652 - s. Suppose -1/5*q**2 + 7/5*q**3 + 6/5*q**5 + y*q**4 + 0 - 1/5*q = 0. Calculate q.
-1, -1/2, 0, 1/3
Let v(k) be the third derivative of 0*k - 2/15*k**4 - 1/75*k**5 - 2/5*k**3 + 0 - 59*k**2. Let v(h) = 0. What is h?
-3, -1
Let i(j) = -2*j**3 - 29*j**2 - 99*j - 1707. Let r be i(-15). Suppose 1/6*x**r + 1/3*x**2 - 13/6*x + 5/3 = 0. Calculate x.
-5, 1, 2
Suppose -90*v + 355 = -455. Let y(n) be the first derivative of -n + v + n**2 - 1/3*n**3. Factor y(f).
-(f - 1)**2
Let a(s) = -57*s**3 + 34*s**2 + 112*s + 26. Let x(l) = -l**3 - 2*l**2 + 2. Let c(r) = -a(r) + 5*x(r). Factor c(n).
4*(n - 2)*(n + 1)*(13*n + 2)
Let r(o) be the second derivative of -o**4/20 + 77*o**3/5 - 459*o**2/10 - 2*o - 1645. Factor r(m).
-3*(m - 153)*(m - 1)/5
Let j(a) be the third derivative of -40*a**2 - 431/10*a**5 - 1/105*a**7 + 0 + 37/30*a**6 - 703/3*a**4 + 0*a - 1444/3*a**3. Let j(d) = 0. Calculate d.
-1, 38
Let z(h) be the first derivative of -16*h + 2*h**3 - 6*h**2 + 32 + 1/2*h**4. Factor z(o).
2*(o - 2)*(o + 1)*(o + 4)
Let m(w) be the second derivative of w**5/15 - 7*w**4/6 - 38*w**3/9 + 8*w**2 - 528*w. Find h, given that m(h) = 0.
-2, 1/2, 12
Let j(y) = y**2 + 1. Let c(x) = 6*x + 711 + 3*x**2 - 727 - 23*x. Let r(b) = -5*c(b) + 10*j(b). Suppose r(n) = 0. Calculate n.
-1, 18
Let v(j) = 20*j**2 + 14896*j + 4627740. Let z(n) = 7*n**2 + 4965*n + 1542582. Let l(u) = 3*v(u) - 8*z(u). Factor l(x).
4*(x + 621)**2
Suppose -541684*w**2 + 744154*w - 728777 + 330422*w + 192953 + 2936*w**3 - 4*w**4 = 0. What is w?
1, 366
Suppose 0 = -5*x - 5*u - 15, 0 = 130*x - 126*x - 4*u - 28. Factor -3/8*h**x + 1/4*h + 1.
-(h - 2)*(3*h + 4)/8
Determine h so that -40*h + 92*h - 2*h**3 + 221*h - 19*h - 32*h**2 + 68*h = 0.
-23, 0, 7
Let o(f) be the third derivative of 3*f - 2*f**2 + 0 + 72*f**5 + 1/42*f**7 + 2*f**6 + 1440*f**4 + 17280*f**3. Determine p, given that o(p) = 0.
-12
Suppose 207564 = -3*a + 207570. Find y, given that 0 - 28/17*y + 2/17*y**a = 0.
0, 14
Let l(z) be the second derivative of -1/21*z**7 - 2/3*z**4 - 4*z**3 + 9/10*z**5 + 0*z**2 + 0*z**6 + 0 + 115*z. Let l(j) = 0. Calculate j.
-3, -1, 0, 2
Let r be (-470)/325 + (-6)/15 + 2. Let g(y) = -1154*y - 11538. Let m be g(-10). Factor r*c**m + 288/13 + 48/13*c.
2*(c + 12)**2/13
Let c(d) be the second derivative of -188/3*d**3 - 24*d**2 - 51/5*d**6 - 413/10*d**5 - 20/21*d**7 + 2 + 2*d - 77*d**4. Solve c(a) = 0.
-3, -2, -2/5, -1/4
Let -4/5*k**3 - 2/5*k**5 + 496/15*k**2 - 52/15*k**4 + 198/5*k - 84/5 = 0. What is k?
-7, -3, -2, 1/3, 3
Solve -96/13*h + 1120/13 + 2/13*h**2 = 0 for h.
20, 28
Suppose -5*l + 112 = 102. Let g(s) be the second derivative of 0*s**3 + 1/60*s**4 - 1/20*s**l - 1/300*s**6 + 0*s**5 - 8*s + 0. Factor g(m).
-(m - 1)**2*(m + 1)**2/10
Suppose -34*j - 3264 = -130*j. Let r(k) be the first derivative of 0*k**2 + 0*k + j - 4/3*k**3. Suppose r(o) = 0. Calculate o.
0
Factor -169*o**4 - 57*o**2 - 31*o**4 + 60*o**5 + 591*o**3 + 12*o**2 - 282*o**3 - 114*o**3.
5*o**2*(2*o - 3)**2*(3*o - 1)
What is f in -10*f**4 - 56 - 28 - 2*f**5 + 64*f**2 + 127*f - 191*f - 12 + 24*f**3 = 0?
-6, -2, -1, 2
Let a(o) = -o**4 - 4*o**3 + 2*o**2 + 3*o. Let c(t) = -52*t**3 - 328*t**2 - 268*t. Let v(u) = -4*a(u) - c(u). Factor v(p).
4*p*(p + 1)*(p + 8)**2
Let m = 64584 + -64584. Factor 8/11*u**2 + 0 - 32/11*u**3 + 14/11*u**4 + m*u.
2*u**2*(u - 2)*(7*u - 2)/11
Suppose -42 - 5*p**2 + 180 - 3*p**2 - 2844*p - 112*p**2 - 2673*p = 0. Calculate p.
-46, 1/40
Let s(k) be the third derivative of 0*k**4 + 0 + 1/2880*k**6 + 0*k + 1/480*k**5 - 3*k**2 + 20/3*k**3. Let h(o) be the first derivative of s(o). Factor h(f).
f*(f + 2)/8
Let p(m) be the second derivative of 5*m**4/12 + 125*m**3/3 - 255*m**2/2 + 2*m + 1839. Suppose p(j) = 0. What is j?
-51, 1
Let r(g) be the second derivative of 2*g**6/15 + 6*g**5/5 + 4*g**4/3 - 16*g**3 - 64*g**2 + 6*g - 5. Factor r(n).
4*(n - 2)*(n + 2)**2*(n + 4)
Let i(b) = -41*b**2 + 67*b - 22. Let r be i(1). Suppose -36/5*f - 7/5*f**r + 38/5*f**2 - 4/5*f**3 + 9/5 = 0. What is f?
-3, 3/7, 1
Let p = -21/541 + 4433/2705. Factor -24/5*g - 4/5*g**3 + p + 18/5*g**2.
-2*(g - 2)**2*(2*g - 1)/5
Find o, given that -36*o**2 + 38*o**2 - 81*o**2 - 51*o**2 - 11983*o**3 - 165*o + 11988*o**3 + 810 = 0.
-3, 2, 27
Let q(u) be the first derivative of 1/15*u**5 + 613/9*u**3 - 23/6*u**4 + 43 - 322*u**2 + 588*u. Let q(k) = 0. What is k?
2, 21
Suppose y = 7*g - 6*g + 3, -1 = -3*g + y. Suppose -3*k**5 - 7*k**g + 3*k**4 + 3*k**3 + 4*k**2 + 0*k**2 + 6*k**3 - 6*k = 0. Calculate k.
-1, 0, 1, 2
Let d = -75593 + 75598. Let -1/4*a**d + 25/2 - a**3 + 2*a**4 + 5/4*a - 29/2*a**2 = 0. What is a?
-2, -1, 1, 5
Suppose -8*f + 113 = -47. Let m(k) be the second derivative of -1/12*k**4 + f*k + 1/9*k**3 + 0 + 0*k**2 + 0*k**5 + 1/90*k**6. Factor m(l).
l*(l - 1)**2*(l + 2)/3
Factor 315342*s**2 - 314622*s**2 - 311*s + 2*s**4 - 74*s**3 - 337*s.
2*s*(s - 18)**2*(s - 1)
Let t be 293 + -253 + 320/(-24). Factor t*r + 1/3*r**2 + 1600/3.
(r + 40)**2/3
Let z(k) = k**3 - 22*k**2 - 21*k - 44. Let a be z(23). Factor -22*i**2 + 40*i**2 - 144 + 24*i - 19*i**a.
-(i - 12)**2
Find z such that -944163/7 + 3366/7*z - 3/7*z**2 = 0.
561
Let z(m) be the second derivative of m**5/20 - 3*m**4/4 - 8*m**3 - 25*m**2 + 43*m + 1. Let j(o) be the first derivative of z(o). Find d, given that j(d) = 0.
-2, 8
Let i(x) = 10*x**2 + x + 972. Let r(f) = 115*f**2 + 15*f + 11665. Let d(k) = 35*i(k) - 3*r(k). Find a, given that d(a) = 0.
-13, 15
Factor -74 + 25 - 11 - 4*u**2 + u - 112 + 175*u.
-4*(u - 43)*(u - 1)
Solve -4*z**2 + 1/6*z**5 + 4*z**4 + 0 + 143/6*z**3 - 24*z = 0.
-12, -1, 0, 1
Let n(u) be the second derivative of -u**4/48 - 143*u**3/24 + 447*u**2/4 + 5184*u. Factor n(v).
-(v - 6)*(v + 149)/4
Find p, given that 1/8*p**4 - 1/8*p**3 - 1/2*p**2 + 1/2*p + 0 = 0.
-2, 0, 1, 2
Let l = -524 - -528. Factor -l + 16 + r**2 - 6 - 6 + 40*r.
r*(r + 40)
Let r(t) = -1626*t - 8127. Let g be r(-5). Factor -3/2*q + 27/4*q**4 + 12*q**g + 15/4*q**2 + 0.
3*q*(q + 1)**2*(9*q - 2)/4
Factor -165*h + 94/3*h**2 + 0 + 1/3*h**3.
h*(h - 5)*(h + 99)/3
Let a(w) be the first derivative of -78*w**5/85 - 23*w**4/17 + 14*w**3/17 + 24*w**2/17 - 8*w/17 - 239. Determine l, given