0. Let j(l) = l**2 - 2*l - 2. Let k(u) = 2*u**2 + 63*u - 68. Let v(o) = m*k(o) + 4*j(o). Let v(n) = 0. Calculate n.
-66, 1
Suppose -4*y - t + 10 = 0, 0*y - y = -t. Suppose 2*o - f = -y*o + 115, -2*f = -o + 20. Factor -12*r**4 + o*r**3 + 6*r - 13*r**4 + 2*r + 36*r**2.
-r*(r - 2)*(5*r + 2)**2
Let l be (534/15)/(6/15). Suppose -l*x + 9 = -86*x. Suppose 0 + 0*u - 2/5*u**4 - 2/5*u**x + 0*u**2 = 0. Calculate u.
-1, 0
Let g = 3318 + -3313. Let h(l) be the third derivative of 0*l**3 + 0 + 1/15*l**g + 0*l + 3*l**2 + 1/2*l**4. Factor h(x).
4*x*(x + 3)
Let p = 23 - 14. Let c be 13 + (19 - 28) + 3 + 0. Suppose -p*j**2 - 21*j + 9 + 15*j - j**3 + c*j = 0. What is j?
-9, -1, 1
Let l(f) = -15*f**2 - 1188*f - 70807. Let c(r) = -20*r**2 - 1187*r - 70808. Let w(k) = 2*c(k) - 3*l(k). Factor w(z).
5*(z + 119)**2
Let f(b) = 77*b**4 + 126*b**3 + 9*b**2 - 32*b + 8. Let l(k) = k**4 + k**2 + k - 1. Let z be (5/20)/((-7)/(-28)). Let s(g) = z*f(g) + 4*l(g). Factor s(i).
(i + 1)**2*(9*i - 2)**2
Let j(m) = -7*m**2 + 25*m + 6. Let k(b) = -16*b**2 + 45*b + 14. Let r(p) = -7*j(p) + 3*k(p). Factor r(a).
a*(a - 40)
Suppose 22*z = 2940 + 7466. Let p = -5199/11 + z. Let 2/11*x + 2/11*x**2 - p = 0. Calculate x.
-2, 1
Let l(o) be the third derivative of o + 2/15*o**7 + 9/5*o**6 + 40*o**2 - 40/3*o**3 + 6*o**4 + 0 + 103/15*o**5. Suppose l(v) = 0. What is v?
-5, -2, -1, 2/7
Let j = 3214 + -3211. Let p(k) be the first derivative of -40*k + 385/4*k**4 + 49*k**5 - 110*k**j - 130*k**2 - 14. Suppose p(h) = 0. Calculate h.
-2, -2/7, 1
Let b(l) be the second derivative of -l**8/4032 - l**7/1080 + l**6/360 - 19*l**4/4 - 35*l. Let j(r) be the third derivative of b(r). Factor j(v).
-v*(v + 2)*(5*v - 3)/3
Let 44*a**2 - 288 - 427*a + 564 - 597*a = 0. What is a?
3/11, 23
Let d(a) be the third derivative of -a**5/15 - 11*a**4 - 130*a**3/3 + 46*a**2 - 6*a. Factor d(z).
-4*(z + 1)*(z + 65)
Let b(i) be the second derivative of i**5/60 - 193*i**4/18 - 43*i**3/2 + 10424*i. Factor b(m).
m*(m - 387)*(m + 1)/3
Let z(b) be the second derivative of -b**6/1080 + b**5/135 - 5*b**4/216 + b**3/27 - 13*b**2/2 - 38*b. Let h(q) be the first derivative of z(q). Factor h(o).
-(o - 2)*(o - 1)**2/9
Let c be (-4369)/257 - (-1 + -25). Let h(a) be the first derivative of 5/3*a**3 + c - 30*a - 5/2*a**2. Factor h(r).
5*(r - 3)*(r + 2)
Let o(x) = -x**2 - 58*x + 1189. Let k be o(-74). Let f(i) be the second derivative of 0*i**2 - k*i + 2/9*i**4 + 0 + 2/9*i**3 + 1/15*i**5. Factor f(h).
4*h*(h + 1)**2/3
Let g(t) be the first derivative of 7*t**6/6 + 44*t**5/5 - 51*t**4/4 - 116*t**3/3 - 14*t**2 + 422. Determine f so that g(f) = 0.
-7, -1, -2/7, 0, 2
Let k(t) = -145*t - 2898. Let b be k(-20). Let u be (-115)/(-100) - (-4)/(-10). Factor 0 + u*d**b - 3/2*d + 9/4*d**3.
3*d*(d + 1)*(3*d - 2)/4
Let f = 2132/3 - 14921/21. Let y(p) be the first derivative of 30/7*p + f*p**3 + 3/2*p**2 + 13. Factor y(s).
3*(s + 2)*(s + 5)/7
Let h = -12/15253 + 122060/45759. Factor -20/9*u - h + 1/9*u**3 - 2/9*u**2.
(u - 6)*(u + 2)**2/9
Let f be (-1 + (-51)/(-9))/((-6)/(-9)). Suppose f*o - 2*o - 60 = 0. Determine p so that -190*p**3 + 0 - 6 - o*p**2 + 187*p**3 - 15*p = 0.
-2, -1
Let z(r) be the first derivative of -2*r**5/45 + 233*r**4/9 - 36502*r**3/9 + 108112*r**2/9 - 107648*r/9 - 746. Determine h, given that z(h) = 0.
1, 232
Let l(b) be the first derivative of b**5/5 + 19*b**4/4 - 8*b**3 - 38*b**2 + 80*b - 10811. Suppose l(r) = 0. Calculate r.
-20, -2, 1, 2
Let l be ((-1)/(-4))/(6712/(-1120) + 6). Factor k**2 + 13*k**2 + k**3 + l + 37 + 60*k.
(k + 2)*(k + 6)**2
Let k(h) be the first derivative of -9*h**4/10 - 26*h**3/3 - 68*h**2/5 - 24*h/5 + 609. Factor k(u).
-2*(u + 1)*(u + 6)*(9*u + 2)/5
Let k(o) be the first derivative of o**6/360 + o**5/40 - o**4/6 - 7*o**3 + o - 61. Let w(i) be the third derivative of k(i). Determine b so that w(b) = 0.
-4, 1
Let h(s) be the first derivative of -s**4/4 - s**3 + s**2/2 + 3*s - 521. Factor h(r).
-(r - 1)*(r + 1)*(r + 3)
Let m(n) = -226*n**2 - 1352*n + 26. Let f be m(-6). Factor 5/9 + 1/9*i**f - 2/3*i.
(i - 5)*(i - 1)/9
Determine u, given that 4278*u + 1090861 + 434246 - 17*u**2 + 20*u**2 = 0.
-713
Let h = -194 - -196. Factor 361*o**3 + 52*o**4 + 2 - 84*o + 35 + 36*o**5 - 29 + 152*o**4 + 150*o**h.
(o + 2)**3*(6*o - 1)**2
Let i be (-25)/20*(21/(-3) + -21*(-108)/420). Factor -3/2*m**i - 15123/2 - 213*m.
-3*(m + 71)**2/2
Let d(p) = 45*p**2 - 1280*p + 1445. Let o(g) = 5*g**2 - 142*g + 161. Let u(w) = -4*d(w) + 35*o(w). Suppose u(l) = 0. Calculate l.
1, 29
Let s(v) = 4*v**3 + 110*v**2 + 188*v + 97. Let r(o) = 3*o**3 + 106*o**2 + 187*o + 96. Let t(h) = 5*r(h) - 4*s(h). Factor t(l).
-(l - 92)*(l + 1)**2
Let d = -12565 + 12568. Let u(f) be the second derivative of 0 + 28*f + 5/12*f**4 - 15/2*f**2 + 5/3*f**d. Factor u(h).
5*(h - 1)*(h + 3)
Let v(p) be the first derivative of -p**6/10 - 183*p**5/25 - 135*p**4/4 + 189*p**3/5 + 1539*p**2/5 + 4762. Solve v(r) = 0 for r.
-57, -3, 0, 2
Find r, given that 1803*r**2 - 11*r**3 - 15440*r + 6665*r**2 - 26*r**3 - 15*r**3 - 2576 = 0.
-2/13, 2, 161
Determine p so that -1420/7*p**4 - 2180/7*p**2 + 0 - 52*p - 3252/7*p**3 + 16/7*p**5 = 0.
-1, -1/4, 0, 91
Let j(x) be the second derivative of 13/6*x**2 + 1/36*x**4 - 78*x + 0 + 7/9*x**3. Factor j(g).
(g + 1)*(g + 13)/3
Let l(n) be the second derivative of n**4/12 + 17*n**3/6 + 27*n**2/2 + 13*n - 10. Let o(q) = 4*q + 1. Let g(z) = 2*l(z) - 18*o(z). Let g(a) = 0. Calculate a.
1, 18
Let i be 531/(-590) + 4/8*2. Let x(j) be the first derivative of -1/2*j**3 + 0*j**4 + 19 + 0*j + i*j**5 + 1/2*j**2. Determine y so that x(y) = 0.
-2, 0, 1
Let b(z) be the second derivative of -z**6/180 - 2*z**5/5 + 33*z**4/4 + 780*z**3 - 114075*z**2/4 + 3394*z. Factor b(x).
-(x - 15)**2*(x + 39)**2/6
Let p(t) be the second derivative of 10*t - 6/5*t**3 - 6/5*t**2 + 9 + 7/20*t**4. Suppose p(c) = 0. Calculate c.
-2/7, 2
Determine q so that 770 - 40*q**2 - 21*q**2 - 2*q**2 - 26*q**2 - 955*q + 44*q**2 = 0.
-22, 7/9
Factor 2245 + 5*d**2 + 621*d - 1399 + 228*d - 2*d**2.
3*(d + 1)*(d + 282)
Let g(x) be the first derivative of -5*x**3 - 84 + 40*x + 115/2*x**2. What is v in g(v) = 0?
-1/3, 8
Let x(d) be the second derivative of -d**4/78 + 88*d**3/39 + 180*d**2/13 + 1909*d - 1. Factor x(l).
-2*(l - 90)*(l + 2)/13
Let x(t) = 130*t**3 - 29*t**2 + 161*t + 187. Let y(v) = 111*v**3 - 27*v**2 + 162*v + 186. Let z(f) = -6*x(f) + 7*y(f). Find g such that z(g) = 0.
-10, -1, 6
Factor 6 - 23/2*i - 1/2*i**4 + 9/2*i**2 + 3/2*i**3.
-(i - 4)*(i - 1)**2*(i + 3)/2
Let f be (9 - 5) + (-3 + 32 - 2). Let y = 33 - f. Solve -5*o**2 + 4*o + 4*o + y*o = 0.
0, 2
Let o(u) be the third derivative of -u**6/900 - 97*u**5/450 - 32*u**4/45 + 126976*u**3/45 + 2*u**2 - 3798. Factor o(m).
-2*(m - 31)*(m + 64)**2/15
Determine d so that 0 + 19/4*d**3 + 37/2*d**2 - 2*d = 0.
-4, 0, 2/19
Let d(x) be the second derivative of -86*x - 1/18*x**4 + 0*x**3 + 1/126*x**7 + 0*x**2 + 1/45*x**6 + 0 - 1/60*x**5. Find t such that d(t) = 0.
-2, -1, 0, 1
Factor 0*t - 79/3*t**3 - 1/3*t**4 - 76*t**2 + 0.
-t**2*(t + 3)*(t + 76)/3
Factor -93*k - 117*k + 212 - k**2 - 8*k**2 + 7*k**2.
-2*(k - 1)*(k + 106)
Suppose -8966 = -4*z + 5*w, -23*w + 24*w = -2*z + 4476. Let a = 6719/3 - z. Factor a*f + 2/3*f**3 + 4/3*f**2 + 0.
2*f*(f + 1)**2/3
Let a(h) be the second derivative of 2/135*h**6 + 0*h**2 + 1/9*h**4 + 52*h + 7/90*h**5 + 0*h**3 + 0. Factor a(c).
2*c**2*(c + 2)*(2*c + 3)/9
Let h be (-18)/(-30)*15 + (-4047)/513. Factor h*r**2 + 0 + 14/9*r**4 + 0*r - 2/9*r**5 - 22/9*r**3.
-2*r**2*(r - 5)*(r - 1)**2/9
Let 70*t**4 - 63*t**3 - 51*t**2 + 3*t - 28*t**4 + 3 + 66*t**4 = 0. What is t?
-1/3, 1/4, 1
Let o be 3/(15/35) + -2 + (-82)/18. Factor -4/9*g**3 + o*g + 0 - 2/9*g**4 + 2/9*g**2.
-2*g*(g - 1)*(g + 1)*(g + 2)/9
Let k(z) be the first derivative of z**4/5 + 136*z**3/15 + 738*z**2/5 + 5184*z/5 + 1021. Factor k(x).
4*(x + 9)**2*(x + 16)/5
Let b be ((-1)/(-4) - 30/56) + 20298/(-1428) + 16. Find k such that -1/2*k**3 + 0*k - 2 + b*k**2 = 0.
-1, 2
Determine t, given that 304 - 2754*t**2 - 7398*t - 2072 + 1017 + 424*t**4 + 780*t**3 - 16*t**5 - 2414 - 1371 = 0.
-3/2, 3, 28
Let s = -63516/11 - -317591/55. Factor s*y**4 + 3/5*y**3 - 27/5*y - 9/5*y**2 + 0.
y*(y - 3)*(y + 3)**2/5
Factor -7*u - 1/2*u**2 - 20.
-(u + 4)*(u + 10)/2
Let c(d) be the third deriva