g**3 - 15*g.
-g*(g + 3)*(g + 13)
Suppose -5*z - 26 = -5*c + 9, 4*z + 8 = 0. Let s be ((-6)/(-14))/(-1) - (-2)/14*38. Let -c*p**3 + s*p**2 - 7 - 3 + 6*p - p + 5 = 0. What is p?
-1, 1
Factor -161/4*j + 0 - 160*j**3 + 643/4*j**2 - j**4.
-j*(j + 161)*(2*j - 1)**2/4
Let s(o) be the second derivative of -1/24*o**5 + 1/24*o**4 + 10*o + 0*o**3 + 0 - 9/2*o**2. Let g(w) be the first derivative of s(w). Factor g(m).
-m*(5*m - 2)/2
Suppose -104*i + 99*i - 3 = 3*d, 0 = -4*i + 2*d + 2. Factor 0*r**2 + i + 0*r + 2/7*r**3 + 4/7*r**4 + 2/7*r**5.
2*r**3*(r + 1)**2/7
Suppose 380 = -2*x + 4*a, -4*x + 27*a - 26*a - 725 = 0. Let g be (20/(-114) - 0)*216/x. Suppose g*d - 2/19*d**2 - 2/19 = 0. What is d?
1
Factor 81/2*h**2 - 1/2*h**3 - 118*h + 78.
-(h - 78)*(h - 2)*(h - 1)/2
Let g = 359560 - 1078678/3. Factor 0 - 26/3*k - g*k**2.
-2*k*(k + 13)/3
Let n(k) be the third derivative of -k**5/630 + 47*k**4/28 - 842*k**3/63 + 11531*k**2. Find g such that n(g) = 0.
2, 421
Let i(x) be the second derivative of -5/108*x**4 - 107*x - 1/54*x**3 - 1/60*x**5 + 0 + 1/18*x**2. Let i(t) = 0. What is t?
-1, 1/3
Let m = -2282/13 - -1357764/7735. Let s = m + 1212/6545. Factor -s*t**3 + 0 + 2/11*t**5 - 2/11*t**4 + 2/11*t**2 + 0*t.
2*t**2*(t - 1)**2*(t + 1)/11
Suppose 24 = 29*b - 21*b. Solve -4 + 55*h**2 + 2*h**3 - 53*h**2 - 8*h**b + 2*h**4 + 6*h = 0 for h.
-1, 1, 2
Let h = 17176 - 171759/10. Let u(w) be the second derivative of -29*w + h*w**5 + 2/3*w**3 + 1/2*w**4 + 0*w**2 + 0. Determine j, given that u(j) = 0.
-2, -1, 0
Let y = 606 - 563. What is m in m**3 + 122 + 0*m**3 - y + 128*m - 203 - 35*m**2 = 0?
2, 31
Let s(z) be the first derivative of 0*z**2 + 9 - 10/3*z**3 + 0*z**4 + z**5 + 5*z. Factor s(k).
5*(k - 1)**2*(k + 1)**2
Let s(k) = 58*k**3 + 10*k**2 + 16*k. Let u(v) = -503*v**3 + 504*v**3 - 3*v + 2*v + 2*v**2 - v**2. Let g(l) = -2*s(l) - 28*u(l). Factor g(o).
-4*o*(6*o + 1)**2
Let x(d) be the first derivative of d**7/56 - d**6/10 + 200*d - 214. Let n(w) be the first derivative of x(w). Suppose n(q) = 0. What is q?
0, 4
Let b(o) be the first derivative of 5/3*o**2 + 28 - 1/12*o**4 + 8/3*o + 1/9*o**3. Determine l so that b(l) = 0.
-2, -1, 4
Let y(w) = w**4 + 58*w**3 + 447*w**2 + 992*w + 683. Let p(d) = -2*d**4 - 231*d**3 - 1789*d**2 - 3964*d - 2731. Let l(c) = -3*p(c) - 11*y(c). Factor l(n).
-5*(n - 17)*(n + 2)**3
Let t = 256 + -246. Solve 6*x**3 - t*x**3 - 12*x + 8*x**3 - 8 = 0.
-1, 2
Let d(v) be the first derivative of -v**8/420 - v**7/70 + 2*v**5/15 + 4*v**3/3 + 3*v + 13. Let p(c) be the third derivative of d(c). Factor p(a).
-4*a*(a - 1)*(a + 2)**2
Let r(z) be the third derivative of -15*z**4 + 0*z + 0 + 23/20*z**5 - 72*z**3 - 1/40*z**6 - 19*z**2. Factor r(l).
-3*(l - 12)**2*(l + 1)
Let h(j) = j**3 + 6*j**2 - 15*j + 32. Let k be h(-8). Factor -11 + k*a - 9003*a**2 + 32 + 9006*a**2.
3*(a + 1)*(a + 7)
Suppose 0 = 6*f - 2747 + 2741. Let n be ((-7)/35)/f*-10. Factor 0 + 3/5*i**n + 0*i.
3*i**2/5
Factor -2/13*x**2 + 554/13*x - 1100/13.
-2*(x - 275)*(x - 2)/13
Let p(d) be the first derivative of d**7/21 + d**6/3 + 9*d**5/10 + 7*d**4/6 + 2*d**3/3 - 86*d + 55. Let x(v) be the first derivative of p(v). Factor x(r).
2*r*(r + 1)**3*(r + 2)
Let o = 305 + -300. Let s = 1205/266 - 31/38. Factor 0*u + 4/7*u**2 - s*u**3 + 40/7*u**4 + 0 - 18/7*u**o.
-2*u**2*(u - 1)**2*(9*u - 2)/7
Let n(f) be the third derivative of 0 - 1/4*f**4 + 1/10*f**6 - 1/4*f**5 + 40*f**2 + 0*f + 3/2*f**3. Factor n(b).
3*(b - 1)**2*(4*b + 3)
Suppose 36 + 56 = v. Let j = -47 + v. Factor 75*n + j*n**2 + 7*n**2 + 13*n**2 + 10.
5*(n + 1)*(13*n + 2)
Let o(r) be the second derivative of -r**5/30 - 4*r**4/3 + r**3/9 + 8*r**2 + 724*r. Solve o(p) = 0 for p.
-24, -1, 1
Let l(d) = -140*d**3 - 5020*d**2 + 12*d + 250. Let n(m) = -689*m**3 - 25099*m**2 + 62*m + 1251. Let k(s) = -11*l(s) + 2*n(s). Factor k(i).
2*(i + 31)*(9*i - 2)*(9*i + 2)
Let t = 443 - 33. Let w be 3/(-5)*t/(-164). Factor -1/2*s**2 - s + w.
-(s - 1)*(s + 3)/2
Find d, given that -16/3*d - 2/3*d**2 + 6 = 0.
-9, 1
Let c be (60/150)/((-14)/(-105)). Let 3/4*i**2 - 3/4 + 3/4*i**c - 3/4*i = 0. Calculate i.
-1, 1
Let 4/3*f**5 + 28/3*f**2 + 0 - 16*f + 44/3*f**3 - 28/3*f**4 = 0. Calculate f.
-1, 0, 1, 3, 4
Let a(i) be the first derivative of 2*i**6/15 - 3*i**5/5 + i**4/3 + 2*i**3 - 4*i**2 - 36*i - 25. Let b(s) be the first derivative of a(s). Factor b(f).
4*(f - 2)*(f - 1)**2*(f + 1)
Let l be ((-744)/(-217))/(-24)*0. Suppose -1/3*r**3 + l + 0*r**2 + 1/3*r = 0. What is r?
-1, 0, 1
Suppose 5*y - 9*y - 25 = 5*j, -28 = 3*j + 5*y. Let l be j/(-4) - 1196/(-16). Factor -9*s**4 - 3*s**5 + 12 + 30*s**4 - 2*s**3 - 48*s + l*s**2 - 55*s**3.
-3*(s - 2)**2*(s - 1)**3
Solve 52/3*n + 32 - n**3 + 1/3*n**4 - 16*n**2 = 0.
-6, -1, 2, 8
Let y be 15/27*6/500. Let d(z) be the third derivative of -19*z**2 + 0*z**3 + 0 - 1/60*z**4 - y*z**5 + 0*z. Factor d(s).
-2*s*(s + 1)/5
Let o(d) be the third derivative of d**7/42 - 2*d**6/3 - 133*d**5/12 + 10*d**4/3 + 110*d**3 + 583*d**2 + 4*d. Suppose o(a) = 0. Calculate a.
-6, -1, 1, 22
Let k be (-112)/40*((-1450)/1750 - (-3)/(-5)). Suppose 14 = 5*y - 6. Factor 4/3*o + 0 + y*o**2 + 4*o**3 + 4/3*o**k.
4*o*(o + 1)**3/3
Let a = -6677/2 + 3343. Factor -1/2*b**2 + 4*b + a.
-(b - 9)*(b + 1)/2
Factor 472/3*r + 7/6*r**3 + 158/3 - 565/6*r**2.
(r - 79)*(r - 2)*(7*r + 2)/6
Let x(o) be the second derivative of 39/10*o**5 + o + 2/3*o**6 - 116 + 8*o**3 + 4*o**2 + 49/6*o**4. Find k such that x(k) = 0.
-2, -1, -1/2, -2/5
Suppose d - 2*d = 0. Let z be 4/255 + (-179)/(194752/(-128)). Solve 4/15*s**5 + 2/5*s**4 + d*s**2 + z*s**3 + 0 + 0*s = 0.
-1, -1/2, 0
Factor 225*r**2 + 4*r**4 + 104*r**3 + 166*r**2 - 28*r + 24*r + 268*r - 27*r**2.
4*r*(r + 1)*(r + 3)*(r + 22)
Suppose -3*c + 3*f + 141 = 0, -14*f = 5*c - 13*f - 223. Let u be (c/40)/9*4. Factor 0 + 4*o**4 + 0*o - 13/2*o**3 - u*o**5 + 3*o**2.
-o**2*(o - 6)*(o - 1)**2/2
Factor 17/2*t**2 + 15/2 + 31/2*t + 1/2*t**3.
(t + 1)**2*(t + 15)/2
Suppose 2*t = 2*n + 14, -5*t + 5166*n + 27 = 5163*n. Factor -64/3*p**t - 16*p**2 - 2/3 - 32/3*p**4 - 16/3*p.
-2*(2*p + 1)**4/3
Factor 4036/9*y + 2/9*y**2 + 2036162/9.
2*(y + 1009)**2/9
Let f(v) be the second derivative of 3*v**5/110 - 13*v**4/66 - 10*v**3/33 - 41*v + 16. Factor f(a).
2*a*(a - 5)*(3*a + 2)/11
Let u be (0/1)/(-5) + 13. Determine o, given that -8*o**3 + 49*o**4 - 12*o**2 - u*o**4 - 32*o**4 = 0.
-1, 0, 3
Let p(x) = x**2 + 7*x + 8. Let b be p(-6). Suppose 2*f + 21 = -3*o, -4*f = 2087 - 2027. Factor -2/7*t**4 + 0*t + 0*t**o - 32/7 + 16/7*t**b.
-2*(t - 2)**2*(t + 2)**2/7
Let -2/5*p**2 + 24*p + 122/5 = 0. Calculate p.
-1, 61
Let f be 746/(-11) + 4/(-22). Let b = -63 - f. Factor -5*m**b + 10*m**2 - 19*m**3 - 14*m**3 + 20*m**4 + 8*m**3.
-5*m**2*(m - 2)*(m - 1)**2
Let b(w) be the first derivative of 2*w**6/3 + 16*w**5/5 - 3*w**4 - 136*w**3/3 - 104*w**2 - 96*w - 1078. Factor b(o).
4*(o - 3)*(o + 1)*(o + 2)**3
Let -310*b**2 - 3180*b - 4681 - 189560*b**3 + 189555*b**3 - 4319 = 0. Calculate b.
-50, -6
Let w = 16109/3 + -5369. Suppose 0 + w*p**3 + 6*p + 20/3*p**2 = 0. What is p?
-9, -1, 0
Let b(d) be the third derivative of -1/390*d**5 + 0 - 95*d**2 + 23/78*d**4 + 0*d - 529/39*d**3. Solve b(c) = 0.
23
Let v(b) = -b**3 + 393*b**2 - 388*b. Let d(p) = 20*p**3 - 6685*p**2 + 6595*p. Let y(r) = -2*d(r) - 35*v(r). Factor y(g).
-5*g*(g - 1)*(g + 78)
Suppose 415*i - 1112 = -141*i. Factor 13/2*r**3 - i*r + 0 + 7/4*r**4 + 5*r**2.
r*(r + 2)**2*(7*r - 2)/4
Determine u, given that 0*u - 1/5*u**4 - 24*u**2 + 22/5*u**3 + 0 = 0.
0, 10, 12
Let a(s) be the first derivative of -1/2*s**4 + 0*s**3 + 0*s - s**2 + 14 - 1/15*s**5. Let n(r) be the second derivative of a(r). Suppose n(l) = 0. Calculate l.
-3, 0
Let r(b) = 49*b + 106. Let v(p) = 15*p + 35. Let k(w) = 2*r(w) - 7*v(w). Let j be k(-5). Factor -2 - 1/2*m**2 - j*m.
-(m + 2)**2/2
Suppose 2*m = -2*q - 2, -q = 3*m - 0*m - 7. Let s(g) = g**2 - 7*g + 3. Let r be s(7). Let -15*f**m - f**4 + 5*f**4 + 12*f**r + 9*f**2 - 10*f**4 = 0. What is f?
-3/7, 0, 1
Let h = -230 - 236. Let c = -464 - h. Suppose 4/3 - 8/3*x - 1/3*x**3 + 5/3*x**c = 0. Calculate x.
1, 2
Suppose 1943*m - 5393 = -1507. Factor -14/3*a - 1/3*a**m - 13/3.
-(a + 1)*(a + 13)/3
Let -609*k + 180126 - 590*k - 73*k + 2*k**2 + 22122 = 0. What is k?
318
Suppose -413*v = -417*v + 8. Let y = 10 - 0. What is a in -1 + 2*a