(f) = 3 - 9*f**2 + 36*f + 1 - 224*f**3 + 110*f**3 + 113*f**3. Let s be x(-12). Factor -3*z**3 + 3/4*z**5 + 3/2*z**2 - 3/2 + 0*z**s + 9/4*z.
3*(z - 1)**3*(z + 1)*(z + 2)/4
Let p be ((-48)/144)/((-4)/54). Let a = p - 55/14. Solve -2/7*o**3 - 3/7 + 2/7*o - 1/7*o**4 + a*o**2 = 0.
-3, -1, 1
Let a = 193 + -198. Let o be a/(-7)*7/(-105)*-12. Suppose -o*q**2 - 1/7*q**5 - 1/7*q + 2/7 + 2/7*q**3 + 2/7*q**4 = 0. Calculate q.
-1, 1, 2
Let n be ((-21)/(-49))/(46/161). Let v(c) be the first derivative of -7/4*c**2 - 1/10*c**5 - n*c**3 - 3 - c - 5/8*c**4. Solve v(b) = 0.
-2, -1
Let y(d) be the second derivative of 19/30*d**6 + 1/20*d**5 + 1/6*d**7 + 1 + 2*d**2 - 23/12*d**4 - 39*d - 4/3*d**3. What is v in y(v) = 0?
-2, -1, 2/7, 1
Let b(z) = -4*z**2 - 191*z - 2029. Let q be b(-16). Let 8*d**q + 0 + 32/3*d + 4/3*d**4 + 16*d**2 = 0. Calculate d.
-2, 0
Factor -2*v**2 - 8*v**2 + 6*v**2 + 308*v + 137*v - 229*v - 612.
-4*(v - 51)*(v - 3)
Let v = -276705 + 276710. Factor 0 - 4/5*f**2 + 0*f**4 + 0*f + 2/5*f**v - 6/5*f**3.
2*f**2*(f - 2)*(f + 1)**2/5
Let r(b) be the first derivative of -b**8/112 - b**7/84 + b**6/24 + b**5/12 + 9*b**3 + 170. Let l(n) be the third derivative of r(n). Solve l(p) = 0 for p.
-1, -2/3, 0, 1
Let q be 8*((-65)/910)/(-1 - (-51)/63). What is c in -16/3*c + 4 + c**2 + 1/3*c**q = 0?
-6, 1, 2
Let a(c) be the first derivative of c**6/6 - 3*c**5/4 + 5*c**4/4 - 5*c**3/6 + 59*c - 34. Let q(r) be the first derivative of a(r). Factor q(m).
5*m*(m - 1)**3
Let j(n) be the third derivative of -n**5/240 - 35*n**4/96 - 17*n**3/12 + 36*n**2 - 3. Factor j(x).
-(x + 1)*(x + 34)/4
Factor 136/3 + 1/3*s**2 - 137/3*s.
(s - 136)*(s - 1)/3
Let m(o) = -9*o**2 - 309*o - 712. Let u(q) = -2*q**2 - 78*q - 178. Let k(j) = -6*m(j) + 26*u(j). Let k(n) = 0. Calculate n.
-2, 89
Suppose 7/5 - 1/5*x**5 - 2/5*x**2 - 13/5*x - x**4 + 14/5*x**3 = 0. Calculate x.
-7, -1, 1
Let w(h) be the third derivative of -h**6/1080 + h**5/90 - h**4/18 + 31*h**3/3 - 59*h**2. Let v(x) be the first derivative of w(x). Find s such that v(s) = 0.
2
Let n(y) = 4*y**2 + 13*y - 31. Let f be n(9). Factor -5*h**2 - 416*h + 3*h**2 - 4 + f*h.
-2*(h + 1)*(h + 2)
What is b in -748*b - 503*b + 5292 - 156*b**2 + 400*b - 4*b**3 - 409*b = 0?
-21, 3
Let c be (-11)/((-154)/(-4)) + (4/2)/14*86. Factor 3/2*u**5 - 9*u**4 + 6 + c*u**3 + 3*u**2 - 27/2*u.
3*(u - 4)*(u - 1)**3*(u + 1)/2
Let o be 9/(((-21)/2)/7). Let q be (576/(-180))/(o/5). Solve 16/3 + q*n + 2/3*n**4 - 2/3*n**3 - 4*n**2 = 0 for n.
-2, -1, 2
Factor -39576*x**3 + 39696*x**3 - 208 - 325*x**2 - 111*x**2 - 4*x**4 + 528*x.
-4*(x - 26)*(x - 2)*(x - 1)**2
Let t(c) be the third derivative of c**8/504 + 2*c**7/63 - c**6/9 - 4*c**5 + 384*c**3 + 2*c**2 + 526. Factor t(r).
2*(r - 4)**2*(r + 6)**3/3
Let v be 9/5 + 0 - (-4)/20. Let -286*o**v + o**3 + 301*o**2 - 5*o**4 + 4*o**3 + 10 - 25*o = 0. What is o?
-2, 1
Let l = 906862/3 - 302286. Factor -l + 0*c + c**2 + 1/3*c**3.
(c - 1)*(c + 2)**2/3
Let u(v) be the third derivative of -v**6/24 + 37*v**5/15 - 159*v**4/8 + 39*v**3 - 2993*v**2. What is r in u(r) = 0?
3/5, 3, 26
Let p(u) be the third derivative of 0*u - 56*u**2 + 1/300*u**5 + 0 - 1/24*u**4 + 0*u**3. Factor p(w).
w*(w - 5)/5
Find c such that 192/5*c**2 - 49/5*c**4 + 16/5 - 112/5*c + 28/5*c**3 = 0.
-2, 2/7, 2
Let m = -17304 - -17306. Let w(f) be the first derivative of 0*f + 2*f**6 + 8/3*f**3 + 20 + 2*f**m - 8/5*f**5 - 4*f**4. Solve w(p) = 0.
-1, -1/3, 0, 1
Let a(w) be the second derivative of -1 + 17*w + 0*w**5 + 0*w**2 + 0*w**6 + 1/63*w**7 + 0*w**3 + 0*w**4. Solve a(g) = 0.
0
Let l(y) be the second derivative of 1/32*y**4 - 3 + 3/4*y**2 - 1/112*y**7 - 1/16*y**6 - 21/160*y**5 + 1/2*y**3 + 21*y. Let l(r) = 0. What is r?
-2, -1, 1
Let m(g) be the third derivative of g**5/270 - 52*g**4/27 + 10816*g**3/27 + 815*g**2. Suppose m(l) = 0. Calculate l.
104
Let b = -403 + 393. Let m be (-46 - -45)*b/4. Let -m*t**3 + 4*t - 9*t**2 + 0 = 0. What is t?
-4, 0, 2/5
Suppose 2*c - 75 + 55 = 0. What is o in -10 - 181*o**2 + c*o + 182*o**2 + 35 = 0?
-5
Let f = 6552 + -6546. Let g(s) be the second derivative of 7/33*s**3 + 19*s - 2/11*s**2 + 0 + 1/55*s**5 - 4/33*s**4 - 1/231*s**7 + 2/165*s**f. Factor g(p).
-2*(p - 1)**4*(p + 2)/11
Let j(y) be the third derivative of y**5/40 - 211*y**4/2 + 1687*y**3/4 + 2964*y**2 + y. Factor j(a).
3*(a - 1687)*(a - 1)/2
Let z(d) be the third derivative of d**6/280 - 19*d**5/140 - 145*d**4/56 - 125*d**3/14 - 42*d**2 + 6*d. Factor z(f).
3*(f - 25)*(f + 1)*(f + 5)/7
Let w(t) be the first derivative of -2*t**6/21 - 47*t**5/35 - 46*t**4/7 - 263*t**3/21 - 41*t**2/7 + 40*t/7 + 120. Find u, given that w(u) = 0.
-5, -4, -2, -1, 1/4
Let 1/8*w**2 + 0 + 521/8*w = 0. What is w?
-521, 0
Let n be (0 - 480/(-400))/(((-2)/(-5))/1). Suppose 4/13*r**n + 2/13*r**4 - 2/13*r**5 + 0 + 0*r + 0*r**2 = 0. What is r?
-1, 0, 2
Let k(z) be the third derivative of z**5/90 + 83*z**4/18 - 167*z**3/9 - 29*z**2 + 107*z. Factor k(o).
2*(o - 1)*(o + 167)/3
Determine c so that 1/5*c**4 + 41/5*c**2 - 13/5*c**3 - 47/5*c + 18/5 = 0.
1, 2, 9
Let a be 14/35 + (2 - 26/(-10)). Factor -772*x**3 - 60*x - 72 + x**4 - a*x**4 + 28*x**2 + 784*x**3.
-4*(x - 3)**2*(x + 1)*(x + 2)
Factor -160 - 82*r**2 - 724/3*r - 2/3*r**3.
-2*(r + 1)*(r + 2)*(r + 120)/3
Let u(a) be the second derivative of -1/147*a**7 - 2/21*a**4 + 3/70*a**5 - 4/21*a**3 + 0*a**2 + a + 2/105*a**6 + 31. Factor u(k).
-2*k*(k - 2)**2*(k + 1)**2/7
Let l(x) be the second derivative of -x**6/45 - 2*x**5/15 + x**4/9 + 4*x**3/3 - 3*x**2 + 4380*x. Factor l(i).
-2*(i - 1)**2*(i + 3)**2/3
Let z = 500 - 530. Let y be (-18)/z + (2 - (-28)/(-20)). Factor d - y + 1/5*d**2.
(d - 1)*(d + 6)/5
Let i(r) be the second derivative of r**5/10 - r**4/4 - 5*r**3/6 - 3*r**2/2 - 2*r + 15. Let s(m) = -m**2 + m - 1. Let n(c) = i(c) - 3*s(c). Factor n(w).
2*w*(w - 2)*(w + 2)
Let d(f) be the first derivative of -1/10*f**4 + 111 + 88/5*f + 14/15*f**3 + 8*f**2. Suppose d(n) = 0. Calculate n.
-2, 11
Let a = -111615 - -111615. Solve -9/5*z + 3/5*z**3 + a*z**2 - 6/5 = 0 for z.
-1, 2
Suppose -21*t = -18*t + 3*c - 18, 5*t = 4*c + 3. Factor -3*g - 33*g**2 + 0*g**t - g**3 - 3*g**3 + 9*g**2 - 33*g.
-4*g*(g + 3)**2
Let s(w) be the first derivative of 2*w**3/21 - 26*w**2/7 - 66*w - 230. Solve s(t) = 0 for t.
-7, 33
Let b(r) = 6*r**3 + 41*r**2 - 6*r + 10. Let o be b(-7). Let x(t) be the second derivative of 1/18*t**4 - o - 2*t + 0*t**2 - 1/9*t**3. Find h such that x(h) = 0.
0, 1
Suppose 12 = 4*x - 3*m - 7, 0 = -x + 4*m + 8. Let k(l) = -l**3 - 6*l**2 - 6*l - 3. Let g be k(-5). Let -4*h**g + 56 - x*h**2 + 20*h - 64 = 0. What is h?
1/2, 2
Let 1171*k**3 + 5159*k**3 + 35560*k**2 + 3079*k**3 + 5*k**5 + 54760 + 400*k**4 - 419*k**3 - 99715*k = 0. Calculate k.
-37, -8, 1
Solve -57/4*n**4 - 51/4*n**2 - 207/4*n**3 + 27 + 207/4*n = 0.
-3, -1, -12/19, 1
Let b(p) be the first derivative of -p**4/24 + 223*p**3/3 - 49729*p**2 + 44358268*p/3 + 845. Solve b(w) = 0 for w.
446
Suppose 3747/7*m**2 + 1168128/7 + 1171872/7*m + 3/7*m**3 = 0. What is m?
-624, -1
Let q be (786/(-36) - 7/(-14)) + 22. Solve -q - 1/6*v**2 - 2/3*v = 0 for v.
-2
Suppose 0 = -2*p - 4*k + 8*k + 18, -70 = -6*p - 4*k. Let b(q) be the first derivative of -1/3*q**3 - 1/4*q**4 + p + q + 1/2*q**2. Suppose b(o) = 0. What is o?
-1, 1
Factor 0 + 0*s + 160/3*s**3 - 328/3*s**2 + 2/3*s**4.
2*s**2*(s - 2)*(s + 82)/3
Find x such that 7/4*x**4 - 3*x - 7/4*x**2 + 11/4*x**3 + 0 + 1/4*x**5 = 0.
-4, -3, -1, 0, 1
Suppose 7*b + 6314 = -3661. Let u = b - -1429. Factor 0 + 4/15*y**3 + 2/5*y**5 + 0*y + 2/3*y**u + 0*y**2.
2*y**3*(y + 1)*(3*y + 2)/15
Let j be (8 + -5)*(4/(-3) + -1). Let x be j*1 + (96 - 87). Factor -1/3*a**4 - 12*a**x + 11/3*a**3 + 64/3 + 16/3*a.
-(a - 4)**3*(a + 1)/3
Let q(k) be the third derivative of -33*k**2 + 34/3*k**3 + 0*k - 2 - 8/3*k**4 - 1/15*k**5. Factor q(n).
-4*(n - 1)*(n + 17)
Suppose 0*i**3 - 7*i**3 - 56*i**2 + 31*i**3 - i - 10*i**3 + 56 - 13*i**3 = 0. What is i?
-1, 1, 56
Let t(v) = -8*v**3 - 4*v**2 + 5*v - 2. Let l = -32 + 38. Let b(m) = m**3 - 10*m + 4*m + l*m. Let y(f) = -18*b(f) - 2*t(f). Suppose y(k) = 0. Calculate k.
1, 2
Let d(b) be the third derivative of -b**5/105 - 97*b**4/21 - 386*b**3/21 - 1051*b**2. Factor d(h).
-4*(h + 1)*(h + 193)/7
Let n(a) = -3*a - 11. Let d be n(-5). Suppose -4*f - t + 30 = -3*t, d*f + 3