+ 9*j + 7. Let m be s(-4). Factor -3/8*h**q - 3/8*h**m - 15/4*h**2 + 3/2*h**4 + 3/2*h + 3.
-3*(h - 2)**3*(h + 1)**2/8
Let 4/5*v**4 + 24/5*v**3 + 48/5*v + 52/5*v**2 + 16/5 = 0. Calculate v.
-2, -1
Let l be (-2)/(-5 + 4) + 7. Factor l*p**3 - 15*p - 4*p**3 - 8 - 2.
5*(p - 2)*(p + 1)**2
Let w = 27 + -9. Factor 31*j**4 - 18*j**4 + 45*j**3 + 5*j**5 - 35*j**2 - w*j**4 - 20*j**4 + 10*j.
5*j*(j - 2)*(j - 1)**3
Suppose 69*x = 57*x. Let c(o) be the first derivative of 1/3*o**4 + 1/9*o**3 - 1/5*o**5 - 1/3*o**2 + x*o - 6. Let c(t) = 0. Calculate t.
-2/3, 0, 1
Let u(j) be the third derivative of -43*j**2 + 1/300*j**5 + 0 + 0*j + 1/60*j**4 + 0*j**3. Find f such that u(f) = 0.
-2, 0
Let a = -7013 + 7015. What is o in -2/5*o**2 - a*o + 0 = 0?
-5, 0
Let y(h) be the second derivative of h**6/1800 - h**5/300 - h**4/40 - 13*h**3/6 + 10*h. Let b(n) be the second derivative of y(n). Solve b(c) = 0 for c.
-1, 3
Let i(h) be the third derivative of h**7/42 + 3*h**6/8 + 29*h**5/12 + 65*h**4/8 + 15*h**3 + 226*h**2. Factor i(p).
5*(p + 1)*(p + 2)*(p + 3)**2
Suppose -78*o + 87*o + 99 = 0. Let d = o - -16. Find x such that 2/3*x**3 + 0*x + 4/3*x**4 + 2/3*x**d + 0*x**2 + 0 = 0.
-1, 0
Let t(k) = 0*k**3 - 9 + 4*k**2 + 10 - 6*k + k**3. Let y be t(-5). Suppose 24*b - 11 - 12*b**2 + 4 - 3 + 2*b**3 - y = 0. Calculate b.
2
Let r be (-1)/9 - (-475)/2736. Let u(j) be the second derivative of 1/24*j**3 + 0*j**2 + j - 1/120*j**6 + 3/80*j**5 + 0 - r*j**4. Factor u(i).
-i*(i - 1)**3/4
Suppose -x + h = -4, -x - 11*h + 8*h = 0. Let v(b) be the third derivative of -x*b**2 + 0 + 1/100*b**6 + 0*b - 2/45*b**5 - 2/45*b**3 + 13/180*b**4. Factor v(c).
2*(c - 1)**2*(9*c - 2)/15
Let c = -5265 + 36858/7. Find l, given that 24/7*l**2 - 6/7*l**4 + c*l**5 - 9/7*l**3 - 12/7*l + 0 = 0.
-2, 0, 1, 2
Let u(q) be the second derivative of -q**7/42 + 4*q**6/45 - q**5/30 - q**4/3 - q**3 + 10*q. Let o(a) be the second derivative of u(a). Factor o(b).
-4*(b - 1)**2*(5*b + 2)
Let j(s) be the first derivative of s**6/240 + 3*s**5/80 - 5*s**3 - 11. Let q(t) be the third derivative of j(t). What is u in q(u) = 0?
-3, 0
Let w(u) = u**3 + 3*u - 1. Let o(q) = -q**3 + 3*q**2 + 6*q - 2. Let t(p) = -o(p) + 2*w(p). Factor t(j).
3*j**2*(j - 1)
Let f(b) be the first derivative of -3*b**4/4 - 6*b**3 - 15*b**2/2 + 18. Determine r, given that f(r) = 0.
-5, -1, 0
Let z(j) = 37 - 8*j + 12 + 12*j - 11*j. Let w be z(7). Factor w*f + 0 + f**3 - 1/2*f**2.
f**2*(2*f - 1)/2
Let w be 1 + -13 + (-24130)/(-1995). Factor -w*j**2 - 4/21 + 2/7*j.
-2*(j - 2)*(j - 1)/21
Let g(c) = -5*c**2 + 15*c + 30. Let v(l) = -l - 3. Let q(m) = 3*m + 8. Let p(b) = -3*q(b) - 8*v(b). Let u(s) = g(s) + 10*p(s). Factor u(z).
-5*(z - 3)*(z + 2)
Let 745*f + 1545*f**2 + 5988 - 1368*f + 13*f**4 - 1017*f - 5448 - 460*f**3 + 2*f**4 = 0. What is f?
2/3, 1, 2, 27
Let c(s) be the first derivative of 3*s**4/4 - 7*s**3 + 9*s**2 + 575. Suppose c(n) = 0. What is n?
0, 1, 6
Let z be 4/5*10/4. Solve -2*g**z + g**2 + 0*g**2 = 0.
0
Let q(d) be the first derivative of -d**6/840 - d**5/70 - d**4/14 - 4*d**3/21 + 17*d**2 - 1. Let m(v) be the second derivative of q(v). Factor m(r).
-(r + 2)**3/7
Let f(a) = -a**3 + 18*a**2 - 16*a + 14. Let s be f(16). Let t = -270 + s. Factor 6*w + 9/2*w**2 - 3/2*w**3 + t.
-3*w*(w - 4)*(w + 1)/2
Let u(x) = -x + 4. Let h be u(-2). Factor -23 - 52*d - 10*d**2 - h*d**2 + 12*d**3 - 1.
4*(d - 3)*(d + 1)*(3*d + 2)
Let o(j) = 88*j**2 - 527*j. Let v be o(6). Let g(n) be the first derivative of -v + 10/3*n**2 + 50/3*n + 2/9*n**3. Factor g(w).
2*(w + 5)**2/3
Let l(z) be the first derivative of -z**4/8 + z**3/3 + 11*z**2/4 - 6*z - 74. Factor l(x).
-(x - 4)*(x - 1)*(x + 3)/2
Suppose 0 = -3*h + 4*o + 47, 4*h - 28 = -4*o + 16. Suppose -57 = -6*i - h*i. Determine z, given that i*z + 1/2*z**2 + 9/2 = 0.
-3
Let s(l) be the second derivative of l**7/63 - l**6/5 + 7*l**5/15 - 11*l - 3. Factor s(w).
2*w**3*(w - 7)*(w - 2)/3
Let h be 5 + ((-5 - 0) + -4 - -6). Let x(l) be the first derivative of 1/12*l**h - 7 - 1/18*l**3 + 1/3*l. Factor x(i).
-(i - 2)*(i + 1)/6
Factor -49*j**2 - 51*j**2 - 2 - 55*j**2 + 15*j + 18 + 154*j**2.
-(j - 16)*(j + 1)
Let x(w) = 18*w**3 + 258*w**2 + 2250*w + 4694. Let y(f) = 44*f**3 + 644*f**2 + 5624*f + 11736. Let i(v) = -12*x(v) + 5*y(v). Determine z, given that i(z) = 0.
-14, -3
Let t(w) be the second derivative of w**4/48 + w**3/8 - w**2/2 - 66*w. Suppose t(c) = 0. Calculate c.
-4, 1
Suppose -2*z + 36 = -3*u + 41, -5*u + 5 = -5*z. Factor 0 - 4*m**2 + 10*m**u + 0*m + 3/2*m**5 - 7*m**4.
m**2*(m - 2)**2*(3*m - 2)/2
Suppose 5*l**5 - 58/3*l**2 - 76/3*l**4 - 4*l + 8/3 + 41*l**3 = 0. Calculate l.
-1/3, 2/5, 1, 2
Factor 28*w**3 - 55*w**3 - 194*w + 24*w**3 - 5400 + 174*w**2 - 2146*w.
-3*(w - 30)**2*(w + 2)
Let m(w) be the second derivative of 5*w**7/42 + 2*w**6 + 12*w**5 + 80*w**4/3 - 81*w. Factor m(b).
5*b**2*(b + 4)**3
Let b be (4 + -3)/(15/9). Let j = 164 + -162. Factor -6/5*x + 0 + b*x**j.
3*x*(x - 2)/5
Let d(r) = r**4 + r**3 + r + 1. Let h(q) = -16*q**4 + 84*q**3 - 340*q**2 + 396*q - 172. Let t(c) = 12*d(c) + h(c). Factor t(a).
-4*(a - 20)*(a - 2)*(a - 1)**2
Factor 864*t**2 - 1696/7*t - 1064*t**3 + 160/7 + 98*t**4.
2*(t - 10)*(7*t - 2)**3/7
Suppose 11*h - 7*h + 8 = 0. Let m(n) = -7*n**4 - n**3 + 5*n. Let q(r) = 3*r**4 - 2*r. Let x(c) = h*m(c) - 5*q(c). Factor x(s).
-s**3*(s - 2)
Let m(i) be the first derivative of -i**3/3 + 38*i**2 + 77*i - 161. Find t, given that m(t) = 0.
-1, 77
Let o(q) be the second derivative of -5*q**4/12 - 385*q**3/3 - 29645*q**2/2 + 167*q. Suppose o(b) = 0. What is b?
-77
Let u(b) = -b**4 - b**3 + 2*b**2 - b - 1. Let a(n) = -25*n**4 - 35*n**3 + 10*n**2 - 70*n - 30. Let o(v) = -a(v) + 30*u(v). Factor o(d).
-5*d*(d - 4)*(d + 1)*(d + 2)
Factor -2/9*r**3 + 0*r**2 + 0 + 0*r.
-2*r**3/9
Let o(r) = r**3 - 10*r + 8. Let d be o(3). Suppose 4*v + 4*n + 12 = -8, d*n + 25 = 3*v. Factor -3/4*y**4 + v*y + 0*y**3 + 0 + 3/4*y**2.
-3*y**2*(y - 1)*(y + 1)/4
Let i = -15709 - -172803/11. Factor -2/11*z**5 - 2/11*z + 0*z**2 + i*z**3 + 0 + 0*z**4.
-2*z*(z - 1)**2*(z + 1)**2/11
Let s = -493 - -493. Let z(j) be the first derivative of 0*j + 2/35*j**5 + s*j**2 + 5 - 1/7*j**4 + 2/21*j**3. Determine g so that z(g) = 0.
0, 1
Let t(i) be the first derivative of i**6/54 - 11*i**4/36 - 2*i**3/3 - 4*i**2/9 - 32. Factor t(s).
s*(s - 4)*(s + 1)**2*(s + 2)/9
Let n(t) = -8*t**3 + 71*t**2 - 363*t + 5. Let p(j) = -7*j**3 + 70*j**2 - 363*j + 4. Let a(l) = 4*n(l) - 5*p(l). Determine c, given that a(c) = 0.
0, 11
Let g(d) be the third derivative of d**9/1512 - d**8/840 - d**7/420 + d**6/180 - 2*d**3/3 - 12*d**2. Let r(v) be the first derivative of g(v). Solve r(k) = 0.
-1, 0, 1
Let o be (-3 - 1)/((-72)/54). Let m(a) be the first derivative of 0*a**o - 8 + 2/3*a**2 - 1/12*a**4 + 0*a. Factor m(t).
-t*(t - 2)*(t + 2)/3
Factor 4/3 - 1/3*i**3 - 4/3*i**2 + 1/3*i.
-(i - 1)*(i + 1)*(i + 4)/3
Let w(j) be the first derivative of -3*j**5/40 - 7*j**4/12 - 17*j**3/12 - 3*j**2/2 + 7*j + 8. Let i(s) be the first derivative of w(s). What is b in i(b) = 0?
-3, -1, -2/3
Let 89 + 0*w**4 - 153 - 96*w**2 - 4*w**4 + 128*w + 32*w**3 = 0. Calculate w.
2
Let o = 30961/60 - 516. Let p(v) be the third derivative of 7/120*v**4 + 0*v - 1/10*v**3 + 0 + 4*v**2 - o*v**5 + 1/600*v**6. Factor p(q).
(q - 3)*(q - 1)**2/5
Let t(c) = 8*c**5 - 7*c**4 - 8*c**3 + 10*c**2 - 3*c - 3. Let m(h) = -9*h**5 + 6*h**4 + 9*h**3 - 10*h**2 + 4*h + 4. Let v(r) = 3*m(r) + 4*t(r). Factor v(w).
5*w**2*(w - 2)*(w - 1)*(w + 1)
Let i(l) = 9*l - 365. Let h be i(41). Factor -1/5*w**3 + 0 + 6/5*w**h - 2/5*w**2 + 0*w.
w**2*(2*w + 1)*(3*w - 2)/5
Let x(m) = -15*m**2 + 22*m - 61. Let g(z) = 7*z**2 - 11*z + 30. Let c(q) = -13*g(q) - 6*x(q). Factor c(h).
-(h - 8)*(h - 3)
Let b(y) = -75*y**2 + 327*y - 360. Let n(m) = -150*m**2 + 653*m - 719. Let t(u) = 7*b(u) - 3*n(u). Factor t(w).
-3*(5*w - 11)**2
Let q = -2169 - -2169. Let g be -3*(-2 + 114/63). Suppose q*l + g*l**2 + 0 - 2/7*l**4 + 2/7*l**3 = 0. Calculate l.
-1, 0, 2
Factor 296 + 1530*d**3 + 4768*d**2 + 934*d + 583*d + 153*d - 1466*d**3 + 702*d.
4*(d + 74)*(4*d + 1)**2
Let n be (2 - -10) + 4*-1. Factor n - 21*w**2 - 63*w**3 - 45*w**2 + 3*w - 7*w.
-(3*w + 2)**2*(7*w - 2)
Factor -4/3*j**4 - 52/3*j**2 + 0 - 8*j - 32/3*j**3.
-4*j*(j + 1)**2*(j + 6)/3
Let u(o) = -16*o**2 - 256*o -