(p - 1)*(p + 1)/7
Let y be 208/(-468) - (-8)/18. Let g(d) be the first derivative of 3/5*d**5 + 0*d**3 + 0*d + y*d**2 + 3/4*d**4 + 32. Factor g(f).
3*f**3*(f + 1)
Let m(o) be the third derivative of -o**5/90 - 41*o**4/36 - 26*o**3/3 + o**2 + 116. What is b in m(b) = 0?
-39, -2
Let x(b) be the second derivative of -b**6/10 - 6*b**5/5 - 19*b**4/4 - 6*b**3 + 6356*b. Factor x(g).
-3*g*(g + 1)*(g + 3)*(g + 4)
Suppose 2 = 2*q - q. Let x = -145938 - -145941. Suppose x*j - 117/4*j**3 + 0 + 105/4*j**4 + 0*j**q = 0. What is j?
-2/7, 0, 2/5, 1
Let s(j) = j**3 - 9*j**2 - 3*j - 1. Let f be s(11). Suppose -17*u**5 - f*u**2 - 268*u**4 - 35*u**3 + 443*u**3 + 32*u + 73*u**5 = 0. What is u?
0, 2/7, 1/2, 2
Let d(c) be the third derivative of c**5/630 + 59*c**4/252 - 20*c**3/21 - c**2 - 330*c. Factor d(i).
2*(i - 1)*(i + 60)/21
Suppose -6*a - 7*a = -1014. Solve 560*y - a*y**2 - 70*y**2 + 15680 + 153*y**2 = 0.
-56
Suppose 5*o = -5*d - 80, -2*o = o - 4*d + 20. Let w be o + 23 + (-141)/15. Factor 2/5*v - w*v**3 - v**4 + 0 - 1/5*v**2.
-v*(v + 1)**2*(5*v - 2)/5
Factor -7/3*q**3 - 40/3*q**2 + 0 - 44/3*q + 1/3*q**4.
q*(q - 11)*(q + 2)**2/3
Factor -10*l**5 - 16*l**3 + 36*l**4 + 11*l**5 + 3*l**5 - 8*l**5 - 16*l**3.
-4*l**3*(l - 8)*(l - 1)
Let y(g) be the second derivative of -g**5/70 - 109*g**4/14 - 9280*g**3/7 - 25600*g**2 - 46*g + 42. Solve y(d) = 0.
-160, -7
Let g(x) be the third derivative of x**6/288 + x**5/32 - 15*x**4/16 - 13*x**3/2 + x**2 + 93. Let u(a) be the first derivative of g(a). Factor u(z).
5*(z - 3)*(z + 6)/4
Suppose 40*v**2 + 129*v**2 + 23*v**2 - 4*v**4 - 40*v**2 - 1177*v**3 + 1109*v**3 = 0. What is v?
-19, 0, 2
Let u(f) be the second derivative of -21/20*f**5 - 1 + 17/4*f**4 + 9*f**2 - 4*f - 17/2*f**3 + 1/10*f**6. Suppose u(g) = 0. What is g?
1, 2, 3
Let u(a) = 106*a + 6573. Let c be u(-62). Factor 7/6*b - 1/6*b**2 - c.
-(b - 6)*(b - 1)/6
Factor -2/11*t**2 + 128/11*t - 1950/11.
-2*(t - 39)*(t - 25)/11
Let m(p) be the first derivative of 3*p**4/4 - 71*p**3 + 306*p**2 - 3979. Factor m(c).
3*c*(c - 68)*(c - 3)
Factor 0*m + 0*m**2 - 14/3*m**4 + 0 - 8*m**3 - 1/3*m**5.
-m**3*(m + 2)*(m + 12)/3
Factor 60 - 3*j**2 - 16*j**3 + 4*j**3 + 13*j**3 - 6*j**2 - 16*j.
(j - 10)*(j - 2)*(j + 3)
Let j(c) be the first derivative of 66 - 128*c - 16*c**2 - 2/3*c**3. Find w such that j(w) = 0.
-8
Let d(z) = z**3 - 226*z**2 + 225*z - 4. Let s = -760 - -764. Let u(g) = -225*g**2 + 225*g - 5. Let f(x) = s*u(x) - 5*d(x). Solve f(j) = 0 for j.
0, 1, 45
Let r(l) be the second derivative of -l**4/24 - 1283*l**3/6 - 1646089*l**2/4 + 115*l + 2. Suppose r(t) = 0. Calculate t.
-1283
Let t(s) be the second derivative of -249*s + 0 - 1/96*s**4 - 1/8*s**2 + 1/16*s**3. Factor t(d).
-(d - 2)*(d - 1)/8
Let c(s) be the third derivative of 4/5*s**5 + 0*s - 1 - 1/5*s**6 + 6*s**4 - 114*s**2 - 3/35*s**7 + 16*s**3 - 1/112*s**8. Factor c(k).
-3*(k - 2)*(k + 2)**4
Let c(o) be the third derivative of 0*o + 1/66*o**4 - 1/330*o**5 - 20 + 2*o**2 + 1/11*o**3. Factor c(y).
-2*(y - 3)*(y + 1)/11
Let m(g) be the first derivative of -2/15*g**3 - 1/10*g**4 + 0*g + 2/5*g**2 + 82. Factor m(u).
-2*u*(u - 1)*(u + 2)/5
Let s(i) be the second derivative of -3/5*i**3 + 30*i - 1/50*i**5 - 13*i**2 + 0 + 1/5*i**4. Let j(p) be the first derivative of s(p). Factor j(d).
-6*(d - 3)*(d - 1)/5
Let l be (15/(-10))/(-2 - (-38)/20). Factor 33*f - 50*f**3 + 53*f**3 + 0 + l + 21*f**2.
3*(f + 1)**2*(f + 5)
Let l(w) be the third derivative of -w**4/8 - 11*w**3 + 236*w**2. Let y be l(-22). Factor 6/11*q + 1/11*q**2 + y.
q*(q + 6)/11
Let d(m) be the third derivative of 15*m**2 + 0*m**3 + 1/896*m**8 - 3/560*m**7 + 0 - 19/320*m**6 + 9/32*m**4 + 3/160*m**5 + 4*m. Let d(w) = 0. What is w?
-3, -1, 0, 1, 6
Let b(t) be the second derivative of t**7/2520 - t**6/180 - 7*t**5/40 - t**4/2 + 2*t**3 - 14*t - 1. Let u(l) be the third derivative of b(l). Factor u(m).
(m - 7)*(m + 3)
Let g(c) = -c**3 + 18*c**2 - 64*c - 140. Let m be g(11). Let d(l) be the second derivative of 3*l + 1/14*l**2 + 1/84*l**4 + 1/21*l**m + 0. Factor d(w).
(w + 1)**2/7
Let k be 26*(-150)/(-1560)*12*(4 + 0). Find g such that -k*g - 3/2*g**2 - 2400 = 0.
-40
Let g(a) = -3*a**4 - 57*a**3 + 501*a**2 - 1139*a + 714. Let t(f) = -3*f**4 - 57*f**3 + 501*f**2 - 1138*f + 717. Let q(i) = -5*g(i) + 4*t(i). Factor q(v).
3*(v - 3)**2*(v - 1)*(v + 26)
Let v = 1647 + -230579/140. Let u = 167/140 + v. Factor u*n**2 - 8/5 - 2/5*n**3 + 0*n.
-2*(n - 2)**2*(n + 1)/5
Let y(l) be the first derivative of 9/10*l**5 + 0*l**2 - 21/4*l**4 - 5/2*l**3 + 0*l - 152. Factor y(k).
3*k**2*(k - 5)*(3*k + 1)/2
Factor -48 + 31*n + 55*n - 13*n - 2*n**2 - 108*n.
-(n + 16)*(2*n + 3)
Suppose -8 = 512*r - 510*r. Let m be (r/10)/(5/(-25)). Factor 0 + 5/2*s + 1/2*s**m.
s*(s + 5)/2
Let q(c) be the first derivative of c**4/3 + 4*c**3/3 + 82*c + 69. Let g(r) be the first derivative of q(r). Factor g(x).
4*x*(x + 2)
Suppose -5*b + 10*b**3 - 20*b**2 - 18*b**3 - 3*b = 0. What is b?
-2, -1/2, 0
Let o be (36/(-24))/((-1)/4). Suppose 45 = 3*q + 9*f - o*f, 0 = -2*f + 10. Solve 20*h + 40*h + 94*h**3 - 28*h + q*h**4 + 116*h**2 = 0 for h.
-8, -1, -2/5, 0
Let h(z) be the second derivative of 0*z**3 + 1/14*z**7 + 0*z**2 + 0 - 3/10*z**6 - 32*z + 0*z**4 + 3/10*z**5. Solve h(q) = 0.
0, 1, 2
Let v(k) be the second derivative of 3*k**5/80 - 3*k**4/16 - 9*k**3 + 243*k**2/2 - 6*k + 311. Solve v(d) = 0 for d.
-9, 6
Let i(b) be the third derivative of 1/12*b**5 - 25/24*b**4 - 20*b**3 + 7*b + 18*b**2 + 0. Factor i(q).
5*(q - 8)*(q + 3)
Let m be (-3)/2*((-12064)/(-702))/((-14)/21). Find h, given that m*h - 1/3*h**2 - 3364/3 = 0.
58
Factor 286*d**2 + 68*d - 3*d**4 - 1253*d - 81*d**3 + 272*d**2 + 21*d + 792.
-3*(d - 2)**3*(d + 33)
Let o(u) be the first derivative of -246 + 5/16*u**4 + 11/12*u**3 - 3/4*u - 13/8*u**2. Determine i, given that o(i) = 0.
-3, -1/5, 1
Let l(n) be the second derivative of -1/75*n**6 + 1/30*n**4 + 0 + 0*n**2 - 1/30*n**3 + 1/210*n**7 + 0*n**5 - 28*n. Factor l(x).
x*(x - 1)**3*(x + 1)/5
Let r be 9 + -2 + 2 + (-255)/(-120)*-4. Let s(d) be the first derivative of r*d**4 + 0*d**2 + 0*d**3 + 0*d + 21. Factor s(x).
2*x**3
Let n(o) be the first derivative of o**5/90 - 2*o**4/27 + 4*o**3/27 + o - 29. Let g(a) be the first derivative of n(a). What is b in g(b) = 0?
0, 2
Let y(g) be the second derivative of -5*g**4/12 - 155*g**3/6 - 325*g**2 + 875*g. Factor y(c).
-5*(c + 5)*(c + 26)
Let 159/2*v + 27/2 - 9*v**2 = 0. What is v?
-1/6, 9
Let v = -590 + 592. Factor -v*y - 180*y**2 - 8*y + 178*y**2 + 12.
-2*(y - 1)*(y + 6)
Suppose -4*h - 2*z = 11 + 7, -21 = h - 5*z. Let p(n) = n**2 - 15*n - 9. Let a(d) = -2*d**2 + 15*d + 8. Let o(l) = h*p(l) - 5*a(l). Factor o(y).
(y + 2)*(4*y + 7)
Let g(l) be the first derivative of 5 - 1/3*l**3 - 17*l + 0*l**2 + 1/18*l**4. Let r(u) be the first derivative of g(u). Determine d so that r(d) = 0.
0, 3
Let s(n) be the second derivative of -n**5/510 - n**4/34 + 16*n**3/51 + 14*n**2 + 121*n. Let y(a) be the first derivative of s(a). Factor y(j).
-2*(j - 2)*(j + 8)/17
Let z(s) = 59*s**2 + 116*s - 274. Let o(t) = 9*t**2 + 19*t - 46. Let m(u) = -13*o(u) + 2*z(u). Find q, given that m(q) = 0.
5, 10
Let v(d) be the first derivative of -121*d**4/21 - 44*d**3/21 - 2*d**2/7 + 82*d + 21. Let i(u) be the first derivative of v(u). Find y, given that i(y) = 0.
-1/11
Suppose 0 = 18*c - 9*c + 36. Let z be (c - (3 - -2)) + 12. Factor 10*l + 1/2*l**4 - 7/2 - 9*l**2 + 2*l**z.
(l - 1)**3*(l + 7)/2
Let o(w) be the first derivative of w**7/315 + 2*w**6/135 + 2*w**5/135 - 123*w**2/2 - 62. Let s(q) be the second derivative of o(q). Factor s(j).
2*j**2*(j + 2)*(3*j + 2)/9
Let q(y) be the second derivative of y**4/12 + 13*y**3/3 - 28*y**2 + 2911*y. Factor q(o).
(o - 2)*(o + 28)
Let x(f) be the first derivative of 19 - 1/3*f**2 - 1/18*f**4 - 2/9*f**3 - 27*f. Let j(k) be the first derivative of x(k). Let j(n) = 0. Calculate n.
-1
Let f(y) = -32*y**4 + y**3 + 4*y**2 - 25*y - 36. Let t(d) = 26*d**4 - 2*d**3 - 6*d**2 + 26*d + 36. Let u(m) = 4*f(m) + 5*t(m). Factor u(p).
2*(p - 3)**2*(p + 1)*(p + 2)
Factor 466*r - 54*r**2 + 512 + 19*r**3 - 18*r + 26*r**3 - 8*r**2 - 43*r**3.
2*(r - 16)**2*(r + 1)
Let w = 34 - 29. Suppose -9*v + w = -13. Factor j**v - 58*j**3 + 57*j**3 - 2*j**2 + 2*j.
-j*(j - 1)*(j + 2)
Suppose -m + 641 - 57 = -4*a, -2