- 3)**2
Factor 1/7*c**3 + 1546572/7*c - 370146232/7 - 2154/7*c**2.
(c - 718)**3/7
Suppose -105 = -3*v + 5*j, -5*v + 175 = -10*j + 8*j. Suppose 4*y + m - 16 = 0, 5*m + v = y + 52. Factor 9/2*w - 3*w**y + 0 + 3/4*w**4 + 3/4*w**2.
3*w*(w - 3)*(w - 2)*(w + 1)/4
Let p(n) be the third derivative of n**7/504 + 11*n**6/144 - 7*n**5/4 - n**4/12 - 23*n**3/3 + 71*n**2. Let k(t) be the second derivative of p(t). Factor k(z).
5*(z - 3)*(z + 14)
Let s(h) = 3*h**3 + 13*h + 12. Let x be s(-4). Let u = x + 3950/17. Factor -u - 10/17*o**2 - 2/17*o**3 - 14/17*o.
-2*(o + 1)**2*(o + 3)/17
Let n(g) = g + 4. Let a be n(-2). Let l = -155443/3 + 51815. Factor 14/3*v**a + 6*v**3 + 10/3*v**4 + 4/3*v + 0 + l*v**5.
2*v*(v + 1)**3*(v + 2)/3
Let s(f) be the second derivative of f**6/360 + 5*f**5/12 - 2*f**2 + 11*f + 2. Let i(x) be the first derivative of s(x). Suppose i(o) = 0. What is o?
-75, 0
Let p = 578 - 558. Let -5*n**2 - p - 146*n + 61*n + 65*n = 0. What is n?
-2
Let h(q) = -185761*q + 557285. Let y be h(3). Let k be (1 + 6/10)/6. Factor 2/15*n**3 - 8/15*n**y + 2/3*n - k.
2*(n - 2)*(n - 1)**2/15
Let p be (-24)/20 - (-2)/10. Let h(u) = -u - 1. Let m(c) = -3*c + 7*c**2 - 14 + 6*c**2 - 17*c**2 + 8*c + 9*c. Let v(f) = p*m(f) + 2*h(f). Solve v(j) = 0.
1, 3
Let p(z) be the first derivative of z**4/4 - 4370. Let p(m) = 0. Calculate m.
0
Let h(k) = k**3 - 8*k**2 + 13*k - 4. Let y be h(6). Suppose -2*p = -d - 3 + y, -15 = -3*d. Factor -2*i + 6*i + i**2 - 2 - p*i.
(i - 1)*(i + 2)
Let f(v) = 17*v. Let k be f(-2). Let t = k - -37. Factor 2*d + 4*d**4 + 8*d**t - 2*d + 90*d**2 - 86*d**2.
4*d**2*(d + 1)**2
Let m = -69513/7 - -9905. Let g = m + 181/7. Determine l, given that g*l**2 + 0 - 3/7*l = 0.
0, 1
Let b(l) be the first derivative of -l**4/48 - l**3/3 - 7*l**2/8 + 166*l + 138. Let i(x) be the first derivative of b(x). Factor i(r).
-(r + 1)*(r + 7)/4
Let c(f) = f**3 - 6*f**2 + 4*f - 13. Let g(u) = 6*u**2 + u - 1. Let h be g(1). Let s be c(h). Factor i**2 - 3*i**5 - 15*i**3 + 5*i**2 - s*i**4 + 23*i**4.
-3*i**2*(i - 2)*(i - 1)**2
Let m(c) be the third derivative of c**5/20 - 103*c**4/8 - 52*c**3 + 289*c**2. What is x in m(x) = 0?
-1, 104
Let m(s) be the first derivative of 0*s**3 + 2/15*s**5 + 0*s**2 + 0*s**4 + 1/9*s**6 - 20 + 0*s. Suppose m(p) = 0. Calculate p.
-1, 0
Let j(q) be the first derivative of 30 - 2*q + 9/8*q**4 - 37/6*q**3 + 10*q**2. Factor j(f).
(f - 2)**2*(9*f - 1)/2
Let w = 327424 - 2283039/7. Let s = 1279 - w. Solve -69/7*c**3 + 48/7*c**5 + 3*c - 3/7 + s*c**4 - 3*c**2 = 0 for c.
-1, 1/4, 1
Let u(y) = 102*y**2 - 75*y - 5. Let w(b) = -35*b**2 + 25*b + 2. Let k = 277 - 288. Let a(g) = k*w(g) - 4*u(g). Find s, given that a(s) = 0.
2/23, 1
What is g in 789*g**2 + 0*g**5 - 3657 + 411*g**4 - 2*g**5 - 336*g**4 - 2244*g + 5*g**5 + 549*g**3 - 699 = 0?
-11, -3, -2, 2
Let s(r) be the first derivative of r**3/6 - 15*r**2/2 + 28*r + 1198. Factor s(p).
(p - 28)*(p - 2)/2
Let h(o) = o**3 + 6*o**2 - 13*o - 2. Let i be h(2). Factor -8236*m**4 + 8242*m**i + 8*m**3 - 2*m - 2*m - 10*m**2.
2*m*(m - 1)*(m + 2)*(3*m + 1)
Let c(f) be the second derivative of -1 + 46*f - 7/18*f**3 - 1/36*f**4 - 5/3*f**2. Let c(v) = 0. Calculate v.
-5, -2
Let w(g) be the third derivative of -g**5/20 + 10*g**4/3 - 26*g**3/3 + 471*g**2. Factor w(v).
-(v - 26)*(3*v - 2)
Factor 1380*o**2 - 2/7*o**3 - 2221800*o + 1192366000.
-2*(o - 1610)**3/7
Let l(d) = 5*d**3 + 3*d**2 + 7*d - 8. Let r be l(4). Factor 403*i**2 + 15*i**3 - 12*i**3 - 24*i - r*i**2 - 36.
3*(i - 2)*(i + 1)*(i + 6)
Let u = -20306 - -162469/8. Let t(l) be the third derivative of 0 + 0*l - 1/120*l**6 + 17/60*l**5 - 27/2*l**3 - u*l**4 - 27*l**2. Factor t(p).
-(p - 9)**2*(p + 1)
Factor -46*l**3 - 25 - 104*l**3 + 14 - 29 + 157*l**2 + 127*l**3 - 202*l.
-(l - 5)*(l - 2)*(23*l + 4)
Let y(n) = n**2 - 460*n + 3618. Let u be y(8). Let f(h) be the first derivative of 4/21*h**3 - 1/14*h**4 + 0*h + 0*h**u - 25. Factor f(g).
-2*g**2*(g - 2)/7
Let k be 14/10 + (-19411)/(-4935). Let v(t) be the first derivative of k*t**3 + 8*t + t**4 + 9 + 10*t**2. Suppose v(b) = 0. Calculate b.
-2, -1
Let i(q) be the first derivative of -404/3*q**2 - 4/9*q**3 - 144 - 40804/3*q. Suppose i(b) = 0. Calculate b.
-101
Let t(f) be the second derivative of -f**7/840 + 43*f**3/6 - 2*f - 25. Let j(x) be the second derivative of t(x). Factor j(z).
-z**3
Let q(a) = 4*a**4 - 202*a**3 + 2294*a**2 + 5204*a + 2702. Let z(p) = 12*p**4 - 607*p**3 + 6883*p**2 + 15614*p + 8105. Let h(n) = -7*q(n) + 2*z(n). Factor h(u).
-4*(u - 26)**2*(u + 1)**2
Let v(q) be the first derivative of 22201*q**4/16 - 37101*q**3/4 + 1491*q**2/8 - 5*q/4 - 11752. Factor v(a).
(a - 5)*(149*a - 1)**2/4
Let x(r) be the third derivative of -r**8/672 + r**7/84 + r**6/240 - 17*r**5/120 - r**4/4 - 875*r**2. Determine i so that x(i) = 0.
-1, 0, 3, 4
Let d(c) = c**3 - 5*c**2 - 18*c + 60. Let y be d(6). Let p be (-50)/y - 16/(1 + 3). Find x, given that -8/3*x + p*x**2 + 32/3 = 0.
8
Let v(p) = 2*p**4 - 33*p**3 + 34*p**2 - 9*p - 6. Let r(j) = 3*j**4 - 33*j**3 + 32*j**2 - 6*j - 4. Let t(g) = 3*r(g) - 2*v(g). Let t(o) = 0. Calculate o.
0, 1, 28/5
Let n(t) = -24*t**2 - 98*t + 209. Let b(m) = 20*m**2 + 96*m - 210. Let h(j) = 7*b(j) + 6*n(j). Factor h(g).
-4*(g - 18)*(g - 3)
Let o(z) = 4*z**4 - 16*z**3 - 68*z**2 - 16*z. Let r(y) = -5*y**4 + 21*y**3 + 92*y**2 + 22*y. Let s(l) = -11*o(l) - 8*r(l). Factor s(w).
-4*w**2*(w - 3)*(w + 1)
Factor -138*c + 14 - 26 + 762*c**2 - 759*c**2 + 147.
3*(c - 45)*(c - 1)
Suppose 365 = -37*l + 1623. Let y be 14/5 + (-1)/(-5). Find n, given that 5*n**4 + l*n**2 - 9*n**y - 14*n**2 - 11*n**3 = 0.
0, 2
Let d = -519 + 498. Let r(p) = p**2 - 21*p - 4. Let h(n) = -5*n**2 + 61*n + 10. Let g(b) = d*r(b) - 6*h(b). Solve g(f) = 0.
-8, -1/3
Suppose 50*w - 30 = 40*w. Let -4*s**3 + 5*s**4 + 17*s**2 + 19*s**w - 32*s + 37*s - 2*s**2 = 0. What is s?
-1, 0
Let u be (-2 - 21/(-6))*(-3740)/(-102). Let u*q**2 - 2*q**3 - 6*q - 33*q**2 - 8*q - 38*q**2 = 0. What is q?
-7, -1, 0
Factor 63/2*m**2 - 1/4*m**4 + 0 + 0*m - 125/4*m**3.
-m**2*(m - 1)*(m + 126)/4
Let l(u) be the first derivative of -57 + 2/9*u - 1/9*u**2 - 2/27*u**3 + 1/18*u**4. Determine n so that l(n) = 0.
-1, 1
Let i(y) = y**3 - y**2 + 24*y - 218. Let j be i(5). Factor -j*r + 5/2 - 1/2*r**2.
-(r - 1)*(r + 5)/2
Let b be 56/(-14) + ((-34)/493 - (-3610)/203). Determine p so that 52/7*p + b + 2/7*p**2 = 0.
-24, -2
Let g(x) be the first derivative of -x**5/40 - 7*x**4/24 - 2*x**3/3 + 4*x**2 - 74*x + 83. Let k(r) be the first derivative of g(r). Factor k(z).
-(z - 1)*(z + 4)**2/2
Let w(f) = -4*f**2 + 753*f + 5. Let c(l) = -7*l**2 + 1131*l + 8. Let h(a) = -5*c(a) + 8*w(a). Factor h(j).
3*j*(j + 123)
Let x(y) be the third derivative of 0*y - 2/945*y**7 + 0 - 4/27*y**4 + 32/9*y**3 - 1/27*y**6 - 29/135*y**5 + 19*y**2. What is r in x(r) = 0?
-4, -3, 1
Determine j, given that -2 - 17*j + 4*j**2 - 21*j - 27*j - 27*j + 90*j = 0.
-1/2, 1
Suppose 0 = 2*f - 2*n - 24, 0 = -5*f + 350*n - 349*n + 28. Suppose 45/2*u**5 - 93*u**2 - 5/2*u**3 + 2*u + 67*u**f + 4 = 0. What is u?
-2, -1/5, 2/9, 1
Factor -2/15*d**2 - 18/5*d + 56/15.
-2*(d - 1)*(d + 28)/15
Suppose 45*o = 50*o - 10. Factor -2*s**3 + o*s**2 + 1915*s**5 + 3*s**3 - 2*s**4 - 1916*s**5.
-s**2*(s - 1)*(s + 1)*(s + 2)
Let b = -5536 - -5542. Let x(z) be the third derivative of 0 - 1/60*z**b - 29*z**2 - 1/6*z**4 + 0*z + 0*z**3 - 1/10*z**5. Suppose x(c) = 0. Calculate c.
-2, -1, 0
Let -62 + 419*k - 85 + 43 - 288*k - 2*k**2 - 237*k = 0. Calculate k.
-52, -1
Let m(t) = 12*t**3 - 6*t - 3. Let h be m(3). Factor -3*v**2 - 2*v**2 + 312*v - h*v + 2*v**2.
-3*v*(v - 3)
Let x = -43649/4 - -10913. Let x*c**2 - 15/4*c + 3 = 0. Calculate c.
1, 4
Let w(h) be the second derivative of -h**5/4 - 79*h**4/3 - 21*h**3/2 - 55*h - 11. Factor w(r).
-r*(r + 63)*(5*r + 1)
Let a(x) be the third derivative of -80*x**2 - 4/15*x**3 + 1/6*x**4 - 1/25*x**5 + 0*x + 0. Solve a(g) = 0 for g.
2/3, 1
Let r(x) be the first derivative of -48 + 18*x - 19/2*x**2 + 1/3*x**3. Factor r(i).
(i - 18)*(i - 1)
Let y(t) be the third derivative of -t**7/280 - 9*t**6/80 - 9*t**5/16 + 37*t**4/8 - 21*t**3/2 - 2257*t**2 - t. Suppose y(z) = 0. What is z?
-14, -6, 1
Suppose -19*y + 22*y - 94 = -4*d, y - d - 22 = 0. Solve y*c**5 + 12*c**2 - 29*c**5 + 51*c**4 - 60*c**4 = 0.
-2, 0, 1
Let j(r) = -3*