lculate n.
-1, 0
Let b(o) be the first derivative of -o**7/168 + 7*o**6/36 - 13*o**5/24 + 35*o**3/3 - 188. Let t(d) be the third derivative of b(d). Factor t(v).
-5*v*(v - 13)*(v - 1)
Let 0 + 5*a**4 + 6*a**3 + 0*a + 1/3*a**5 - 104/3*a**2 = 0. Calculate a.
-13, -4, 0, 2
Let z be ((-27)/(-81))/((-1)/(-20448)*-5). Let m = z + 1364. What is b in 16/5 - 12/5*b - m*b**2 = 0?
-4, 1
Suppose -3 = -3*k, -4*z + 5 = 2*k - 5. Let t(p) = p**3 + 6*p**2 - p - 3. Let g be t(-6). Factor -z*n - n**2 + 4*n**2 + 3*n**g - 2*n - 2*n.
3*n*(n - 1)*(n + 2)
Suppose 3*u - 24 = 0, 158*l - 160*l + 18*u = 144. Factor 0*v - 2/9*v**2 + l + 2/9*v**3.
2*v**2*(v - 1)/9
Solve -4*c**3 + 268/3*c + 188/3*c**2 + 68/3 = 0 for c.
-1, -1/3, 17
Let c(w) be the first derivative of -w**6/120 + 3*w**5/40 + 6*w**3 - 5. Let r(i) be the third derivative of c(i). Factor r(s).
-3*s*(s - 3)
Let f = -93 + 105. Factor 25*n**2 - 80 + f*n - 23*n + 91*n.
5*(n + 4)*(5*n - 4)
Let c(m) = -m**4 + 3*m**3 + m**2 + m + 1. Let s(b) = 4*b**4 - 48*b**3 + 124*b**2 - 16*b - 44. Let n(d) = -4*c(d) + s(d). Find r, given that n(r) = 0.
-1/2, 1, 3, 4
Let k(h) be the third derivative of h**5/150 + 86*h**4/15 + 343*h**3/15 - 529*h**2 - 3*h. Solve k(i) = 0 for i.
-343, -1
Let d(w) be the second derivative of w**7/21 - 64*w**6/15 + 479*w**5/5 + 352*w**4 + 363*w**3 + 4852*w. Suppose d(b) = 0. Calculate b.
-1, 0, 33
Let f(z) be the first derivative of 4*z**3/9 - 360*z**2 + 97200*z + 5220. Solve f(k) = 0 for k.
270
Suppose 3*f + 155 - 131 = 0. Let s be (-9 - -7)*f/72. Find k such that 4/9 + s*k**2 - 2/3*k = 0.
1, 2
Suppose -306*v + 314*v = 3864. Let x = v - 483. Find k, given that 2/3*k**3 + 0 - 14/3*k**2 + x*k = 0.
0, 7
Suppose -102 + 474 + 387 + 199 - 481*g + g**2 = 0. Calculate g.
2, 479
Let o(x) = 5*x**2 - 19*x - 46. Let i(a) = -33*a**2 + 116*a + 277. Let v(b) = -6*i(b) - 39*o(b). Solve v(g) = 0.
-11, -4
Suppose -4*p = -24*v + 22*v + 14, -19 = -5*v + 2*p. Let j(y) be the first derivative of 11 + 0*y**2 - 2/5*y**5 + 0*y - 3/2*y**4 - 4/3*y**v. Factor j(r).
-2*r**2*(r + 1)*(r + 2)
Let j(x) = -36*x**3 + 332*x**2 - 112 - 262*x**2 - 3*x - 3*x. Let z(r) = 5*r**3 - 10*r**2 + r + 16. Let p(i) = -6*j(i) - 44*z(i). Factor p(s).
-4*(s - 4)*(s - 2)*(s + 1)
Let s(n) be the first derivative of 3*n**5/40 + 25*n**4/72 - n**3/6 + 115*n + 88. Let c(g) be the first derivative of s(g). What is h in c(h) = 0?
-3, 0, 2/9
Let r(q) be the first derivative of q**4/60 - q**3/30 - q**2/5 + 56*q - 47. Let y(p) be the first derivative of r(p). Factor y(b).
(b - 2)*(b + 1)/5
Let l(a) be the third derivative of 0*a + 0 - 1/8*a**4 + 1/40*a**6 - 1/210*a**7 + 0*a**3 + 1/60*a**5 - 31*a**2. Find u, given that l(u) = 0.
-1, 0, 1, 3
Factor -3 + 1/8*k**3 + 13/8*k**2 + 5/4*k.
(k - 1)*(k + 2)*(k + 12)/8
Let z(l) be the second derivative of -l**4/66 + 1198*l**3/33 - 358801*l**2/11 - 4*l - 89. What is h in z(h) = 0?
599
Let u(v) be the third derivative of 1/10*v**5 - v**2 + 0*v + 21 + 1/120*v**6 + 5/24*v**4 + 0*v**3. Find a, given that u(a) = 0.
-5, -1, 0
Let t(q) be the second derivative of -16 - 1/6*q**4 + 5/6*q**3 - 4/3*q**2 - 1/60*q**5 - 6*q. Suppose t(o) = 0. Calculate o.
-8, 1
Let n be (77/(-5880))/(-11)*1. Let c(j) be the third derivative of -n*j**7 + 0*j + 0*j**5 + 0*j**3 - 1/1344*j**8 + 0*j**4 + 0*j**6 + 0 + 13*j**2. Factor c(o).
-o**4*(o + 1)/4
Suppose 5*h = -2*x - 85, -5*x + 5 = -6*x. Let f(w) = w**3 + 15*w**2 - 4*w - 34. Let o be f(h). Factor -57 - p**2 + o - 116 + 42*p - 2*p**2.
-3*(p - 7)**2
Suppose -q - 5*x = 4*q - 20, 5*q = -2*x + 17. Factor -21*i**q + 3*i**4 + 17*i**3 + 6*i**5 + 4*i**3.
3*i**4*(2*i + 1)
Let y(m) = -5*m**3 - 3*m**2 + 66*m + 122. Let k(f) = -6*f**3 - 3*f**2 + 66*f + 123. Let g(t) = 2*k(t) - 3*y(t). Factor g(a).
3*(a - 5)*(a + 2)*(a + 4)
Let h(l) = 4*l**2 + 42*l - 266. Let x(b) = -b**2 + 3. Let w(g) = -h(g) - 2*x(g). Find d such that w(d) = 0.
-26, 5
Let r(c) = 9*c**2 + 60*c + 312. Let w(d) = 2*d**2 - 2*d - 1. Let y(v) = -r(v) + 3*w(v). Factor y(z).
-3*(z + 7)*(z + 15)
Factor 12*j**3 + 236*j + 51 + 170*j**2 - 92*j**3 - 211 - 2*j**4 - 164*j**2.
-2*(j - 1)**2*(j + 2)*(j + 40)
Let r(f) = 1613*f + 38712. Let o be r(-24). Determine v so that o - 11/3*v + 1/3*v**2 = 0.
0, 11
Let o(d) be the first derivative of -20*d**5 + 195*d**4 - 392*d**3 + 296*d**2 - 96*d + 1031. Find t, given that o(t) = 0.
2/5, 1, 6
Let q = 519 + -515. Factor -13*m**3 - 22*m**2 - m**3 + 12*m + 7*m**4 + 5*m**q - 8*m.
2*m*(m - 2)*(m + 1)*(6*m - 1)
Suppose 0 = -359*p + 353*p + 2586. Factor -p*d**3 + 0*d**5 - 16*d**4 - 2*d**5 + 419*d**3 - 2*d**5.
-4*d**3*(d + 1)*(d + 3)
Factor -l**3 - 36 - 83*l - 45/2*l**2.
-(l + 4)*(l + 18)*(2*l + 1)/2
Let g = 176 + 69. Suppose -22*c + 10*c = 0. Suppose c*b**2 - 5*b**2 - 8*b - g - 8*b + 86*b = 0. What is b?
7
Find h such that 143641/2 - 379*h + 1/2*h**2 = 0.
379
Suppose -7*v = -i - 30, -3*v + 9 - 14 = -4*i. Factor -5/4*b**4 + 3/2*b**2 - 1/4 - 1/4*b + 3/4*b**v - 1/2*b**3.
(b - 1)**3*(b + 1)*(3*b + 1)/4
Suppose 8*b - 297 - 559 = 0. Factor 12*i**5 - 20*i**5 - 33*i**3 - 109*i**4 + b*i**3 + 5*i**5.
-i**3*(i + 37)*(3*i - 2)
Let p = -7/673 + 799/12114. Let g(r) be the second derivative of -22*r - 2/15*r**5 + p*r**4 + 0*r**2 + 0 + 0*r**3. Let g(u) = 0. What is u?
0, 1/4
Let o = 399 + -397. Factor 139*u**2 + 13*u - 143*u**o - 108 + 99*u.
-4*(u - 27)*(u - 1)
Let l be (5 + (189/(-15))/3)*45/6. Let y(i) be the third derivative of 0 - l*i**2 - 1/33*i**3 + 1/88*i**4 + 0*i - 1/1320*i**6 + 0*i**5. Solve y(p) = 0.
-2, 1
Factor 2/3*h + 16/9 - 7/9*h**2.
-(h - 2)*(7*h + 8)/9
Find u such that -u**5 + 5 - 5 + 44*u**3 - 190678*u**2 - u**5 + 190710*u**2 + 10*u**4 = 0.
-2, -1, 0, 8
Suppose -i = -45 + 42. Factor -i + p + 7*p + 5 + 4*p**2 - 14.
4*(p - 1)*(p + 3)
Suppose 18 = 3*a - 2*a. Let o(h) = 11*h**2 + 12*h + 7. Let z(l) be the second derivative of l**4/12 - l**2/2 - 2*l + 2. Let r(p) = a*z(p) - 2*o(p). Factor r(k).
-4*(k + 2)*(k + 4)
Suppose 764/5*j + 762/5 + 2/5*j**2 = 0. What is j?
-381, -1
Let c(w) be the second derivative of 0 - 42*w - 7/60*w**5 + 5/36*w**4 + 1/9*w**3 + 0*w**2. Factor c(p).
-p*(p - 1)*(7*p + 2)/3
Let u(q) be the first derivative of -117 + 1/3*q**2 - 4/3*q + 2/9*q**3. Factor u(m).
2*(m - 1)*(m + 2)/3
What is l in 2896/5*l + 24012/5*l**3 + 3364/5*l**4 + 96/5 + 23448/5*l**2 = 0?
-6, -1, -2/29
Let u(v) be the first derivative of v**3/4 - 297*v**2/4 - 597*v/4 + 2485. Factor u(k).
3*(k - 199)*(k + 1)/4
Suppose 4*j + 434 = 3*l, -l - 4*j + 588 = 3*l. Let v = l - 141. Determine h so that -3*h**2 - 3/2*h**v + 3*h**3 + 3/2 - 3/2*h + 3/2*h**4 = 0.
-1, 1
Solve -30 + 3*v**3 + 7*v**3 + 26*v**2 - 70*v**2 - v**4 - v**3 + 35*v**2 - 49*v = 0 for v.
-1, 5, 6
Suppose 16*t - 13*t - 18 = -2*l, 38 = 4*t + 5*l. Find s such that -1/10*s**4 + 0*s**3 + 1/5*s**t + 0*s - 1/10 = 0.
-1, 1
Let y(u) = 9*u**2 - 5*u + 4. Let j be y(2). Let i be j/(-120)*(0 + -12). Solve -2/7 + 2/7*q**2 - 2/7*q**i + 2/7*q = 0 for q.
-1, 1
Let d(s) = -s**3 - 23*s**2 + 6*s + 43. Suppose -5*w - 75 = -20*w. Let x(o) = -o**3 + o**2 - 2*o - 1. Let t(r) = w*x(r) - d(r). Determine u so that t(u) = 0.
-1, 2, 6
Let q(h) be the first derivative of 0*h**2 + 2/5*h**5 + 0*h + 50/3*h**3 + 5*h**4 - 62. Factor q(f).
2*f**2*(f + 5)**2
Let x(d) be the third derivative of -d**6/180 - 326*d**5/45 + 1307*d**4/36 - 218*d**3/3 - 3473*d**2. Factor x(s).
-2*(s - 1)**2*(s + 654)/3
Let t(f) = -f + 16. Let l be t(9). Let m(j) = 22*j - 152. Let b be m(l). Suppose -48/5 + 6*w**5 - 84/5*w**b + 48/5*w**4 + 168/5*w - 114/5*w**3 = 0. Calculate w.
-2, 2/5, 1
Let n = 917 + -913. Solve 48*h + 17*h**4 - 88 + 40 - 14*h**n - 12*h**3 = 0 for h.
-2, 2
Let w(p) be the second derivative of -p**6/180 - 67*p**5/120 - 37*p**4/2 - 195*p**3 - 900*p**2 - p + 2917. Let w(g) = 0. Calculate g.
-30, -4, -3
Let o = 3018402 + -3018400. Let x = 13 - 8. Suppose 4/7*d**x - 2/7 + 10/7*d**4 - 8/7*d**o - 8/7*d + 4/7*d**3 = 0. Calculate d.
-1, -1/2, 1
Suppose 14*g - 9*g = -2*l + 31, 5*g - 2*l + 1 = 0. Let 0 + 8*j**4 + 16/7*j**2 + 86/7*j**g - 24/7*j + 10/7*j**5 = 0. Calculate j.
-3, -2, -1, 0, 2/5
Suppose -19516*s + 645 = -19501*s. Let w(g) be the second derivative of -2/5*g**5 + s*g - 5/4*g**4 + 8/15*g**6 + 4/3*g**3 + 0 - 1/2*g**2. Factor w(x).
(x - 1)*(x + 1)*(4*x - 1)**2
Let s be (-105704)/(-7602) + 8/(-14). Let u(m) be the first derivative of -2