 i(w) be the first derivative of 7*w**6/2 + 18*w**5/5 - 48*w**4 + 86*w**3 - 117*w**2/2 + 12*w - 487. Factor i(o).
3*(o - 1)**3*(o + 4)*(7*o - 1)
Let x(h) be the first derivative of 16*h - 4/3*h**2 - 4/3*h**3 + 1/6*h**4 + 76. Factor x(f).
2*(f - 6)*(f - 2)*(f + 2)/3
Suppose -11*p - 3*u - 69 = -12*p, 257 = 3*p + u. Let h be 4/(-54)*p/(-28). Factor -2/9*z**3 + 2/9*z - 2/9 + h*z**2.
-2*(z - 1)**2*(z + 1)/9
Let w(l) = -10*l**2 + 1533*l - 6. Let n(o) = -12*o**2 + 1540*o - 8. Let j(g) = 3*n(g) - 4*w(g). Find m such that j(m) = 0.
0, 378
Let g(j) be the first derivative of -j**4/5 - 92*j**3/15 - 192*j**2/5 - 432*j/5 + 3981. Factor g(n).
-4*(n + 2)*(n + 3)*(n + 18)/5
Factor -249654 - 3280*v + 38*v**2 + 37*v**2 + 127*v**2 - 206*v**2 - 422746.
-4*(v + 410)**2
Let d(q) be the third derivative of 0 + 13/45*q**6 + 212*q**2 + 0*q**3 + 0*q - 5/252*q**8 + 2/45*q**7 - 28/45*q**5 - 4/3*q**4. Let d(p) = 0. Calculate p.
-2, -3/5, 0, 2
Let t(n) be the first derivative of -1/4*n**2 + 11*n + 0*n**3 - 9 - 1/60*n**6 + 0*n**5 + 1/12*n**4. Let a(v) be the first derivative of t(v). Factor a(m).
-(m - 1)**2*(m + 1)**2/2
Let r(p) be the third derivative of -17/30*p**6 - 2/105*p**7 - 5/2*p**4 + 0 - 31/15*p**5 - 194*p**2 + 0*p + 0*p**3. Solve r(y) = 0.
-15, -1, 0
Let n be (1752/(-108))/(-2 + (-176)/(-84)). Let v = n - -171. Suppose -2*k**2 - 2/3*k + 2 + v*k**3 = 0. What is k?
-1, 1, 3
Let a be (-2)/((-126)/175) - 4/(-18). Factor 6*p + 7*p**3 - 3*p + a*p - p + 12*p**2.
p*(p + 1)*(7*p + 5)
Let j(r) = 3*r**2 + 356*r - 14644. Let l be j(-151). Determine a, given that -8/11*a + 0 + 8/11*a**2 + 10/11*a**4 + 26/11*a**l = 0.
-2, -1, 0, 2/5
Let l(q) be the second derivative of 1/6*q**4 - q**2 + 0*q**6 - 20 - 1/2*q**3 - 6*q - 1/42*q**7 + 1/5*q**5. Determine a so that l(a) = 0.
-1, 1, 2
Let n = -616 - -694. Factor -i**4 + 1201*i - 50*i**3 + 6*i**4 + n*i**2 - 1501*i + 107*i**2 + 180.
5*(i - 3)**2*(i - 2)**2
Suppose 0 = -1910*d + 5346 + 1997 - 333 + 2540. Factor 28 - 64/7*f**4 + 268/7*f**2 - 68*f - 16/7*f**d + 92/7*f**3.
-4*(f - 1)**3*(2*f + 7)**2/7
Let p(n) be the first derivative of 68 + 8/5*n**5 - 2*n**2 + 2*n**6 - 16*n**3 + 8*n - 10*n**4. Factor p(u).
4*(u - 2)*(u + 1)**3*(3*u - 1)
Let w(g) = 4*g**2 - 3*g + 2. Let b(m) = 4*m**2 - 4*m + 1. Suppose 19*r - 16*r + 6 = -3*i, -5*i + r - 22 = 0. Let d(u) = i*b(u) + 3*w(u). Factor d(z).
-(z - 2)*(4*z + 1)
Let o(f) be the second derivative of -f**4/12 - 2*f**3/3 + f**2 - 125*f. Let d(m) = -1. Let k(r) = 3*d(r) - o(r). Factor k(c).
(c - 1)*(c + 5)
Suppose -5*w = -5, -4*z + 4*w - 9*w - 199 = 0. Let x(k) = -25*k**2 + 303*k - 3217. Let g(c) = -3*c**2 + 38*c - 402. Let r(l) = z*g(l) + 6*x(l). Factor r(b).
3*(b - 20)**2
Let i(x) be the third derivative of x**6/1440 + x**5/60 - 3*x**4/32 - 35*x**3/6 + 78*x**2. Let s(k) be the first derivative of i(k). Factor s(z).
(z - 1)*(z + 9)/4
Let u(y) be the second derivative of -20/3*y**3 + 0*y**2 + 3*y**4 - 13 + y + 1/5*y**5. Factor u(l).
4*l*(l - 1)*(l + 10)
Let r be 1 - 2/(3 - 1). Let p = -167419 + 167423. Suppose 0*g**2 + 0*g**3 + 2/19*g**5 + r + 2/19*g**p + 0*g = 0. Calculate g.
-1, 0
Let t(v) be the second derivative of -2/21*v**7 + 22/15*v**6 + 0*v**2 + 0*v**3 - 7*v**5 + 0 + 25/3*v**4 - 53*v. Solve t(r) = 0 for r.
0, 1, 5
Determine t so that 58*t**2 - 6*t**3 - 45*t - 21*t**4 + 27 + 48*t**3 + 3*t**5 - 50*t**2 - 14*t**2 = 0.
-1, 1, 3
Let f(v) be the second derivative of v**7/1260 - v**6/810 - 7*v**5/540 - v**4/54 - 61*v**3/6 + 31*v. Let i(d) be the second derivative of f(d). Factor i(u).
2*(u - 2)*(u + 1)*(3*u + 1)/9
Let j(s) = -s**3 + 31*s**2 + 5*s - 151. Let c be j(31). Let q(z) be the second derivative of 0 - z**2 + 1/12*z**c + 1/6*z**3 + 25*z. Factor q(u).
(u - 1)*(u + 2)
Let u(s) be the first derivative of s**5/24 + 5*s**4/12 + 5*s**3/4 + 5*s**2/3 + 162*s + 42. Let c(v) be the first derivative of u(v). Let c(n) = 0. Calculate n.
-4, -1
Let a = -2330/723 + 857/241. Factor -1/2*r**4 - a*r + 0 + 1/6*r**5 + 1/6*r**3 + 1/2*r**2.
r*(r - 2)*(r - 1)**2*(r + 1)/6
Let c(x) be the second derivative of 3*x**3 + 0 + 3/20*x**5 + 28*x + 9/4*x**4 - 24*x**2. Factor c(r).
3*(r - 1)*(r + 2)*(r + 8)
Suppose 8*z - 39 = -15. Determine l so that 114 - 8*l - z*l**3 - 63 + 45*l**2 - 91*l + 6*l**3 = 0.
-17, 1
Let k(t) be the first derivative of -129 + 12/5*t - 2/15*t**3 - 1/5*t**2. Determine b, given that k(b) = 0.
-3, 2
Let a(n) = -36*n**3 - 381*n**2 - 585*n - 66. Let r(x) = -x**3 - 2*x**2 + x - 2. Let v(w) = -a(w) + 33*r(w). What is o in v(o) = 0?
-103, -2, 0
Find t such that -25*t**3 - 264*t + 452*t**2 + 176 + 304 + 1110*t + 484*t - 137*t**2 = 0.
-3, -2/5, 16
Let g(t) be the third derivative of -105*t**2 + 0*t**3 + 0*t**4 - 2/525*t**7 - 1/1680*t**8 + 0*t - 1/120*t**6 - 1/150*t**5 + 0. Suppose g(n) = 0. What is n?
-2, -1, 0
Let p(g) be the third derivative of 0 - 1/45*g**5 - g**2 - 1/180*g**6 - 1/36*g**4 + 70*g + 0*g**3. Solve p(v) = 0 for v.
-1, 0
Let j(k) = 19835*k - 59503. Let f be j(3). Suppose 4/5*n - 2/5*n**f - 2/5*n**3 + 0 = 0. Calculate n.
-2, 0, 1
Suppose -41*v - 105664 + 105746 = 0. Find f, given that v*f**4 - 74/5*f**3 - 136/5*f + 32/5 + 168/5*f**2 = 0.
2/5, 1, 2, 4
Factor 1179921*r**3 + r**4 + 3*r**4 + 2700*r - 980*r**2 + 0*r**4 - 1179853*r**3.
4*r*(r - 5)**2*(r + 27)
Suppose 7*j - 1709 = -92. Factor 66 + 18 - 216*d**3 + 300*d - 229*d**3 + j*d**2 + 460*d**3.
3*(d + 1)*(d + 14)*(5*d + 2)
Factor 271/5*p + 45*p**3 + 9/5 + 411*p**2.
(p + 9)*(15*p + 1)**2/5
Let q(l) be the third derivative of 1/420*l**5 + 0 - 1/7*l**3 + 0*l - 1/168*l**4 - 84*l**2. Factor q(m).
(m - 3)*(m + 2)/7
Let g be 14/2 - (-28)/(-14). Suppose q - 5*b = 15, g*b + 4 = -11. Factor 8*x**2 - 5*x**2 - 3*x + q*x - 6.
3*(x - 2)*(x + 1)
Suppose 14*d + 4*c = 15*d + 1039, -3*d - c = 3078. Let b = -3080/3 - d. Suppose 5/12*j**2 - 1/6*j + 0 + 11/12*j**3 + b*j**4 = 0. Calculate j.
-2, -1, 0, 1/4
Let t = -70750/3 - -23586. Let a(m) be the first derivative of -32*m + 8*m**2 - m**4 + 1 + t*m**3. Factor a(i).
-4*(i - 2)**2*(i + 2)
Let v(s) = -4*s**3 + 23*s**2 - 259*s + 243. Let r(b) = -10*b**3 + 70*b**2 - 780*b + 728. Let h(x) = -3*r(x) + 8*v(x). Find t, given that h(t) = 0.
-20, 1, 6
Let z = 156722 + -156719. Let -2/7*n**2 + 0 + 4/21*n + 2/21*n**z = 0. Calculate n.
0, 1, 2
Suppose 14351*d**2 + 2675*d - 5330 + 14344*d**2 - 28700*d**2 = 0. What is d?
2, 533
Let f be 9*(4 + (3 - 15)). Let t = -70 - f. Factor s + 4*s - 3*s + 6 - 10*s + t*s**2.
2*(s - 3)*(s - 1)
Let g(y) = -8*y**4 - 37*y**3 + 246*y**2 + 960*y - 2282. Let u(r) = 2*r**4 + 9*r**3 - 62*r**2 - 240*r + 570. Let q(a) = -6*g(a) - 22*u(a). Factor q(n).
4*(n - 4)*(n - 2)*(n + 6)**2
Let f(m) = 34*m + 205. Let h be f(-8). Let x be -68 - h - 4*-1. Factor -4/7*s**x + 4/7*s - 3/7 + 2/7*s**2 + 1/7*s**4.
(s - 3)*(s - 1)**2*(s + 1)/7
Let y(v) be the third derivative of v**7/105 + 31*v**6/10 + 2883*v**5/10 + 47*v**2 + 26. Factor y(d).
2*d**2*(d + 93)**2
Let w(s) be the second derivative of -3*s**7/28 - 77*s**6/10 + 323*s**5/40 + 71*s**4/3 - 53*s**3/3 - 52*s**2 + s - 1076. Solve w(m) = 0.
-52, -2/3, 1
Let 668/9*u**2 + 1330/9*u + 664/9 + 2/9*u**3 = 0. What is u?
-332, -1
Suppose -36 + 1/5*k**3 - 49/5*k**2 + 184/5*k = 0. What is k?
2, 45
Suppose j - 4 = -10*f + 9*f, -3*j = -f - 4. Solve 0*n**j + 26358*n + 6*n**2 - 26358*n + n**3 = 0 for n.
-6, 0
What is i in -164*i - 189*i**2 + 160*i**3 - 67*i**2 - 354*i**2 - 64*i**4 + 1290*i**2 + 4*i**5 - 616 = 0?
-2, -1, 1, 7, 11
Let y(z) be the second derivative of -z**4/20 - 113*z**3/30 - 37*z**2/5 + 2437*z. Let y(h) = 0. Calculate h.
-37, -2/3
Let m = 33 + -39. Let h(v) = v**2 + 7*v + 8. Let a be h(m). Factor -101 - 2*o**4 + a*o**2 + 101.
-2*o**2*(o - 1)*(o + 1)
Let n be 5/60*((-48)/(-15) - 6069/(-255)). Find k, given that -n*k + 3/4*k**2 - 15/2 = 0.
-2, 5
Let r(f) be the third derivative of f**7/735 + f**6/30 - 31*f**5/210 + 4*f**4/21 + 48*f**2 - 12*f. Factor r(m).
2*m*(m - 1)**2*(m + 16)/7
Let l = -44620/13 - -223308/65. Factor -l*t + 24/5 + 2/5*t**2.
2*(t - 6)*(t - 2)/5
Let i = 4364 - 21816/5. Let a(r) be the first derivative of -12*r + i*r**5 + 8/3*r**3 - 20 + 8*r**2 - 4*r**4. Factor a(q).
4*(q - 3)*(q - 1)**2*(q + 1)
Suppose 4*u + 0*u = 12. Factor -70*x**2 - 14*x**3 + 75*x - x**4 - 2*x**4 - 35*x**2 + 47*x**u.
-3*x*(x - 5)**2*(x - 1)
Let d be (0 + 3)/((-15)/(-10)). Suppose -