ative of g(x). Factor s(c).
3*(c - 3)*(c + 1)**2
Let w(m) = -2*m**3 + 23*m**2 + 15*m - 32. Let u be w(12). Factor -9*z**2 + 160 - 160 - u*z.
-z*(9*z + 4)
Let p be -430*323/(-34) - 3*1. Factor -4085*d**3 + p*d**3 - 3*d**2 - 111*d - 54 - 57*d**2.
-3*(d + 1)**2*(d + 18)
Let y(q) = q. Let w = -68 - -3. Let t = w - -67. Let p(r) = 16*r**2 + 102*r + 24. Let j(c) = t*y(c) - p(c). Suppose j(h) = 0. What is h?
-6, -1/4
Let j = -367986 - -367986. Solve -3/7*q**2 - 81/7*q + j = 0.
-27, 0
Determine h so that -1/3*h**4 - 55/3*h**3 + 118/3 - 293/3*h + 77*h**2 = 0.
-59, 1, 2
Suppose -2*s + 22*d + 50 = 0, 0 = 4*s - 2*d - 32 + 16. Factor 1764/5*v**2 + 3/5*v**4 - 8232/5*v + 0 - 126/5*v**s.
3*v*(v - 14)**3/5
Let c(l) be the first derivative of 3*l**4/20 - 3*l**3/5 - 3*l**2/10 + 9*l/5 - 5021. Factor c(w).
3*(w - 3)*(w - 1)*(w + 1)/5
Let g = 1952 - 1947. Let r(v) be the third derivative of -1/144*v**4 + 0 + 0*v - 1/360*v**5 + 0*v**3 + g*v**2. What is t in r(t) = 0?
-1, 0
Let a(m) = m**3 + 93*m**2 + 600*m - 9. Let c be a(-7). Suppose -2/9*u**c + 0 - 2/3*u**3 + 8/9*u - 8/9*u**2 + 8/9*u**4 = 0. What is u?
-1, 0, 1, 2
Let o(b) be the second derivative of 28/27*b**3 + 32/9*b**2 - 1/90*b**5 - 5*b + 2/27*b**4 - 19. Factor o(i).
-2*(i - 8)*(i + 2)**2/9
Find k, given that -2951 + 0*k**2 - 5*k**2 + 3291 + 335*k = 0.
-1, 68
Let s be 0/(-31 + 38 + -10). Factor -1/2*v**4 - 7*v**3 + 0 + s*v**2 + 0*v.
-v**3*(v + 14)/2
Let a(z) be the first derivative of 3*z**5/35 + 1245*z**4/14 - 6408. Factor a(g).
3*g**3*(g + 830)/7
Suppose -t + 2862 = 3*t - 2*h, -4*t = h - 2847. Determine n, given that -354*n**2 + 124*n - 363*n**2 + t*n**2 = 0.
0, 31
Let n = -353249 - -1766254/5. Let -6/5*f + 3/5*f**3 + n*f**4 + 3/5*f**5 + 0 - 9/5*f**2 = 0. Calculate f.
-2, -1, 0, 1
Let g be -5*3/(-10) - (-38)/4. Let n be g/44*-2 - (-19)/14. Find r, given that -5/7*r**4 - n*r + 5/7*r**2 + 0 + 1/7*r**5 + 5/7*r**3 = 0.
-1, 0, 1, 2, 3
Factor -564/5*v**2 + 2/5*v**3 + 564/5 - 2/5*v.
2*(v - 282)*(v - 1)*(v + 1)/5
Factor -2/15*l**2 - 34/3 - 44/15*l.
-2*(l + 5)*(l + 17)/15
Let a(j) be the third derivative of -2*j**7/105 - 11*j**6/15 - 32*j**5/5 + 48*j**4 + 2*j**2 + 269*j. Factor a(g).
-4*g*(g - 2)*(g + 12)**2
Let r(b) be the second derivative of -b**8/2240 + b**7/280 + b**6/240 - 3*b**5/40 - 21*b**4 - b - 6. Let y(v) be the third derivative of r(v). Factor y(p).
-3*(p - 3)*(p - 1)*(p + 1)
Let x be ((-140)/224)/((10/(-54))/(16/24)). Let 3/8*t**5 + 3/2*t**4 + 3/8*t + x*t**3 + 0 + 3/2*t**2 = 0. What is t?
-1, 0
Let x(m) be the first derivative of -59 + 3/25*m**5 + 16/5*m**3 + 0*m**2 + 0*m - 6/5*m**4. Factor x(o).
3*o**2*(o - 4)**2/5
Let h be 500/(-200) + (3 - 164/(-56)). Find j such that h*j**2 + 26/7*j + 6/7*j**3 + 9/7 - 1/7*j**4 = 0.
-1, 9
Let d = -993 - -1483. Find r such that d*r**3 - 475*r**3 + 9*r**2 + 151*r**2 - 33*r**4 + 100*r - 17*r**4 - 5*r**5 = 0.
-10, -1, 0, 2
Let l(o) = 240*o + 235. Let t(u) = u**2 - 14*u - 8. Let k(d) = -2*d - 1. Let y(b) = -6*k(b) + t(b). Let w(i) = -l(i) - 5*y(i). Determine v, given that w(v) = 0.
-45, -1
Let a(i) be the first derivative of -4*i**3/3 + 7*i - 59. Let q(h) = -7*h**2 + 13. Let g(j) = 5*a(j) - 3*q(j). Factor g(r).
(r - 2)*(r + 2)
Let h(w) be the second derivative of -1/72*w**5 + 0*w**4 - 17/6*w**3 + 0 - 8*w + 0*w**2 + 1/216*w**6. Let d(s) be the second derivative of h(s). Factor d(n).
5*n*(n - 1)/3
Let o(g) = -4*g**4 - 990*g**3 - 6*g - 3. Let y(t) = 4*t**4 + 988*t**3 + 8*t + 4. Let s(p) = 4*o(p) + 3*y(p). Solve s(r) = 0 for r.
-249, 0
Let i(a) be the third derivative of 0*a + 0 + 0*a**3 - 1/84*a**8 + 2/3*a**4 - 4/15*a**5 - 1/10*a**6 + 8/105*a**7 + 63*a**2. Find w, given that i(w) = 0.
-1, 0, 1, 2
Let -128*t - 250*t**2 + 118*t**2 + 134*t**2 = 0. Calculate t.
0, 64
Suppose -g = -3*g - 5*i - 18, 0 = -4*g - i. Let o be 1/g + 4/(-8). Solve 0 + 3/4*p**5 + 1/2*p**4 - o*p**2 - 3/4*p**3 + 0*p = 0 for p.
-1, -2/3, 0, 1
Let b(n) be the second derivative of 0 + 1/6*n**4 - 105*n + 5/3*n**3 + 0*n**2. Suppose b(g) = 0. Calculate g.
-5, 0
Let j(q) be the second derivative of 26*q**6/15 + 74*q**5/5 - 8*q**4 - 3937*q + 1. Suppose j(x) = 0. Calculate x.
-6, 0, 4/13
Let u(c) be the third derivative of c**5/20 - 75*c**4/2 + 299*c**3/2 - 316*c**2 + c. Let u(y) = 0. Calculate y.
1, 299
Let r = -31 - -38. Let a(t) = -4*t + 31. Let n be a(r). Factor -110*l**3 + 44*l**3 - 16*l - 9*l**5 - n - 54*l**2 - 39*l**4 - 5*l.
-3*(l + 1)**4*(3*l + 1)
Let k(i) be the third derivative of -i**5/90 - 25*i**4/18 + 17*i**3/3 - 787*i**2. Solve k(d) = 0 for d.
-51, 1
Solve 464/11*z + 966/11 - 114/11*z**2 + 4/11*z**3 = 0 for z.
-3/2, 7, 23
Suppose 3 = -5*i + 13. Find l, given that -2899*l**2 - 75*l**4 - 19*l**3 + 40*l + 2719*l**i + 249*l**3 = 0.
0, 2/5, 2/3, 2
Let b(y) be the first derivative of -2*y**6/3 - 148*y**5/25 - 89*y**4/5 - 20*y**3 - 36*y**2/5 + 2945. Solve b(d) = 0 for d.
-3, -1, -2/5, 0
Determine h, given that 4930*h - h**3 - 857*h**2 + 9164712 - 23162233 - 179173*h + 134*h**2 = 0.
-241
Let p(f) be the first derivative of f**4/16 + 2*f**3 - 159*f**2/8 - 203*f/2 - 4814. Let p(t) = 0. What is t?
-29, -2, 7
Let k(x) be the third derivative of 0*x + 0 + 0*x**4 - 1/84*x**8 - 4/15*x**5 + 0*x**3 - 52*x**2 + 0*x**6 + 2/35*x**7. Factor k(j).
-4*j**2*(j - 2)**2*(j + 1)
Suppose -9*p - 182 = -7*p. Let d = -88 - p. Factor 0 + 2/7*l**d + 8/7*l**5 + 0*l + 0*l**2 + 10/7*l**4.
2*l**3*(l + 1)*(4*l + 1)/7
Let a(f) = -2*f**2 - 4*f + 50. Let q be a(0). Find o, given that q*o**2 + 5*o**5 - 6678*o**4 - 17 + 6658*o**4 - 5*o - 13 = 0.
-1, 1, 2, 3
Let 30752/11 + 2/11*q**2 - 496/11*q = 0. Calculate q.
124
Factor -102*s + 18/5*s**3 - 104/5*s**2 - 108/5.
2*(s - 9)*(s + 3)*(9*s + 2)/5
Let y(u) = -9*u - 43. Let r be y(-5). Factor 618*s**2 - 2*s**4 + 18*s**3 - 314*s**r - 50*s - 334*s**2.
-2*s*(s - 5)**2*(s + 1)
Let b(n) be the second derivative of -15 + 128*n**2 + 2*n + 61/5*n**5 - 8/15*n**6 - 416/3*n**3 - 69*n**4. Find i, given that b(i) = 0.
-1, 1/4, 8
Let q be 18/(-9) + 2 - 0/4. Suppose q = -2*x + 6*x. Factor 2/3*b**3 + 2/9*b**2 + 0 + x*b.
2*b**2*(3*b + 1)/9
Let s = -1 - -4. Suppose 0 = -5*q + 4*v + 23, 8*v - 4*v - 47 = -5*q. Factor q*p - 9*p + p**3 - s*p**3 + 4*p**2.
-2*p*(p - 1)**2
Suppose 21*r - 22 - 20 = 0. Let a(l) = 18*l**3 - 18*l**2 - 102*l - 22. Let h(i) = -37*i**3 + 39*i**2 + 205*i + 43. Let m(s) = r*h(s) + 5*a(s). Factor m(t).
4*(t - 3)*(t + 2)*(4*t + 1)
Let q(m) be the first derivative of -33 - 48/25*m**5 - 18/5*m**4 - 3/5*m**2 + 3*m**3 + 0*m. Factor q(b).
-3*b*(b + 2)*(4*b - 1)**2/5
Let a(q) be the second derivative of -q**6/105 - 18*q**5/35 - 59*q**4/7 - 1340*q**3/21 - 1725*q**2/7 + 7478*q. Solve a(j) = 0.
-23, -5, -3
Determine m so that -119 - 1/6*m**2 - 359/6*m = 0.
-357, -2
Let l(p) be the first derivative of 1/9*p**3 + 1/12*p**4 - 2 + 0*p**2 - 1/15*p**5 - 1/18*p**6 + 0*p. Factor l(m).
-m**2*(m - 1)*(m + 1)**2/3
Let j be 9/6*(-8)/(-6). Let h = 85206/7 + -12172. Factor -4/7*c**j - 2/7*c + h.
-2*(c + 1)*(2*c - 1)/7
Let d(h) = h**3 - 50*h**2 + 47*h + 98. Let x be d(49). Suppose -z = -x*z - 3. Let -1/12*t**z + 0 + 1/12*t + 0*t**2 = 0. Calculate t.
-1, 0, 1
Factor -162/5*b - 164/5 + 2/5*b**2.
2*(b - 82)*(b + 1)/5
Determine y so that -116/13*y**2 + 2/13*y**5 - 20/13*y**4 - 24/13 + 72/13*y**3 + 86/13*y = 0.
1, 3, 4
Let y(x) = -4*x + 54. Let t be y(11). Solve 12*p**4 + 44*p**3 - t*p**2 + 461*p - 445*p + 58*p**2 = 0 for p.
-2, -1, -2/3, 0
Let a(n) = 14*n**2 - 226*n + 1290. Let v(r) = -25*r**2 + 451*r - 2609. Let q(t) = -11*a(t) - 6*v(t). Factor q(i).
-4*(i - 6)*(i + 61)
Let c(x) = 2*x**3 + 279*x**2 + 94*x - 6207. Let d be c(-139). Let -1/4*o**3 - d*o + 15/2*o**2 - 128 = 0. What is o?
-2, 16
Let b(h) be the first derivative of h**4/26 - 100*h**3/39 + 33*h**2/13 + 34848*h/13 + 7548. Factor b(x).
2*(x - 33)**2*(x + 16)/13
Let b be 20 + (-9 - -4) + (6 - 0). Suppose 0 = 3*r - 6, -5*h + b = -5*r + 6. Factor 24*s - 21/2*s**4 - 6 - 75/2*s**2 + 57/2*s**3 + 3/2*s**h.
3*(s - 2)**2*(s - 1)**3/2
Let g(p) = 6*p**3 + 10*p**2 + 32*p - 202. Let w(t) be the first derivative of t**4/4 - t**3/3 - t + 15. Let n(d) = g(d) - 10*w(d). Solve n(s) = 0.
-3, 4
Let c(q) be the first derivative of 3*q**2 - 22 + 31*q**3 + 1 - 15*q**3 - 17*q**3. Factor c(i).
-3*i*(i - 2)
Let i(w) = -13*w**3 - 1333*w**2 - 1328*w - 4. Let o(k) = -160*k**3 - 15995*k**2 - 15935*