19. Let j(t) be the third derivative of l(t). Factor j(f).
2*(f - 10)*(f + 1)
Let m be 4/(-14) + 120/28. Suppose -m = -j - j. Let 9*t - 2 - 6*t**j + 2*t**2 + 3*t**2 - 3*t**2 = 0. What is t?
1/4, 2
Let n(z) be the second derivative of 243/2*z**2 + 1/4*z**4 + 20*z - 9*z**3 + 0. Find k, given that n(k) = 0.
9
Let t = -33 + 36. Let k be (12/(-10))/(t/30*-4). Let -k - 3/2*r**3 + 0*r**2 + 9/2*r = 0. What is r?
-2, 1
Let u be (2907/(-54))/19 - (-2)/(-12). Let n be 6 - -1 - (7 + u). Suppose 0 + 0*q**4 + 0*q**2 - 1/3*q**5 + 0*q + 1/3*q**n = 0. Calculate q.
-1, 0, 1
Let o(l) = -10*l**4 + 74*l**3 - 181*l**2 + 147*l - 36. Let q(u) = u**2 + u. Let b(y) = -o(y) - 3*q(y). Factor b(z).
2*(z - 3)**2*(z - 1)*(5*z - 2)
Find n such that -287*n**2 + 816*n**2 + 776*n + 46*n**3 - 776*n + n**4 = 0.
-23, 0
Factor 6*d**2 - 3/4*d**3 + 0 + 27/4*d.
-3*d*(d - 9)*(d + 1)/4
Let v = 177 - 170. Suppose 0 = -v*p - 3 + 17. Suppose 0*q + 2/9*q**3 + 0 - 2/9*q**p = 0. Calculate q.
0, 1
Let v(d) = 31*d**2 - d - 2. Let q be v(-1). Suppose 17*x - q = 2*x. Factor 2/3 + 1/3*c**x + c.
(c + 1)*(c + 2)/3
Find a, given that 6*a**5 - 135 - 6*a**2 - 3*a**5 + 978*a**4 - 66*a**3 + 207*a + 0*a**3 - 981*a**4 = 0.
-3, 1, 5
Suppose 108 = -4*w + 8*w + 2*r, w + 5*r = 45. Factor 5*p**2 + w - 44 + 19.
5*p**2
Factor -49/5*z - 2/5 - 14*z**2 - 23/5*z**3.
-(z + 1)*(z + 2)*(23*z + 1)/5
Suppose 0*f = -5*f + 25. Suppose -2*c - o + f*o - 2 = 0, 3*c + o = 11. Factor -8*r**2 + 4*r**c + 6*r**2 + 0*r + 0*r - 2*r**4.
-2*r**2*(r - 1)**2
Suppose -16/3*i**3 - 1/6*i**5 + 0 + 16/3*i**2 + 0*i + 5/3*i**4 = 0. What is i?
0, 2, 4
Factor -90 - 55*c - 3*c**2 - 8*c**2 - 3*c**2 + 9*c**2.
-5*(c + 2)*(c + 9)
Factor -6 + 2/5*n**3 - 2/5*n**2 - 34/5*n.
2*(n - 5)*(n + 1)*(n + 3)/5
Let w be (7 + -8)*(-1 - 2). Let b be ((-10)/w)/(8/(-12)). Factor -y**5 - 2*y**4 - y**b + 0*y**5.
-2*y**4*(y + 1)
Let a(j) = -j**3 - 10*j**2 - 10*j - 2. Let i be a(-9). Let g be i*1 + 18/(-6). Factor g*k + k - 12 - k**2 - 2*k**2 + 7*k.
-3*(k - 2)**2
Let c(u) = 2*u**2 + 2*u + 2. Let v be c(-1). Factor -10*f**2 + 3 - 4 + 9*f**v - 2*f.
-(f + 1)**2
Let k = 5845/468 + -162/13. Let l(u) be the third derivative of 0*u**5 + 0 - 2*u**2 + 0*u + k*u**4 - 1/180*u**6 + 0*u**3. Find j such that l(j) = 0.
-1, 0, 1
Let c = 11 - 33. Let q be (-5)/30 - c/60. What is t in -1/5*t**3 + 1/5 - q*t**2 + 1/5*t = 0?
-1, 1
Factor -642*m - 21*m**3 - 54 - 614*m + 36*m**2 + 1295*m.
-3*(m - 2)*(m - 1)*(7*m + 9)
Let h(x) be the second derivative of 14*x**5/5 + 5*x**4/2 + 2*x**3/3 - 260*x. Suppose h(u) = 0. What is u?
-2/7, -1/4, 0
Suppose 0 = 3*w + 3*z - 30, -4*z + 34 = 347*w - 345*w. Factor 2/5*f**w - 2*f - 2/5*f**2 - 6/5.
2*(f - 3)*(f + 1)**2/5
Let g(j) be the second derivative of j**6/90 - 3*j**5/20 + 2*j**4/9 + j + 169. Factor g(c).
c**2*(c - 8)*(c - 1)/3
Determine l so that -40 - 57*l**5 + 41*l**2 - 34*l**3 + 32*l + 59*l**5 + 2*l**4 - 3*l**2 = 0.
-5, -1, 1, 2
Let q = 459 + -457. Let x(n) be the second derivative of 0*n**3 + 0 + 1/40*n**5 + 0*n**q + 1/180*n**6 + 1/36*n**4 - 7*n. What is o in x(o) = 0?
-2, -1, 0
Let m = 489/974 + -1/487. Let -3/2*z**3 + 3/2*z + m*z**2 + 1/2*z**4 - 1 = 0. Calculate z.
-1, 1, 2
Let s(l) be the third derivative of 36*l**2 + 1/80*l**5 + 1/8*l**4 + 0 + 0*l**3 + 0*l. Factor s(f).
3*f*(f + 4)/4
Factor -15/4*v + 5/4*v**2 - 25/2.
5*(v - 5)*(v + 2)/4
Let s(p) be the second derivative of p**8/112 + 3*p**7/70 + p**6/40 - 3*p**5/20 - p**4/4 - 5*p**2 + 41*p. Let o(l) be the first derivative of s(l). Factor o(u).
3*u*(u - 1)*(u + 1)**2*(u + 2)
Suppose 144*g = 224*g. Let -4/15*z**2 + 2/15*z**3 + 0*z + g = 0. Calculate z.
0, 2
Factor -159*v + 19683 - 477*v**2 + 480*v**2 - 327*v.
3*(v - 81)**2
Let n = 484 - 16938/35. Let w(v) be the second derivative of -n*v**5 - 10*v + 0*v**4 - 2/105*v**6 + 2/7*v**2 + 0 + 4/21*v**3. Factor w(q).
-4*(q - 1)*(q + 1)**3/7
Let l(s) be the first derivative of 4 + 1/72*s**6 + 0*s**5 + 0*s + 0*s**3 + 1/6*s**2 - 5/48*s**4. Determine f so that l(f) = 0.
-2, -1, 0, 1, 2
Let j(s) = s**3 - 64*s**2 - 30*s - 4. Let w(d) = 31*d**2 + 15*d + 2. Let n(m) = -6*j(m) - 13*w(m). Find f, given that n(f) = 0.
-2, -1, -1/6
Let f be (0*4/16)/(-2). Let u(p) = -2*p**3 + 5*p**2 + 8*p + 16. Let q be u(4). Suppose -3/2*r**3 + 0*r**2 + q + 9/2*r**4 + f*r + 6*r**5 = 0. Calculate r.
-1, 0, 1/4
Let b = -829/888 + 2363/1480. Let l = 2/555 + b. Suppose -2/3 + 5/3*k**2 + l*k**3 + 1/3*k = 0. What is k?
-2, -1, 1/2
Let v(a) be the first derivative of 2*a**3/9 + 11*a**2/3 + 3. Factor v(w).
2*w*(w + 11)/3
Suppose -2*m - 3*l - 2 = 0, 4*m + 2 = -0*m - 5*l. Determine t, given that 28*t**3 + 26*t**4 - 8*t**m + 10*t**4 + 0*t**3 = 0.
-1, 0, 2/9
Let d(b) be the first derivative of -b**4/12 - 5*b**3/9 + 11*b**2/3 - 16*b/3 + 166. Solve d(f) = 0 for f.
-8, 1, 2
Let v(m) be the second derivative of 5/3*m**4 + 0*m**2 - 4*m + 0 + 2/15*m**6 + 4/3*m**3 + 4/5*m**5. Let v(i) = 0. What is i?
-2, -1, 0
Suppose p + 17 = 4*i, -4 - 2 = -3*i + 3*p. What is f in 0*f**2 - 5*f - 7*f**2 + f + i*f**2 = 0?
-2, 0
Factor -2*r**3 + 0*r**3 + 8*r + 199 - 183 + 3*r**2 - 7*r**2 + 0*r**2.
-2*(r - 2)*(r + 2)**2
Let t(y) be the first derivative of y**4/22 - 52*y**3/33 + 49*y**2/11 - 48*y/11 + 491. Find o, given that t(o) = 0.
1, 24
Let u = 297/86 + -40637/1806. Let c = 138/7 + u. Factor -4/3 + d**2 + 4/3*d - c*d**3 - 1/3*d**4.
-(d - 1)**2*(d + 2)**2/3
Let k(r) be the second derivative of r**6/195 + 27*r**5/130 - 14*r**4/39 - r + 55. Factor k(u).
2*u**2*(u - 1)*(u + 28)/13
Let m(d) = 16*d**4 + 158*d**3 + 187*d**2 + 39*d - 3. Let s(g) = -48*g**4 - 476*g**3 - 560*g**2 - 116*g + 8. Let v(f) = 8*m(f) + 3*s(f). Let v(b) = 0. What is b?
-9, -1, -1/4, 0
Let z(a) be the third derivative of -a**7/1050 + 7*a**5/300 - a**4/20 - 6*a**2 - 1. Factor z(l).
-l*(l - 2)*(l - 1)*(l + 3)/5
Let t(y) = -2*y**3 - 36*y**2 - 69*y - 10. Let h(z) = 6*z**3 + 108*z**2 + 208*z + 32. Let s(k) = 5*h(k) + 16*t(k). Factor s(c).
-2*c*(c + 2)*(c + 16)
Let h(p) be the first derivative of 38/7*p**2 - 32/7*p + 122/21*p**3 + 1/2*p**4 + 27. Determine x, given that h(x) = 0.
-8, -1, 2/7
Let d(c) be the second derivative of 2*c**6/15 - 19*c**5/5 + 16*c**4/3 + 24*c**3 - 554*c. Find w such that d(w) = 0.
-1, 0, 2, 18
Let c = 3 - -2. Suppose -15 = -5*k - 6*g + g, c*g + 9 = 3*k. Suppose 4/5*t**k - 2/5*t**5 + 2/5 - 2/5*t - 4/5*t**2 + 2/5*t**4 = 0. What is t?
-1, 1
Let l(h) be the first derivative of h**3/12 - 49*h**2/2 - 197*h/4 + 551. Find o such that l(o) = 0.
-1, 197
Let c = 225 - 221. Let a(b) be the second derivative of -1/15*b**3 + 1/10*b**2 + 0 + 1/60*b**c - b. Factor a(g).
(g - 1)**2/5
Let z be 4/16*(-384)/(-224). What is m in 3/7*m**3 - z*m + 3/7*m**2 - 3/7 = 0?
-1, 1
Let v be ((2/(-6))/((-10)/(-15)))/(-10). Let g(p) be the second derivative of v*p**4 + 0*p**2 - 5*p + 0*p**3 + 0. Factor g(m).
3*m**2/5
Let i(d) = -2*d**2 - 38*d + 84. Let j be i(-21). Solve -2/13*g**5 - 2/13*g + 8/13*g**4 - 12/13*g**3 + j + 8/13*g**2 = 0 for g.
0, 1
Let f(q) be the second derivative of -43*q - 1/12*q**4 - 2/9*q**3 + 1/60*q**5 + 2 + 0*q**2. Suppose f(w) = 0. Calculate w.
-1, 0, 4
Let m(i) be the third derivative of 0*i**3 + 0*i**4 + 1/10*i**6 + 2/15*i**5 - 1/84*i**8 + 0*i + 0 - 5*i**2 + 0*i**7. Factor m(x).
-4*x**2*(x - 2)*(x + 1)**2
Solve -14/13*a**4 + 6/13*a**3 + 0 + 0*a**2 + 4/13*a**5 + 0*a = 0.
0, 1/2, 3
Let a(l) be the second derivative of 0*l**2 + 0 + 0*l**3 - 1/5*l**5 - 4*l + 1/6*l**4 + 1/15*l**6. Factor a(w).
2*w**2*(w - 1)**2
Let f be (12/9)/((-4)/(-3)). Let i = -3/4 + f. Suppose -i*r + 1/2 - 1/4*r**2 = 0. What is r?
-2, 1
Let i(s) be the third derivative of s**5/150 + 7*s**4/15 + 9*s**3/5 - 11*s**2 + 15*s. Determine o, given that i(o) = 0.
-27, -1
Let s = -56 + 58. Solve -5*n**3 - 11*n + s*n**2 + n - 17*n**2 = 0.
-2, -1, 0
Suppose -3*f - c + 0*c + 6 = 0, 2*c = 0. Let p be -1 + (2 + 5 - f). Factor 5/2*y**2 - 2*y**3 + 1/2*y**p + 0 - y.
y*(y - 2)*(y - 1)**2/2
Suppose -2*s + 150 - 18 = 0. Let h = 70 - s. Let -1/9 - 4/9*c + 2/9*c**3 - 4/9*c**2 + 5/9*c**h + 2/9*c**5 = 0. What is c?
-1, -1/2, 1
Let z be 14/392*24 - (-58)/14. Let n(p) be the second derivative of -3/25*p**z - 4*p + 0 + 8/15*p**4 - 8/15*p**3 + 0*p**2. Factor n(k).
-4*k*(k - 2)*(3*k - 2)/5
Let j(d) be the first derivative of 2*d**3/63 + 23*d**2/21 + 143. Factor j(n).
2*n*(n + 23)/21
Suppose -s = -4*m - 0