second derivative of -r**6/135 + r**4/6 - r - 8. Solve y(m) = 0.
-3, 0, 3
Let m(q) = 28*q**3 + 3349*q**2 + 5*q. Let x(v) = -68*v**3 - 8372*v**2 - 12*v. Let r(o) = -12*m(o) - 5*x(o). Determine a, given that r(a) = 0.
-418, 0
Let o(d) be the first derivative of 361/3*d + 27 + 19/3*d**2 + 1/9*d**3. What is z in o(z) = 0?
-19
Let b(z) be the first derivative of 99 + 3/10*z**4 + 2/3*z**3 - 2/5*z**2 + 0*z. Factor b(j).
2*j*(j + 2)*(3*j - 1)/5
Factor 3*r**2 + 5488*r + 1008 - 4780*r + 396.
3*(r + 2)*(r + 234)
Let w(b) = 6*b**3 - 363*b**2 - 277*b + 90. Let d(t) = -13*t**3 + 725*t**2 + 554*t - 179. Let v(g) = 8*d(g) + 20*w(g). Factor v(f).
4*(f - 92)*(f + 1)*(4*f - 1)
Let b(f) be the third derivative of 0 + 0*f + 5329/8*f**4 + 73/10*f**5 + 0*f**3 - 5*f**2 + 1/40*f**6. Factor b(g).
3*g*(g + 73)**2
Let r(k) be the second derivative of -k**4/9 - 5324*k**3/9 - 3543122*k**2/3 + 16*k + 153. Let r(b) = 0. What is b?
-1331
Let r(z) = -19*z - 13. Let o be r(-7). Let b(c) = -60*c - c**2 + o*c + 1 - 61*c. Let g(l) = 3*l**2 - 2*l - 7. Let h(w) = 10*b(w) + 5*g(w). Factor h(m).
5*(m - 5)*(m + 1)
Let b be (-2867)/305 - -10 - (0 + (-17)/(-30)). Let k(y) be the second derivative of -1/5*y**3 - 2/5*y**2 - b*y**4 - 28*y + 0. Factor k(m).
-2*(m + 1)*(m + 2)/5
Factor 1761/7*h - 15/7*h**2 - 702/7.
-3*(h - 117)*(5*h - 2)/7
Let z(y) be the first derivative of 15*y**4/4 - 1745*y**3/3 + 2305*y**2/2 - 575*y - 1147. Suppose z(t) = 0. What is t?
1/3, 1, 115
Let p(i) be the first derivative of 2*i**4/21 + 13*i**3/7 - 10*i**2/7 + 4*i + 86. Let t(k) be the first derivative of p(k). Factor t(g).
2*(g + 10)*(4*g - 1)/7
Let r(x) be the second derivative of -x**7/21 + 31*x**6/3 - 667*x**5 + 8655*x**4 - 49275*x**3 + 143883*x**2 + 938*x + 3. Find f such that r(f) = 0.
3, 73
Suppose 1399*x = 1416*x. Suppose -3*p - 5*l - 19 = x, p + 2*l = -p - 6. Factor 35*b**p + 1715/3 + 5/3*b**3 + 245*b.
5*(b + 7)**3/3
Let p(j) be the second derivative of -2*j**7/63 - 17*j**6/45 - 7*j**5/5 - 13*j**4/18 + 50*j**3/9 + 8*j**2 + 5*j + 91. Find g such that p(g) = 0.
-4, -3, -2, -1/2, 1
Let x(b) be the first derivative of -b**4/16 + 19*b**3/12 + 23*b**2/2 - 1372. Factor x(f).
-f*(f - 23)*(f + 4)/4
Factor 16/3*c**2 - 1/6*c**5 - c**3 - 5/3*c**4 + 47/6*c + 3.
-(c - 2)*(c + 1)**3*(c + 9)/6
Let o be 1/((-4)/(-2))*0. Let q = 4259 + -4257. Determine t so that -3*t**2 + t**q - 2*t**3 + o*t**2 = 0.
-1, 0
Let y = -136380 - -272769/2. Let 6*a - 3/2*a**5 + y*a**3 + 3*a**4 + 0 - 12*a**2 = 0. Calculate a.
-2, 0, 1, 2
Let b be -4 + 7 + -7 - 146. Let h be (-25)/b - 26/(-60). Factor 4/5 - 1/5*x**2 + h*x.
-(x - 4)*(x + 1)/5
Let h(u) be the second derivative of 16*u**3 - 14*u - 1/30*u**6 + 2 - 13/3*u**4 + 3/5*u**5 - 32*u**2. Factor h(t).
-(t - 4)**2*(t - 2)**2
Suppose -14*b = 10*b - 1536. Suppose 4*c**3 + 64 - b - 4*c**2 - 2*c**4 + 6*c**2 - 4*c = 0. Calculate c.
-1, 0, 1, 2
Let j(i) be the third derivative of i**8/1344 - i**7/210 - 11*i**6/480 - i**5/40 - 8*i**2 + 55. Solve j(b) = 0 for b.
-1, 0, 6
Let h be -3 + 2 - (-3 - (-1 - 102)). Let j = -98 - h. Factor 20 + 22 + 3 - 2*d**3 - 25*d**2 - 15*d - 3*d**j.
-5*(d - 1)*(d + 3)**2
Factor 62650*l + 158466 + 35105*l + 6332088*l**5 + 150*l**4 + 2730*l**3 - 6332085*l**5 + 23520*l**2.
3*(l + 7)**4*(l + 22)
Let d be (19/(4104/(-512)))/((-38)/11571). Determine u, given that 6272/9 + 226/9*u**2 + d*u + 2/9*u**3 = 0.
-56, -1
Let a(t) = -27*t**3 - 9*t**2 - 20*t - 22. Let r be a(-6). Find p such that -106*p**3 - 4840*p + 105*p**3 + 300763 + 4341*p + 201*p**2 - r*p - 7362*p = 0.
67
Let l be ((14 + -11)*-2)/((-3)/4). Suppose 0*b**2 + 3*b**2 + 15*b - l*b - 10*b = 0. What is b?
0, 1
Let p be 90/4*(-16)/(-6). Let w(g) = -3*g + 10*g**2 - p - 3*g + 4*g - 13*g. Let k(v) = -5*v**2 + 7*v + 30. Let u(z) = -5*k(z) - 2*w(z). Factor u(m).
5*(m - 3)*(m + 2)
Let j be ((-158)/(-474))/(2/24). Let k(i) be the third derivative of -7/30*i**6 + 0*i**j + 0*i - 2*i**2 + 0 + 0*i**3 - 2/15*i**5. Factor k(m).
-4*m**2*(7*m + 2)
Let p(x) be the first derivative of 3*x**5/35 - 3*x**4/7 - 3*x**3/7 + 15*x**2/7 + 24*x/7 - 1112. Factor p(b).
3*(b - 4)*(b - 2)*(b + 1)**2/7
Let s be (-32)/432*9*75/(-350). Suppose 0 + 1 = -u - 4*f, -5*u = -5*f - 20. Factor 121/7 - 99/7*b - s*b**3 - u*b**2.
-(b - 1)*(b + 11)**2/7
Let k(u) be the first derivative of -u**4/5 - 8*u**3/3 + 226*u**2/5 - 408*u/5 - 3508. Factor k(g).
-4*(g - 6)*(g - 1)*(g + 17)/5
Let z(l) = -8404*l + 4. Let u be z(0). Solve 4/15 - 2/5*c - 14/5*c**2 - 6/5*c**u - 10/3*c**3 = 0.
-1, 2/9
Suppose -20*n = -28*n + 448. Let 87*r**3 - 171*r**3 - 14*r**5 - 94*r**4 + 32*r - n*r**2 - 84*r**3 = 0. Calculate r.
-4, -2, -1, 0, 2/7
Let t(u) be the second derivative of -7/6*u**3 - 96*u + 0*u**2 + 1/20*u**5 - 1/2*u**4 + 0. Factor t(g).
g*(g - 7)*(g + 1)
Let r be -7*(-24)/126*(-1584)/(-55). Let r - 48/5*b + 3/5*b**2 = 0. What is b?
8
Let i(u) = -u**2 + 2*u + 5. Let r(q) = 2*q**2 - 6*q - 11. Suppose -32*l = -39*l - 35. Let h(k) = l*i(k) - 2*r(k). Factor h(w).
(w - 1)*(w + 3)
Let o be (32/10)/(9 + (-627)/70). Let j = -223/6 + o. Find k such that -j*k**2 + 0*k + 15*k**3 - 3/2*k**4 + 0 = 0.
0, 5
Suppose -1235*r + 142 = -1164*r. Let i(f) be the first derivative of 4/15*f - 1/15*f**r + 15 - 2/45*f**3. Determine n so that i(n) = 0.
-2, 1
Let u(a) = -a**2. Let s(c) = -4*c - 4. Let n(o) = 2*o**2 - 101*o - 809. Let k be n(-7). Let t = 5 + -9. Let d(g) = k*u(g) + t*s(g). Find w, given that d(w) = 0.
-2
Let r be (-3)/(24/(-59)) + (-35)/(-50)*-10. Determine t so that 27/4 + r*t**2 - 57/8*t = 0.
1, 18
Factor 1/4*h**2 + 79/2 - 81/4*h.
(h - 79)*(h - 2)/4
Let j(c) = -c**3 + 22*c**2 - 18*c - 45. Let b be j(21). Find h, given that -33*h - 6*h**4 + h**4 + 9*h**3 + 2*h**4 + 9*h**2 + b = 0.
-2, 1, 3
Factor 99*r**4 - 22621*r**5 - 22620*r**5 + 73*r**3 + 45247*r**5 - 25*r**3.
3*r**3*(r + 16)*(2*r + 1)
Suppose -a = 4*a + 370. Let b = a + 76. Suppose -t**5 + t**3 - 874*t**2 + 874*t**b = 0. What is t?
-1, 0, 1
Solve -4/5*v**2 - 1932/5 + 656/5*v = 0 for v.
3, 161
Factor -70*i**4 + 74*i**4 - 112*i - 48*i**3 + 20 + 10 - 13 + 19 + 120*i**2.
4*(i - 9)*(i - 1)**3
Let v(c) = c**3 - 13*c**2 + 25*c - 29. Let l be v(11). Let h(i) be the first derivative of -18*i**4 + 52/3*i**3 + 11 + 0*i - l*i**2. Factor h(z).
-4*z*(2*z - 1)*(9*z - 2)
Factor -3448449/4 - 1/4*o**2 + 1857/2*o.
-(o - 1857)**2/4
Let a(d) be the first derivative of -d**4/2 + 10*d**3 + 52*d**2 + 72*d - 1224. Factor a(b).
-2*(b - 18)*(b + 1)*(b + 2)
Let w(m) = 4*m**2 + 5*m + 2. Let j = 23 - 33. Let o be w(j). Factor 5*a**4 + 343*a**2 - o*a**2 - 2*a**4 + 3*a**3 - 6 - 15*a + 0*a**3.
3*(a - 2)*(a + 1)**3
Let a(s) = 3*s**4 - s**2 - 2*s - 2. Let c(q) = 19*q**4 - 26*q**3 - 12*q**2 - 8*q - 8. Let b(i) = 4*a(i) - c(i). Factor b(x).
-x**2*(x - 4)*(7*x + 2)
Suppose -3*y + 52 = y. Let g(d) = -d**2 + 13*d + 2. Let r be g(y). Factor -6*n + 2*n - 3*n**2 + 8*n + r*n.
-3*n*(n - 2)
Let m(x) = -x**3 - 5*x**2 + 5*x - 4. Let y be 5 + -4 + (-10 - -3). Let w be m(y). Find i such that -31*i**3 + w + 35*i**3 - 2 + i**4 + 4*i**2 = 0.
-2, 0
Let q(r) be the second derivative of -r**4/96 + r**3/12 + 77*r**2/16 + r - 57. Solve q(m) = 0 for m.
-7, 11
Let s = -1461 - -898. Let r = -561 - s. Solve -1/3*a**r - 1 - 4/3*a = 0 for a.
-3, -1
Let g be (-581)/(-4830) + 26/(-299). Let m(y) be the second derivative of 0*y**2 + g*y**3 + 0 - 4*y + 1/30*y**4. Factor m(r).
r*(2*r + 1)/5
Let y(n) be the first derivative of 1/10*n**4 - 52/15*n**3 + 0*n + 169/5*n**2 + 67. Solve y(a) = 0 for a.
0, 13
Let d(y) be the second derivative of y**6/15 - 13*y**4/6 - 4*y**3 + 2340*y. Factor d(w).
2*w*(w - 4)*(w + 1)*(w + 3)
Let -160/11 - 68/11*z + 2/11*z**3 + 10/11*z**2 = 0. What is z?
-8, -2, 5
Let q(j) be the first derivative of -1/120*j**6 + 5 + 35/2*j**2 - 1/6*j**4 + 1/12*j**5 + 0*j + 0*j**3. Let w(u) be the second derivative of q(u). Factor w(v).
-v*(v - 4)*(v - 1)
Let m(h) be the third derivative of h**5/15 - 68*h**4/3 - 274*h**3/3 - 49*h**2 - 8. Factor m(r).
4*(r - 137)*(r + 1)
Let v(x) be the third derivative of x**5/80 - 97*x**4/16 - 195*x**3/8 - 610*x**2. Suppose v(z) = 0. Calculate z.
-1, 195
Let c(r) = r**2 + 9*r - 14. Let z be c(-11). Suppose -2 - z = 2*d, 0 = 5*h - 5*d - 15790. Factor -5 + h*j - j**2 - 4*j**2 - 3163*j.
-5*(j + 1)**2
Let t(o) be the third derivative of -o**5/20 + 19*o**4/2 - 2168*o**3/3 + 134