or q(y).
3*(y - 3)*(y + 16)
Let h(w) be the second derivative of 2*w**6/75 - 21*w**5/25 - 157*w**4/15 - 18*w**3 - 356*w + 2. Determine b so that h(b) = 0.
-5, -1, 0, 27
Let u(x) = -x**3 - x**2 + 3*x + 5. Let t be u(0). Suppose -5*y + 4 + 1 = 0, 676 = t*v - 4*y. Solve v - 136 - 3*b**3 + 3*b**5 - 3*b**2 + 3*b**4 = 0 for b.
-1, 0, 1
Let q(o) be the third derivative of o**7/70 - 11*o**6/4 - 45*o**5/4 + 55*o**4/4 + 112*o**3 - o**2 - 278*o. Solve q(b) = 0.
-2, -1, 1, 112
Let f(n) = -2*n**2 + 6*n - 2. Let o be f(4). Let k = -7 - o. Suppose 15*j**k - 11*j**3 + 4*j**5 - 8*j**3 = 0. What is j?
-1, 0, 1
Let u(q) be the second derivative of -q**4/12 - q**3/6 - q**2/2 - 12*q. Let x(c) = c**4 + 18*c**3 + 52*c**2 + 50*c + 19. Let a(p) = -4*u(p) - x(p). Factor a(j).
-(j + 1)**3*(j + 15)
Suppose -2401*v - 15*v + 4962 = 65*v. Suppose 204*o**v + 117/2*o**4 - 687/4*o**3 - 27/4*o**5 - 87*o + 12 = 0. Calculate o.
1/3, 2, 4
Let c(q) = -11*q**3 - 181*q**2 + 94*q + 168. Let l(u) = -45*u**3 - 740*u**2 + 375*u + 670. Let m(j) = 25*c(j) - 6*l(j). Solve m(f) = 0.
-18, -1, 2
Let c = 74 + -85. Let w(g) = 8*g**3 + 11*g - 22. Let b(m) = -3*m**3 - 4*m + 8. Let s(i) = c*b(i) - 4*w(i). Factor s(z).
z**3
Let y(k) = 5*k**2 - 270*k - 572. Let q(j) = -26*j**2 + 1350*j + 2868. Let b(m) = 3*q(m) + 16*y(m). Solve b(g) = 0 for g.
-2, 137
Suppose -5*r + 137 = -3*n + 249, -14 = -n - 3*r. Let y(c) be the first derivative of -3/20*c**4 + 0*c**2 + 4/15*c**3 + 0*c - n. Factor y(f).
-f**2*(3*f - 4)/5
Let s(r) be the third derivative of r**8/5040 + r**7/420 + r**6/90 + r**5/10 - r**3/6 + 15*r**2. Let a(y) be the third derivative of s(y). Factor a(z).
4*(z + 1)*(z + 2)
Let b(j) = -52*j**3 - 70*j**2 + 2518*j + 2590. Let f(i) = -44*i**3 - 69*i**2 + 2519*i + 2589. Let m(q) = -5*b(q) + 6*f(q). Find z such that m(z) = 0.
-34, -1, 19
Let l(r) be the third derivative of r**5/12 + 125*r**4/24 + 95*r**3 + 355*r**2 + 3. Determine y, given that l(y) = 0.
-19, -6
Let q(w) be the first derivative of 2/3*w**5 - 4*w**2 - 168 + 80/9*w**3 - 9/2*w**4 + 0*w. Let q(a) = 0. What is a?
0, 2/5, 2, 3
Let s(f) = f**2 + 2*f + 4. Let c be s(-4). Let i be (4/c)/((-2)/(-18)). Determine n, given that -797*n + i*n**4 + 797*n - 3*n**2 = 0.
-1, 0, 1
Let c(s) be the second derivative of s**4/3 + 200*s**3/3 + 392*s**2 - 34*s + 8. Determine t, given that c(t) = 0.
-98, -2
Let r(o) be the third derivative of 26*o + 0 + 25/2*o**3 + 1/20*o**7 + 61/80*o**6 - 205/16*o**4 + o**2 + 87/40*o**5. What is b in r(b) = 0?
-5, 2/7, 1
Let v(r) = -r**2 - 13*r - 10. Let d(u) be the third derivative of u**5/20 + 19*u**4/12 + 5*u**3 - 30*u**2. Let c(z) = 6*d(z) + 17*v(z). What is s in c(s) = 0?
-5, -2
Let h(t) be the third derivative of -1/2520*t**6 - 7/6*t**3 + 0*t + 3*t**2 + 0 + 1/56*t**4 + 1/420*t**5. Let b(i) be the first derivative of h(i). Factor b(o).
-(o - 3)*(o + 1)/7
Let q = -27 + 33. Let a(k) = k**3 - 5*k**2 - 5*k + 7. Let f be a(q). Factor 39 - r**4 - f*r**2 - 12*r - 43 + 0*r**3 - 6*r**3.
-(r + 1)**2*(r + 2)**2
Let t(g) be the third derivative of 0*g + 1/240*g**5 - 1/16*g**4 - 7/24*g**3 + 0 + 92*g**2. Factor t(f).
(f - 7)*(f + 1)/4
Let f(h) be the second derivative of -14/9*h**3 - 49*h**2 + 2 - 1/54*h**4 - 12*h. Factor f(u).
-2*(u + 21)**2/9
Let d(m) be the first derivative of 3*m**5/40 - 3*m**4/8 - 4*m**3 - 9*m**2 - 26*m - 83. Let x(n) be the first derivative of d(n). Factor x(l).
3*(l - 6)*(l + 1)*(l + 2)/2
Let o(q) be the first derivative of 4*q**6/9 - 26*q**5/15 - 94*q**4/3 - 38*q**3 + 3006. Let o(t) = 0. Calculate t.
-19/4, -1, 0, 9
Let b be (-5 + (-500)/(-105))*-8*(-6)/(-30). Let l(x) be the first derivative of -b*x**3 - 29 + 3/7*x**2 + 2/7*x. Suppose l(c) = 0. Calculate c.
-1/4, 1
Let j(q) be the second derivative of -5/36*q**4 - 1/180*q**6 + 0*q**2 + 4 - 14*q + 11/120*q**5 + 0*q**3. Factor j(s).
-s**2*(s - 10)*(s - 1)/6
Let o(l) be the third derivative of 0 + 1/48*l**4 - 1/120*l**5 + 0*l + 1/6*l**3 + 113*l**2. Let o(x) = 0. Calculate x.
-1, 2
Let i be 28/266 + (-177)/57. Let a be i/(-6)*(3 + -3). Factor -4/7*b**2 + 0 + 2/7*b**3 + a*b.
2*b**2*(b - 2)/7
Let k(u) be the first derivative of 1/30*u**5 - 25/6*u + 4/3*u**3 - 5/6*u**2 + 5/12*u**4 + 61. Find v such that k(v) = 0.
-5, -1, 1
Let w be ((-4508)/686)/((-3)/24). Find a, given that -960/7*a + w*a**2 + 800/7 - 48/7*a**3 + 2/7*a**4 = 0.
2, 10
Let s(w) be the second derivative of w**5/5 - 37*w**4/3 - 320*w**3/3 - 328*w**2 + 7137*w. Factor s(g).
4*(g - 41)*(g + 2)**2
Let c(d) be the first derivative of d**4/14 - 274*d**3/7 - 10313. What is v in c(v) = 0?
0, 411
Let j = 530 + -372. Let r = j - 157. Factor r - 9/4*i + 1/2*i**2.
(i - 4)*(2*i - 1)/4
Let h(c) = 33*c + 51. Let o be h(8). Suppose -13*f + o = -6*f. Factor -120*z**3 + 80*z**2 + f*z**4 - 10*z**5 + 5*z**5 - 16*z + 16*z.
-5*z**2*(z - 4)**2*(z - 1)
Let o(f) be the first derivative of f**6/120 - f**5/12 + f**4/3 - 2*f**3/3 - 143*f**2/2 - f + 19. Let m(t) be the second derivative of o(t). Factor m(n).
(n - 2)**2*(n - 1)
Let b(i) = 2*i**3 - 480*i**2 - 75855*i - 4019682. Let w(d) = -3*d**3 + 481*d**2 + 75859*d + 4019683. Let n(v) = -4*b(v) - 3*w(v). Factor n(c).
(c + 159)**3
Let m(t) be the second derivative of -30/7*t**3 - 2/49*t**7 - 3/70*t**6 + 12*t + 24/7*t**2 - t**4 + 21/20*t**5 - 8. Determine p so that m(p) = 0.
-4, -1, 1/4, 2
Let h(i) = 4*i**3 - 67*i**2 + 53*i - 77. Let v be h(16). Suppose 0 + 8/7*l - 10/7*l**v - 6/7*l**4 + 2/7*l**5 + 6/7*l**2 = 0. What is l?
-1, 0, 1, 4
Let s(w) = -7*w**2 - 30*w - 67. Let o(p) = p**2 - 1. Suppose -3*h + 8 = 4*b, b + b = 4*h - 18. Let a(m) = b*s(m) - 5*o(m). Let a(l) = 0. Calculate l.
-12, -3
Let o(m) be the second derivative of 289*m**5/10 - 4267*m**4/6 - 1016*m**3/3 - 60*m**2 + 433*m + 3. Factor o(p).
2*(p - 15)*(17*p + 2)**2
Let g(u) be the third derivative of 10*u**7/21 - 3*u**6/2 - 71*u**5/15 + 63*u**4/2 - 196*u**3/3 + 3*u**2 + 31*u. Factor g(a).
4*(a - 1)*(a + 2)*(5*a - 7)**2
Let z(u) be the third derivative of -u**7/2520 + u**6/1440 + 49*u**5/720 - 49*u**4/288 - u**2 - 3*u + 41. Determine o so that z(o) = 0.
-7, 0, 1, 7
Solve 17*d**2 - 46 - 102*d**2 - 3*d + 47 + 91*d**3 - 4*d + 0*d = 0 for d.
-1/7, 1/13, 1
Let i = 1728 + -1659. Let b be i/4 + -12 + (0 - 5). Factor 1/2*v - b - 1/4*v**2.
-(v - 1)**2/4
Let r = 20 - 19. Let a be r/(5/((-75)/(-3))). Factor -8*x**4 - 4*x**3 - 4*x**4 + 9*x + 25 - 23 - 4*x**a - x**5 + 10*x**2.
-(x - 1)*(x + 1)**3*(5*x + 2)
Let s(v) be the third derivative of -v**7/70 + 201*v**6/40 - 12567*v**5/20 + 176435*v**4/8 + 2147466*v**3 + 5059*v**2. Factor s(j).
-3*(j - 71)**3*(j + 12)
Let d(m) be the third derivative of -m**7/70 - 13*m**6/8 - 63*m**5/20 + 65*m**4/8 + 32*m**3 - 2*m**2 + 2080. What is n in d(n) = 0?
-64, -1, 1
Factor 6629261*r**2 + 14773462*r**2 + 9 - 15 + 18 + 32052*r.
3*(2671*r + 2)**2
Let k(q) = -q**3 - 16*q**2 + 47*q - 6. Let x be k(-17). Let p = 516 + x. Factor 4/17*a**2 - 2/17*a**4 - 2/17 + p*a + 0*a**3.
-2*(a - 1)**2*(a + 1)**2/17
Let t(g) = -6*g**3 + 18*g**2 - 150*g - 158. Let c(i) = -20*i**3 + 56*i**2 - 451*i - 475. Let r(j) = 4*c(j) - 13*t(j). Determine y, given that r(y) = 0.
-11, -1, 7
Let u = -39 - -39. Suppose 0 = 3*t - 5*k - 37, 0 = 2*t - u*k - k - 27. Factor t*i**2 + 3*i - 11*i**2 + 3*i**3 - i**3 - i**3 + 1.
(i + 1)**3
Let x(m) = -m**3 - 2*m**2 - 2*m - 1. Let a(o) = 4*o**3 - 8*o**2 - 50*o - 51. Let r(b) = -13*b - 66. Let u be r(-5). Let k(s) = u*a(s) - 5*x(s). Factor k(z).
(z + 2)**2*(z + 14)
Let y(f) = -105*f**2 - 1030*f + 4200. Let c(x) = 8*x**2 + 81*x - 323. Let p(w) = -40*c(w) - 3*y(w). Let p(l) = 0. What is l?
-32, 2
Factor 13784200 + 246*o**2 - 1/5*o**3 - 100860*o.
-(o - 410)**3/5
Suppose l - 3*a - 48 = 0, 5*l = -5*a + 200 - 40. Determine i, given that 25*i**2 + l*i**2 + 157 + 329 - 5*i**3 - i**2 + 2*i**3 - 351*i = 0.
2, 9
Solve -19*f**2 - 118*f**3 - 4361 - 841 + 55*f**2 + 2397*f + 119*f**3 + 64*f**2 = 0.
-51, 2
Suppose -4*z = 2*t - z - 771, 1970 = 5*t - z. What is h in 27*h**2 - t + 491 - 25*h**2 + 28*h = 0?
-7
Let i = 657 - 657. Let l(d) be the first derivative of -7/2*d**4 + 0*d**3 - 6/5*d**5 + 4*d**2 + 16 + i*d. Factor l(g).
-2*g*(g + 1)*(g + 2)*(3*g - 2)
Let r(p) = -18*p - 51. Let l be r(-7). Let l*h**2 + h + 7*h + 12 + h - 78*h**2 = 0. Calculate h.
-1, 4
Determine i, given that -26 + 92 + 454 + 10*i**2 - 40*i**2 + 5*i**3 