2 + 8*z. Suppose b(g) = 0. What is g?
-1, 1, 3, 5
Let j(c) = 2*c**3 + 40*c**2 + 73*c + 23. Let h be j(-18). Factor -10 + 5/2*g**2 + h*g**3 - 20*g.
5*(g - 2)*(g + 2)*(2*g + 1)/2
Let k(s) = s**5 + s**4 + s**3 - s**2 - s - 2. Let c(h) = -6*h**5 + 46*h**4 - 575*h**3 - 2021*h**2 - 2128*h - 719. Let p(x) = -c(x) - 5*k(x). Factor p(z).
(z - 27)**2*(z + 1)**3
Let u(o) be the third derivative of -1/90*o**5 + 0 + 24*o**2 + 2/9*o**3 + 0*o + 1/36*o**4. Factor u(p).
-2*(p - 2)*(p + 1)/3
Let f(o) be the third derivative of 0*o**3 + 3*o**2 + 1/315*o**7 - 1/18*o**4 - 1/30*o**5 + 0 + 0*o + 0*o**6. Let f(x) = 0. What is x?
-1, 0, 2
Suppose -v + 3*z - 12 = -0*v, -5*z + 20 = 3*v. Let f(i) be the first derivative of v*i + 1/18*i**3 - 4 + 0*i**2. What is u in f(u) = 0?
0
Let g(z) be the first derivative of z**6/9 - 8*z**5/15 + z**4/6 + 20*z**3/9 - 4*z**2/3 - 16*z/3 - 81. Factor g(r).
2*(r - 2)**3*(r + 1)**2/3
Let c(q) = q**3 + 278*q**2 - 837*q + 566. Let g(p) = -2*p**3 - 276*p**2 + 839*p - 567. Let o(s) = 3*c(s) + 4*g(s). Factor o(b).
-5*(b - 2)*(b - 1)*(b + 57)
Let b be ((-2)/(-6)*9*(-5)/(-3))/1. Suppose 8 - 20*j + 33/2*j**2 - b*j**3 + 1/2*j**4 = 0. Calculate j.
1, 4
Let p(x) = -x**2 - 17*x - 35. Let w(q) = -q**2 - 16*q - 34. Let k(h) = 6*p(h) - 5*w(h). Factor k(g).
-(g + 2)*(g + 20)
Suppose -112 = -45*u + 17*u. Let h(w) be the first derivative of -w**2 - 2/5*w - 16/15*w**3 - 2/5*w**u - 8. Solve h(a) = 0 for a.
-1, -1/2
Let g(o) be the third derivative of 5*o**8/336 + o**7/2 + 33*o**6/8 - 121*o**5/12 + 41*o**2 - 4*o. Factor g(l).
5*l**2*(l - 1)*(l + 11)**2
Let i(b) = -4 - 2 + 4 + 1 + b**2 - 2*b. Let u be i(3). Factor -4*k**u - 12 + 6*k - 6*k + 16*k.
-4*(k - 3)*(k - 1)
Let c(o) be the second derivative of 4*o**6/15 - 93*o**5/10 - 173*o**4/6 - 17*o**3 + 25*o**2 - 343*o. Suppose c(s) = 0. Calculate s.
-1, 1/4, 25
Let w(c) be the second derivative of c**4/12 + 8*c**3 - 49*c**2/2 + 185*c. Factor w(o).
(o - 1)*(o + 49)
Let j = -69 + 62. Let t(r) = 7*r**3 - 5*r - 6. Let z(p) = -13*p**3 + 11*p + 12. Let m(u) = j*t(u) - 4*z(u). Factor m(g).
3*(g - 2)*(g + 1)**2
Let u(t) = 7*t**2 + 11*t + 6. Let n(b) = 2*b**2 - b + 2. Let s(c) = 6*n(c) - 2*u(c). Factor s(j).
-2*j*(j + 14)
Let t(u) = -4*u**2 - 13*u - 8. Let q be t(-5). Let y = -43 - q. Suppose -1/3*h**3 + 0 - 1/6*h**4 + y*h - 1/6*h**2 = 0. Calculate h.
-1, 0
Let m(g) be the third derivative of g**7/350 - g**6/10 + 9*g**5/25 - 6*g**2 + 31. Factor m(p).
3*p**2*(p - 18)*(p - 2)/5
Let z(p) be the first derivative of -p**6/6 - 7*p**5 - 99*p**4 - 432*p**3 + 864*p**2 + 106. Factor z(g).
-g*(g - 1)*(g + 12)**3
Let x = -17837 - -17839. Factor 0 - 2/7*d**x - 4/7*d.
-2*d*(d + 2)/7
Let f(v) be the second derivative of -v**7/147 + 3*v**5/70 + v**4/21 + 18*v. Determine b, given that f(b) = 0.
-1, 0, 2
Let c be 4/(-3) + 16/3. Let t(n) be the third derivative of -1/200*n**6 + 0*n + 1/10*n**3 + 3/100*n**5 + 0 - 8*n**2 - 3/40*n**c. Factor t(f).
-3*(f - 1)**3/5
Suppose 750 = -5*g + 5*x, 3*g - 27*x + 450 = -25*x. Let l be (-2 + g/24)/(6/(-32)). Let 40/3*p - 64/3*p**4 + 160/3*p**3 - l*p**2 - 4/3 = 0. What is p?
1/4, 1
Let q(m) be the first derivative of m**3/7 - 9*m**2/14 - 12*m + 778. Factor q(a).
3*(a - 7)*(a + 4)/7
Let u be (-759 + (-2)/1)/((-6)/6). Factor 756*k**5 - u*k**5 - 45*k - 110*k**3 + 65*k**2 + 40*k**4 + 55*k**2.
-5*k*(k - 3)**2*(k - 1)**2
Let c(d) be the first derivative of -d**3/9 - 14*d**2/3 + 29*d/3 - 536. Factor c(z).
-(z - 1)*(z + 29)/3
Suppose -11*p**5 - 4*p**2 + 406*p + 1 - 371*p + 12 - 34*p**4 - 1 + 26*p**2 - 24*p**3 = 0. What is p?
-12/11, -1, 1
Let k = -24 - -42. Let f be 22/24 + k/(-27). Factor -f*a - 1/4*a**3 - 1/2*a**2 + 0.
-a*(a + 1)**2/4
Let d be (10 + -3 - (1 + 2)) + -2. Factor -19*x + 4*x**3 - d*x**5 + 3*x + 9*x + 5*x.
-2*x*(x - 1)**2*(x + 1)**2
Suppose 8*x = 2 + 38. Factor 10*m + 40*m**2 - 18*m**2 - x*m**3 - 17*m**2.
-5*m*(m - 2)*(m + 1)
Let x = -92 + 95. Let j be x + 1 - 304/(-95). Solve -56/5*z**3 + j*z**5 + 8/5*z**2 + 4*z + 4/5 - 12/5*z**4 = 0.
-1, -1/3, 1
Suppose -3*y = 2*y + 4*d - 72, -y = d - 15. Let c be (12/(-5))/((-2)/(80/y)). Solve -2 - 2/3*x**4 + 20/3*x + 4*x**3 - c*x**2 = 0 for x.
1, 3
Let z(d) be the second derivative of 0*d**2 + 0 + 61/12*d**5 - 40*d + 35/3*d**4 + 7/9*d**6 + 5/126*d**7 + 10*d**3. Factor z(i).
5*i*(i + 1)**2*(i + 6)**2/3
Let p(o) be the third derivative of -o**6/900 + 2*o**5/225 - o**4/60 + o**2 + 7. Factor p(w).
-2*w*(w - 3)*(w - 1)/15
Let n = -3881 + 19411/5. Suppose -4*i + 8 = r, 4*r + 9 = 4*i + 1. Factor r - 6/5*t**2 + 2/5*t - 2/5*t**4 + n*t**3.
-2*t*(t - 1)**3/5
Suppose -979*t + 977*t + 6 = 0. Let r(d) be the first derivative of 0*d - t - 2/15*d**5 + 0*d**2 - 1/6*d**4 + 2/9*d**3 + 1/9*d**6. Let r(f) = 0. Calculate f.
-1, 0, 1
Let v be (-711)/(-60) - -4*(-6)/8. Let u = -29/4 + v. Factor -2/5*b + u*b**4 - 18/5*b**3 + 12/5*b**2 + 0.
2*b*(b - 1)**2*(4*b - 1)/5
Let w(l) be the second derivative of l**4/16 - 37*l**3/4 + 4107*l**2/8 - 81*l - 2. Solve w(y) = 0 for y.
37
Suppose 2*r - 44 = -38. Let v(p) be the third derivative of -1/90*p**5 - 1/3*p**r + 0*p + 0 - 1/9*p**4 + p**2. Let v(g) = 0. What is g?
-3, -1
Let -12*i**2 + 11*i**2 + 2 - 5 + 4 = 0. Calculate i.
-1, 1
Let o = 2047 - 2044. Factor -15/4*u**o + 21/4*u**2 + 3/4*u**4 - 9/4*u + 0.
3*u*(u - 3)*(u - 1)**2/4
Let w(o) = -4*o + 58. Let t be w(14). Factor 2*l**3 - 1 + 32*l**t + 0*l + 3*l**4 - 30*l**2 - 4*l**4 - l**5 - l.
-(l - 1)**2*(l + 1)**3
Let v(h) be the third derivative of h**8/840 + 2*h**7/75 + h**6/5 + 12*h**5/25 - 12*h**2 + 12*h. Factor v(g).
2*g**2*(g + 2)*(g + 6)**2/5
Let a(v) be the second derivative of -v**4/42 + 4*v**3/21 + 3*v**2 + 581*v. Factor a(r).
-2*(r - 7)*(r + 3)/7
Let w = 2/7309 + -694367/43854. Let f = -1033/66 - w. Factor 0*v + 0 - f*v**2 - 6/11*v**4 - 6/11*v**3 - 2/11*v**5.
-2*v**2*(v + 1)**3/11
Let q(d) be the second derivative of 0 - 1/6*d**4 - 2/3*d**2 + 7/9*d**3 - 8*d. Factor q(m).
-2*(m - 2)*(3*m - 1)/3
Let k(t) be the third derivative of 2*t**7/21 + t**6/6 - t**5/4 - 5*t**4/6 - 5*t**3/6 + 206*t**2. Determine c so that k(c) = 0.
-1, -1/2, 1
Let y be (-10)/(-4)*-3*5/(-450). Let l(d) be the first derivative of -1/6*d**2 + 4 + 0*d - 2/9*d**3 - y*d**4. What is p in l(p) = 0?
-1, 0
Suppose -3*r = 6*i - 30, 40*r - 20 = 36*r - 3*i. Find n such that 14/5*n**r + 0 + 6/5*n = 0.
-3/7, 0
Let o = -25 - -126/5. Factor 0*p + 1/5 - o*p**2.
-(p - 1)*(p + 1)/5
Factor 12/7*z**2 - 116/7 - 344/7*z.
4*(z - 29)*(3*z + 1)/7
Let q(b) be the second derivative of -b**4/24 - 25*b**3/6 - 625*b**2/4 + 71*b. Determine l, given that q(l) = 0.
-25
Let j(d) be the third derivative of -8*d**7/945 - 5*d**6/27 - 673*d**5/540 - 25*d**4/18 - 2*d**3/3 + 11*d**2 - 20*d. What is o in j(o) = 0?
-6, -1/4
Let h(w) be the first derivative of -w**4/2 + 16*w**3/3 + 23*w**2 - 60*w + 60. Factor h(n).
-2*(n - 10)*(n - 1)*(n + 3)
Determine b so that -106*b**3 + 40*b**5 - 123*b**3 + 20 + 35*b**2 + 100*b - 10*b**4 + 44*b**3 = 0.
-2, -1/2, -1/4, 1, 2
Let a(n) = 22*n**3 + 52*n**2 - 70*n - 4. Let l(p) = p**3 + 2*p - 3. Let x(v) = -a(v) + 4*l(v). Find h such that x(h) = 0.
-4, 1/9, 1
Let h be 18/9 - 7/((-35)/20). Let y(m) be the second derivative of -1/9*m**3 + 1/45*m**h + 0 + 2/3*m**2 - 1/6*m**4 + 1/30*m**5 - 12*m. Factor y(l).
2*(l - 1)**2*(l + 1)*(l + 2)/3
Let h(n) be the second derivative of -n**6/6 + n**5 - 5*n**4/4 - 79*n. Determine y so that h(y) = 0.
0, 1, 3
Let q be ((-704)/55)/(-16)*20/168. Let y = -2 - -2. Factor 0 + y*z**2 - q*z + 2/21*z**3.
2*z*(z - 1)*(z + 1)/21
Let h(b) = b**2 - b. Let w(u) = 16*u**2 - 32*u + 16. Suppose -34*i = -39*i - 5. Let f(y) = i*w(y) + 12*h(y). Let f(r) = 0. Calculate r.
1, 4
Let u(q) be the third derivative of -q**7/1050 - q**6/100 - 3*q**5/100 - q**4/30 + 33*q**2. Let u(t) = 0. Calculate t.
-4, -1, 0
Suppose -10*a - 24 = -2*a. Let c be ((-6)/(-3) - a) + -3. Factor -c*x**2 + 4/3 + 2/3*x.
-2*(x - 1)*(3*x + 2)/3
Find c such that -1 + 4*c**4 + 7/2*c - 3*c**2 - 2*c**3 - 3/2*c**5 = 0.
-1, 2/3, 1
Let y(b) be the second derivative of -2*b**4/33 - 9*b**3/11 + 7*b**2/11 - 2*b - 4. Factor y(k).
-2*(k + 7)*(4*k - 1)/11
Let f = -192 - -196. Let q(j) be the first derivative of 2*j - 1/3*j**2 - 10/27*j**3 - 1/18*j**f + 2. Solve q(i) = 0.
-3, 1
Let d(x) be the second derivative of x**7/280 + x**6/120 - x**5/20 + x**3/6 + x. Let y(