). Factor n(x).
-5*(x - 7)*(x - 1)
Suppose -11*d = 1 - 1. Let p(y) be the second derivative of 0*y**4 + 0*y**2 + 0 - 3*y + d*y**3 - 1/25*y**5. Factor p(z).
-4*z**3/5
Let a be (-24)/(-10)*115/483. Factor 2/7*j**2 - 2/7*j - a.
2*(j - 2)*(j + 1)/7
Let j(b) be the second derivative of -3*b**5/40 + 2*b**4 + 35*b**3/4 + 27*b**2/2 + 4*b + 40. Solve j(c) = 0 for c.
-1, 18
Let t be 1/(20/30 - (-1)/(-3)). Let v = 708/5 + -141. Let -3/5*h - 6/5*h**2 + 6/5*h**4 + v*h**5 + 0*h**t + 0 = 0. What is h?
-1, 0, 1
Let p(c) be the third derivative of -c**6/280 + 3*c**5/70 - 9*c**4/56 + 2*c**3/7 + 3*c**2 + 5. Factor p(i).
-3*(i - 4)*(i - 1)**2/7
Let t(j) be the second derivative of -j**7/6300 - j**6/900 - j**5/300 - 3*j**4/4 - 10*j. Let b(m) be the third derivative of t(m). Let b(q) = 0. Calculate q.
-1
Factor 56 + 48*n**4 + 4*n**5 - 84*n + 205*n**2 - 96 + 80*n**3 - 213*n**2.
4*(n - 1)*(n + 1)**3*(n + 10)
Let q = -38 + 47. Let -6*a**2 + q*a**3 - 2*a**3 - 4*a**3 = 0. What is a?
0, 2
Let i(x) = 117*x**3 - 57*x**2 - 67*x + 2. Let z(o) = -234*o**3 + 114*o**2 + 135*o - 6. Let p(u) = -9*i(u) - 5*z(u). Factor p(j).
3*(j - 1)*(3*j + 2)*(13*j - 2)
Let w be (16/4)/((-5)/(-2)). Let c(m) = m**2 - 58*m - 116. Let i be c(-2). Factor 4/5*r + 0*r**2 - w*r**3 + 0*r**i + 0 + 4/5*r**5.
4*r*(r - 1)**2*(r + 1)**2/5
Let f(q) be the third derivative of 4*q**5/5 + 49*q**4/8 + 3*q**3/2 + 329*q**2. What is d in f(d) = 0?
-3, -1/16
Let w be (-1 + 2)*(2 - 1)*3. Suppose 2*q + 2*d + 4 = 0, -5 = -q - 4*d - 22. Factor -13*c**2 - 5*c**4 - 4*c + w*c**q + 14*c**4 + 5*c**2.
c*(c - 1)*(3*c + 2)**2
Let z(w) = -4*w**4 + 8 - 2*w + 3*w**4 + 16*w**2 - 4 - 6 + w**3. Let n(u) = -15*u**2 + 3*u + 3. Let m(q) = 2*n(q) + 3*z(q). Suppose m(j) = 0. Calculate j.
-2, 0, 3
Let w = 9348/5 + -1869. Factor -w*q**3 + 0 - 1/5*q**5 + 0*q - 3/5*q**4 - 1/5*q**2.
-q**2*(q + 1)**3/5
Let n(l) be the second derivative of 4*l**7/21 - 17*l**6/9 + 33*l**5/5 - 17*l**4/2 - 4*l**3/9 + 4*l**2 - 4*l + 2. Let n(t) = 0. What is t?
-1/4, 1/3, 2, 3
Let z(c) be the second derivative of c**6/72 - c**5/3 - 15*c**4/8 - 16*c**3/3 - 14*c. Let s(d) be the second derivative of z(d). Suppose s(a) = 0. What is a?
-1, 9
Let l(t) be the first derivative of -t**4/12 + 20*t**3/9 + t**2/6 - 20*t/3 + 45. Suppose l(i) = 0. What is i?
-1, 1, 20
Let p(s) = 4231*s**3 - 6380*s**2 + 1916*s - 156. Let i(r) = -12694*r**3 + 19140*r**2 - 5744*r + 469. Let j(b) = 4*i(b) + 11*p(b). Solve j(z) = 0 for z.
2/11, 8/7
Let v(l) be the first derivative of 4*l**3/3 - 4*l + 78. Suppose v(i) = 0. Calculate i.
-1, 1
Let w(v) be the third derivative of -v**5/90 - v**4/3 + 28*v**3/9 - 8*v**2 - 3. What is q in w(q) = 0?
-14, 2
Let -333/2*z + 273/2 - 3/2*z**3 + 63/2*z**2 = 0. Calculate z.
1, 7, 13
Let m(t) = -t**2 + 4. Let n(b) = b - 11. Let r be n(11). Let a be m(r). Factor -10*s**2 + 10*s**2 + s**a + s**4.
2*s**4
Let n = -22821 - -22821. Factor -55/3*l**4 + 0 - 10/3*l**3 - 25/3*l**5 + 0*l + n*l**2.
-5*l**3*(l + 2)*(5*l + 1)/3
Let g(o) be the third derivative of o**11/166320 + o**10/302400 - 13*o**5/60 - 13*o**2. Let p(d) be the third derivative of g(d). Factor p(h).
h**4*(4*h + 1)/2
Factor 7 + 4*g - g + g**4 + 2*g - 3*g**3 - 5*g**2 - 3 - 2*g.
(g - 4)*(g - 1)*(g + 1)**2
Suppose -5*n + 173 = 3*f, -2*f + 122 = -0*f + 2*n. Suppose -f*c + 64*c = 0. Let c - 2*u - 1/2*u**3 - 2*u**2 = 0. Calculate u.
-2, 0
Suppose -5*z**3 - 4*z**2 + 5*z**2 - 5*z**2 - 6*z**2 = 0. What is z?
-2, 0
Let y = -531 + 531. Let j(p) be the third derivative of -4*p**2 + 0*p**6 - 1/105*p**7 + 0*p**3 + 0*p**4 + 0*p + 0*p**5 + y. Factor j(i).
-2*i**4
Determine g so that -3*g**5 + 14 + 10*g**3 - 2343*g + 16*g**2 - 6*g**4 + 2*g**5 + 2310*g = 0.
-7, -2, 1
Let x = -784 + 786. Let f(z) be the first derivative of 8/3*z**x - 6 - 2*z - 2/45*z**5 + 4/9*z**4 - 44/27*z**3. Determine r so that f(r) = 0.
1, 3
Let p(z) be the second derivative of 0*z**4 + 22*z - 1/10*z**6 + 0*z**2 + 0*z**5 + 0 + 0*z**3 + 1/14*z**7. Factor p(h).
3*h**4*(h - 1)
Let v be 6/5*(-35)/(-63). Solve -2/9*f**4 + 0*f + 0 + 2/9*f**2 - v*f**3 + 2/3*f**5 = 0 for f.
-1, 0, 1/3, 1
Let g be 42/(((-36)/8)/(-3)). Solve 2*r**4 + 26*r**3 - g*r**3 + 0*r**2 + 2*r - 2*r**2 = 0 for r.
-1, 0, 1
Factor 54*y**4 - 56*y**4 - 14*y**3 - 2*y**5 - 2*y - 2 + 4*y**2 + 18*y**3.
-2*(y - 1)**2*(y + 1)**3
Suppose 34*a - 36 - 66 = 0. Let c(b) be the third derivative of 0*b**5 - 1/2*b**4 + 0*b**a + 0*b + 0 + 3/40*b**6 + 2*b**2 - 1/70*b**7. Factor c(q).
-3*q*(q - 2)**2*(q + 1)
Let i be ((-1 + -4)/(4 - -1))/(-4). Factor -i*l**3 + 0 - 1/4*l**4 + 1/4*l**2 + 1/4*l.
-l*(l - 1)*(l + 1)**2/4
Let g(y) be the second derivative of y**7/42 - y**6/15 - y**5/10 + y**4/3 + y**3/6 - y**2 + 4*y. Let g(s) = 0. What is s?
-1, 1, 2
Let r(s) be the second derivative of -s**5/110 + 7*s**4/11 - 160*s**3/11 + 800*s**2/11 - 443*s. Factor r(f).
-2*(f - 20)**2*(f - 2)/11
Let w(r) be the second derivative of -1/90*r**5 - 47*r + 0*r**2 + 0 + 1/9*r**3 + 1/27*r**4. Let w(s) = 0. Calculate s.
-1, 0, 3
Let b = 4024 + -60358/15. Factor 2/15 + b*u**3 - 2/15*u**2 - 2/15*u.
2*(u - 1)**2*(u + 1)/15
Let o(r) be the second derivative of r**6/120 + r**5/40 + 13*r**3/3 + 35*r. Let w(x) be the second derivative of o(x). What is u in w(u) = 0?
-1, 0
Solve -1/4*g**4 + 3/8*g - 1/2*g**3 + 1/4*g**2 + 0 + 1/8*g**5 = 0.
-1, 0, 1, 3
Factor -5/2 + 2*o - 1/2*o**4 + 3*o**2 - 2*o**3.
-(o - 1)**2*(o + 1)*(o + 5)/2
Let t(r) be the second derivative of -5*r**7/42 + 61*r**6/90 - 37*r**5/60 - 49*r**4/36 + 26*r**3/9 - 2*r**2 - 178*r. Determine p so that t(p) = 0.
-1, 2/5, 2/3, 1, 3
Let n(y) be the third derivative of y**5/180 + 31*y**4/24 + 46*y**3/9 + 245*y**2. Suppose n(c) = 0. What is c?
-92, -1
Let k(o) be the second derivative of -o**5/50 - 124*o**4/5 - 61504*o**3/5 - 15252992*o**2/5 - 2*o + 851. Factor k(r).
-2*(r + 248)**3/5
Determine x so that -3/2 - 1/4*x**3 + 0*x**2 + 7/4*x = 0.
-3, 1, 2
Let n(k) be the third derivative of -k**6/160 + k**5/16 - k**4/8 + 59*k**2 + k. Factor n(o).
-3*o*(o - 4)*(o - 1)/4
Factor 16/19 + 2/19*x**3 - 12/19*x - 6/19*x**2.
2*(x - 4)*(x - 1)*(x + 2)/19
Let u(f) be the second derivative of -24*f - 1/20*f**5 + 0 + 1/18*f**3 - 1/18*f**4 + 0*f**2. Determine j, given that u(j) = 0.
-1, 0, 1/3
Let d = 85/444 + -4/37. Let j(x) be the second derivative of 2*x + 0 - x**2 + d*x**4 + 1/6*x**3. Factor j(w).
(w - 1)*(w + 2)
Let g = -3921 + 27455/7. Find r, given that -g - 2/7*r**2 + 10/7*r = 0.
1, 4
Let k = 276047/105 - 2629. Let o(i) be the second derivative of 2*i + 1/20*i**5 + 0*i**2 + 0*i**3 + k*i**6 + 0 - 1/42*i**4. Factor o(a).
a**2*(a + 2)*(4*a - 1)/7
Let f = -3/574 + 15513/2870. Factor 1/5*s**3 + 27/5*s + 9/5*s**2 + f.
(s + 3)**3/5
Let l(u) be the first derivative of -5*u**4/8 + 20*u**3/3 - 75*u**2/4 + 270. Find o such that l(o) = 0.
0, 3, 5
Suppose 24 = q + 4*j, -3*q = -j + 5*j - 48. Suppose -183 + 23 = -10*d. Suppose q*t + d*t**2 - 10*t**3 + 0*t**3 + 14*t**3 = 0. Calculate t.
-3, -1, 0
Suppose 5*a - 3*r = 9, 3*a - 16*r + 7 = -8*r. Determine o, given that 0*o**2 - 4/7 + 2/7*o**a - 6/7*o = 0.
-1, 2
Let y(b) be the first derivative of -b**5/110 + b**4/22 - b**3/11 + b**2/11 + 18*b + 13. Let a(i) be the first derivative of y(i). Factor a(u).
-2*(u - 1)**3/11
Let f(y) be the second derivative of y**6/180 - y**5/15 + y**4/4 - y**3/2 - 31*y. Let b(x) be the second derivative of f(x). Let b(z) = 0. What is z?
1, 3
Let j be 6/(-162)*(-10 - (4 + 1)). Factor 1/9*o**2 - j*o + 4/9.
(o - 4)*(o - 1)/9
Let j be (176/308)/((-16)/(-42)). Find a, given that 0 + j*a + 1/2*a**2 = 0.
-3, 0
Factor -106*l**4 - 10*l**3 - 9*l + 21*l + 111*l**4 - 25*l**2 + 18*l.
5*l*(l - 3)*(l - 1)*(l + 2)
Let s(z) be the second derivative of z**5/20 + z**4/6 + z**3/6 - z - 138. Solve s(q) = 0 for q.
-1, 0
Let f(w) = -w + 5. Let t be f(0). Suppose -t*m = m - 12. Factor 2/3*b**4 + 4/3 + 2/3*b**3 - m*b**2 - 2/3*b.
2*(b - 1)**2*(b + 1)*(b + 2)/3
Let a = 310 - 310. Let g(b) be the third derivative of a*b + 1/27*b**4 - 9*b**2 - 1/270*b**5 + 0*b**3 + 0. Factor g(r).
-2*r*(r - 4)/9
Suppose -t + 19 = 3*g, 2*t - 3*g = -3*t + 5. Let n(u) be the first derivative of 3/10*u**5 + 3*u**3 + 3/2*u - 2 - 3/2*u**t - 3*u**2. Factor n(b).
3*(b - 1)**4/2
Let u = -39 + 43. Let m be u - (0 + 1 + 0). Factor 3*j**4 - 4*j**4 + 2*j**2 + j**5 - 30*j + 2*j**m - 4*j**3 - 1 + 31*j.
(j -