3 - 1. Let t(k) be the third derivative of a(k). Factor t(b).
-b**3
Let f(l) be the first derivative of -l**7/280 + l**6/60 + l**5/40 - l**4/4 - 3*l**3 - 6. Let p(n) be the third derivative of f(n). Find j such that p(j) = 0.
-1, 1, 2
Let k(m) be the third derivative of -m**11/1496880 + m**10/170100 - m**9/68040 + m**5/60 + 2*m**2. Let j(d) be the third derivative of k(d). Factor j(i).
-2*i**3*(i - 2)**2/9
Let y(k) be the third derivative of -k**8/1680 - k**7/525 + k**6/600 + k**5/150 + 7*k**2. Determine j, given that y(j) = 0.
-2, -1, 0, 1
Let a(r) be the first derivative of 0*r - 7 + 3/4*r**2 - 5/4*r**3. Factor a(v).
-3*v*(5*v - 2)/4
Let b(x) = -x**2 - 2*x + 3. Let w(j) = 1. Let s(h) = b(h) - 3*w(h). Factor s(t).
-t*(t + 2)
Let t(g) = -g**3 + 5*g**2 - g + 3. Let m be t(5). Let p = 0 - m. Factor -a**2 + a**3 - a - 2*a**p + 4*a**2 - a**4.
-a*(a - 1)**2*(a + 1)
Let g be (-5 + 3 - -3)*2. Suppose g*f + 16 = 6*f. Let -3/2*o**2 - 1/4*o**f + 5/4*o**3 + 2 - o = 0. What is o?
-1, 2
Let q = 6 + 0. Let a = -5 + 7. Factor -q*c**3 + 4*c**3 + c**4 + 0*c**3 + c**a.
c**2*(c - 1)**2
Let r(i) be the third derivative of i**6/30 + i**5/15 - 13*i**2. Factor r(q).
4*q**2*(q + 1)
Let z = -13 - -17. Suppose 2*y + 4 = z*y. Factor 2/7*b**y + 0*b + 0.
2*b**2/7
Let r = 9/11 + -23/55. Factor -26/5*x**2 - r*x**4 - 24/5*x - 8/5 - 12/5*x**3.
-2*(x + 1)**2*(x + 2)**2/5
Factor -2*m**2 + 2 + 1/2*m - 1/2*m**3.
-(m - 1)*(m + 1)*(m + 4)/2
Let i be -4 - (44/(-10) - 0). Determine o so that 0 + 0*o**2 + 0*o + 8/5*o**4 - 6/5*o**5 - i*o**3 = 0.
0, 1/3, 1
Factor -1/3 + 4/9*z**2 - 1/9*z**4 - 2/9*z + 2/9*z**3.
-(z - 3)*(z - 1)*(z + 1)**2/9
Determine p so that 0 - 1/3*p - 13/6*p**2 - 4*p**3 - 3/2*p**4 = 0.
-2, -1/3, 0
Let r(v) be the second derivative of v**9/90720 + v**8/40320 - v**4/6 + 3*v. Let d(g) be the third derivative of r(g). Factor d(b).
b**3*(b + 1)/6
Factor -8/19*h**2 - 2/19 - 10/19*h.
-2*(h + 1)*(4*h + 1)/19
Let d(w) be the second derivative of -2*w**6/45 + 2*w**5/5 - 13*w**4/9 + 8*w**3/3 - 8*w**2/3 + 9*w. Factor d(n).
-4*(n - 2)**2*(n - 1)**2/3
Let s(k) be the first derivative of -k**6/1980 + k**5/220 - k**3 - 3. Let y(z) be the third derivative of s(z). Suppose y(t) = 0. What is t?
0, 3
Let k(i) be the third derivative of 3*i**2 + 0 + 1/240*i**5 + 0*i**3 + 0*i - 1/32*i**4. Factor k(l).
l*(l - 3)/4
Let o(d) be the second derivative of -d**6/180 - d**5/90 + d**4/36 + d**3/9 + d**2 + 2*d. Let h(g) be the first derivative of o(g). Find x such that h(x) = 0.
-1, 1
Let r be 7/(126/(-4)) + (-78)/(-108). Let r*m**2 + 3/2*m + 1 = 0. What is m?
-2, -1
Let -4*h**2 - 16*h**2 - 4 + 26*h - 3*h**2 + h**2 = 0. What is h?
2/11, 1
Let g(q) = 3*q**4 + 7*q**3 + 4*q**2 - 4. Let v(d) = -5*d**4 - 13*d**3 - 7*d**2 + 7. Let r(s) = 7*g(s) + 4*v(s). Factor r(l).
l**3*(l - 3)
Let c(b) = b**3 - 9*b**2 - 9*b + 1. Let m(a) = 5*a**3 - 55*a**2 - 55*a + 5. Let g(p) = -25*c(p) + 4*m(p). Factor g(l).
-5*(l - 1)**2*(l + 1)
Let m(t) be the third derivative of -t**7/2940 + t**6/630 - t**5/420 - t**3/2 - 3*t**2. Let l(w) be the first derivative of m(w). Factor l(h).
-2*h*(h - 1)**2/7
Factor 1/4*h**2 - 1/8*h**3 + 7/8*h + 1/2.
-(h - 4)*(h + 1)**2/8
What is i in 8/3*i - 4*i**2 + 0 + 3/2*i**3 - 1/6*i**4 = 0?
0, 1, 4
Let d(v) = -v**3 - 9*v**2 - 7*v + 8. Let q(c) = c**2 + c - 8. Let z be q(0). Let f be d(z). Factor f + 2/5*p + 2/5*p**2.
2*p*(p + 1)/5
Let z(y) = -y**3 - 3*y**2 - 2*y - 3. Let f(c) = -6*c**3 - 16*c**2 - 10*c - 16. Let s(n) = 3*f(n) - 16*z(n). Factor s(x).
-2*x*(x - 1)*(x + 1)
Let x(y) be the first derivative of -2/3*y**5 + 0*y + 0*y**2 + 1/9*y**6 - 8/9*y**3 - 3 + 4/3*y**4. Suppose x(l) = 0. Calculate l.
0, 1, 2
Let n be 2 - (-2 + (-4)/(-2)). Let q be (n/4)/((-3)/(-12)). Factor 14/3*j**4 + 0 + 0*j - 10/3*j**3 - 4/3*j**q.
2*j**2*(j - 1)*(7*j + 2)/3
Let h(r) = 18*r**2 + 11*r + 5. Let y(b) be the first derivative of 9*b**3 + 17*b**2/2 + 8*b - 3. Let n(u) = 8*h(u) - 5*y(u). Let n(d) = 0. Calculate d.
-1/3, 0
Find i, given that 2/11*i**5 + 24/11*i + 0*i**4 - 14/11*i**3 + 16/11 - 4/11*i**2 = 0.
-2, -1, 2
Let z = 8240003/13280780 - 105/20276. Let c = -2/131 + z. Suppose c*m**2 - 3/5*m + 1/5 - 1/5*m**3 = 0. Calculate m.
1
Let x(o) be the first derivative of -4*o**3/3 - 6*o**2 - 8*o - 24. Determine m so that x(m) = 0.
-2, -1
Let s(j) be the third derivative of j**9/15120 - j**8/3360 + j**7/2520 + j**4/24 + 2*j**2. Let b(m) be the second derivative of s(m). Find i such that b(i) = 0.
0, 1
Let a(c) = -c - 2. Let w be a(-4). Let 0*j**w - 3*j - 3*j**2 - 2*j**2 + 2*j**2 = 0. What is j?
-1, 0
Let q be 1/((-5)/(-7)) - (-27)/(-45). What is g in 6/5 - 2/5*g**2 + q*g = 0?
-1, 3
Factor -v**3 + 15*v**2 - 31*v**4 + 9*v + 28*v**4 + 4*v**3.
-3*v*(v - 3)*(v + 1)**2
Let h = 10 - 6. Determine r so that 2 + 8*r - 2*r - 3*r**h + 4 - 3 - 6*r**3 = 0.
-1, 1
Suppose 67*m - 10 = 62*m. Factor 0 - 1/3*p - 1/6*p**3 + 1/2*p**m.
-p*(p - 2)*(p - 1)/6
Let b(o) be the first derivative of 2*o**5/5 - 17*o**4/2 + 70*o**3 - 275*o**2 + 500*o - 3. Factor b(x).
2*(x - 5)**3*(x - 2)
Let m = 150 - 148. Let t(d) be the first derivative of 2/3*d**3 + 1 + d**m + 0*d. Factor t(i).
2*i*(i + 1)
Solve 8*h**3 - 22*h**3 + 68*h**2 + 7 - 20*h**3 - 56*h + 9 + 6*h**4 = 0 for h.
2/3, 1, 2
Let h(w) be the first derivative of 5*w**4/24 - 5*w**3/18 - 25*w**2/12 - 5*w/2 + 3. Suppose h(n) = 0. What is n?
-1, 3
Let z(i) = 2*i**2 - 8*i + 11. Let v be z(3). Let x(m) be the third derivative of 0*m + 0*m**3 + 1/40*m**6 + m**2 + 1/10*m**v + 0*m**4 + 0. Factor x(k).
3*k**2*(k + 2)
Let t be 3*1*(-74)/(-444). Factor w**2 + t - 9/4*w.
(w - 2)*(4*w - 1)/4
Factor 100/3 + 40/3*z + 4/3*z**2.
4*(z + 5)**2/3
Let a be ((-8)/(-26))/(6 + 0 + -4). Suppose -a*i**4 + 0*i + 0 - 4/13*i**2 + 6/13*i**3 = 0. Calculate i.
0, 1, 2
Suppose n - 2*d = -35, 0 = 2*n - 5*n + 3*d - 111. Let u = -36 - n. Solve 0 - 3*t**u + 2*t**2 - 1/2*t**5 - 1/2*t + 2*t**4 = 0 for t.
0, 1
Let y be ((-2)/(-384))/(35/28). Let t(s) be the third derivative of 0*s**3 + 0*s**5 + 0*s**4 + y*s**6 + 3*s**2 + 0*s + 1/420*s**7 + 0. Factor t(r).
r**3*(r + 1)/2
Let k(y) be the first derivative of y**6/21 - 4*y**5/7 + 17*y**4/7 - 104*y**3/21 + 37*y**2/7 - 20*y/7 + 12. Factor k(n).
2*(n - 5)*(n - 2)*(n - 1)**3/7
Let c(r) be the second derivative of -7*r**6/45 + 71*r**5/120 - 4*r**4/9 + r**3/9 - 2*r + 2. Determine j, given that c(j) = 0.
0, 1/4, 2/7, 2
Let c(o) be the third derivative of -o**6/660 + 3*o**2. Factor c(w).
-2*w**3/11
Let z(w) be the third derivative of w**6/120 + w**5/60 - w**4/24 - w**3/6 - 7*w**2. Factor z(k).
(k - 1)*(k + 1)**2
Let x = 127/476 - 2/119. Factor x*o**2 - 1/4 + 0*o.
(o - 1)*(o + 1)/4
Let w(n) be the third derivative of -n**4/24 + n**3/2 + 3*n**2. Let q be w(0). Factor 0 - 2/9*l**2 + 2/9*l**q + 0*l.
2*l**2*(l - 1)/9
Let j(v) be the second derivative of -1/24*v**3 - 1/240*v**5 - 2*v + 1/48*v**4 + v**2 + 0. Let m(h) be the first derivative of j(h). Factor m(o).
-(o - 1)**2/4
Let y(x) be the third derivative of -x**7/105 + x**5/15 - x**3/3 - 8*x**2. Factor y(j).
-2*(j - 1)**2*(j + 1)**2
Suppose 24 = 4*g + 4*u, g + 0*g + 19 = 4*u. Let v(h) = h**3 - 3*h**2 + 12*h - 11. Let z(f) = f**2 - 1. Let p(y) = g*v(y) - 3*z(y). Factor p(x).
(x - 2)**3
Let o = -47 - -142/3. Let x = 46/3 + -44/3. Suppose o*l**3 - x*l**4 + 1/3*l**5 + 0*l**2 + 0 + 0*l = 0. Calculate l.
0, 1
Factor -2*g**2 + 112*g - 124*g - 2*g**2.
-4*g*(g + 3)
Let d(g) be the second derivative of 1/14*g**7 + 0*g**6 - 3/20*g**5 + 0*g**4 + g + 0 + 0*g**2 + 0*g**3. Find w, given that d(w) = 0.
-1, 0, 1
Let h**3 + 14*h**3 - 3*h**3 + 16*h**4 + 2*h**2 = 0. What is h?
-1/2, -1/4, 0
Let z(y) be the third derivative of 1/80*y**5 + 0*y**4 - 5*y**2 + 0 + 0*y - 1/8*y**3. Solve z(f) = 0 for f.
-1, 1
Suppose 0 + 1/11*o**4 - 6/11*o**2 + 5/11*o**3 + 0*o = 0. Calculate o.
-6, 0, 1
Let l(v) be the first derivative of -v**7/2100 - v**6/450 - v**5/300 - 2*v**3/3 - 2. Let g(t) be the third derivative of l(t). Factor g(x).
-2*x*(x + 1)**2/5
Let s(m) be the first derivative of m**5 + 5*m**4/2 + 5*m**3/3 - 22. Factor s(q).
5*q**2*(q + 1)**2
Let n(h) be the third derivative of -h**8/3360 - h**4/8 - 3*h**2. Let x(c) be the second derivative of n(c). Suppose x(q) = 0. Calculate q.
0
Let u(n) = n**3 + 5*n**2 - 5*n - 5. Let g be u(-6). Let x = g - -12. Let 23/2*q**3 + 51/4*q**2 + x + 15/4*q