) = 0. Calculate s.
-3, 1
Let i(q) be the first derivative of -2*q**5/5 - q**4/2 + 2*q**3/3 + q**2 + 9. Factor i(b).
-2*b*(b - 1)*(b + 1)**2
Let k(s) be the first derivative of -2 + 3/20*s**5 + 0*s**2 + 1/30*s**6 - 2*s + 1/6*s**3 + 1/4*s**4. Let u(m) be the first derivative of k(m). Factor u(l).
l*(l + 1)**3
Let s(n) = -4*n**2 - n - 3. Let j(x) = 3*x**2 + 2. Let k(d) = -3*j(d) - 2*s(d). Let u(v) = -3*v**2 + 3*v. Let i(a) = -9*k(a) + 4*u(a). Factor i(b).
-3*b*(b + 2)
Let u(r) be the third derivative of -r**6/360 + 2*r**5/45 - 2*r**4/9 + 12*r**2. Factor u(x).
-x*(x - 4)**2/3
Let y(i) be the second derivative of i**4/36 + 7*i**3/9 + 49*i**2/6 - 3*i. Solve y(g) = 0.
-7
Suppose 6 = -l + 4*l. Let t(b) = b**2 - 6*b - 2. Let q be t(7). Factor a**q - 8*a**2 - 3*a**3 + l*a + 15*a**3 + a**5 - 8*a**4.
2*a*(a - 1)**4
Let y be (18/10 + 0)/((-6)/(-4)). Let 9/5*h**2 - 3*h**4 + y - 21/5*h**3 + 21/5*h = 0. Calculate h.
-1, -2/5, 1
Let x(i) be the third derivative of -i**8/1344 + i**7/840 + i**6/240 - 10*i**2. Factor x(o).
-o**3*(o - 2)*(o + 1)/4
Let u(a) be the third derivative of -121*a**5/360 + 11*a**4/12 - a**3 + 19*a**2. Determine x, given that u(x) = 0.
6/11
Suppose -5*z = -19 + 4. Find n, given that -1/2*n**5 + 0*n - 1/2*n**4 + 0*n**2 + 0*n**z + 0 = 0.
-1, 0
Suppose 5*f = 3*f. Let m = 14/15 - 8/15. Factor 0 - m*k**2 + f*k.
-2*k**2/5
Let a = -45/4 + 143/12. Factor -a*b**3 + 1/3*b**2 + 0 - 1/3*b**4 + 2/3*b.
-b*(b - 1)*(b + 1)*(b + 2)/3
Let z(q) be the third derivative of -5*q**8/112 + q**7/35 + q**6/8 - q**5/10 - 28*q**2. What is o in z(o) = 0?
-1, 0, 2/5, 1
Let b(w) be the second derivative of -w**6/40 - w**5/40 + w**4/16 + w**3/12 - 7*w. Solve b(f) = 0 for f.
-1, -2/3, 0, 1
Suppose c + 2*h + 4 = 0, -4*c - 5*h + 5 = -4*h. Let b = 13 - 51/4. Factor b*o + 1/2 - 1/4*o**c.
-(o - 2)*(o + 1)/4
Factor 3/2*y + 0 + 3/4*y**4 - 3/2*y**2 + 3/8*y**5 - 9/8*y**3.
3*y*(y - 1)**2*(y + 2)**2/8
Let n(q) be the second derivative of -2/15*q**6 - 4*q**2 + 2/3*q**3 + q**4 - 1/5*q**5 + 0 + 9*q. Factor n(h).
-4*(h - 1)**2*(h + 1)*(h + 2)
Suppose 2*f + 2*f - 16 = 0, -3*a - 2 = -2*f. Let g be 16/6 - (6 + -5). Solve -5/3*s**3 + 2/3 + 7/3*s**4 + g*s - 3*s**a = 0.
-1, -2/7, 1
Let w be (-798)/(-152)*(-2)/(-7). Solve 0 - t - 1/2*t**3 - w*t**2 = 0 for t.
-2, -1, 0
Find s, given that -7*s**2 - 290*s - 8*s**2 + 295*s - 5*s**4 + 15*s**3 = 0.
0, 1
Let f(u) be the third derivative of 3*u**2 - 1/120*u**6 + 1/8*u**4 + 0 + 1/3*u**3 + 0*u**5 + 0*u. Factor f(s).
-(s - 2)*(s + 1)**2
Let m(i) be the second derivative of -7*i**5/180 - i**4/8 - i**3/9 - 3*i**2/2 + i. Let l(a) be the first derivative of m(a). Factor l(w).
-(w + 1)*(7*w + 2)/3
Let r(j) be the third derivative of -j**5/60 + j**4/4 - 3*j**3/2 + 26*j**2. Factor r(a).
-(a - 3)**2
Suppose -5*j + 2*j = -45. Suppose o - 3*k + j = 0, o = -2*k + 1 + 9. Solve h - 2*h - h**3 + o*h**2 - h**2 + 2*h + 1 = 0.
-1, 1
Let z(v) = v**3 + 18*v**2 + 38*v + 24. Let b(f) = 12*f**3 + 234*f**2 + 495*f + 312. Let t(q) = 2*b(q) - 27*z(q). Factor t(m).
-3*(m + 2)**3
Determine v, given that 8*v**4 + 5*v**2 + 24*v - 33*v**2 + 8 - 6*v**2 - 6*v**3 = 0.
-2, -1/4, 1, 2
Let d be (21/9)/((-2)/(-6)). Suppose l - 3*m = 5*l + d, -23 = l + 5*m. Find r such that -r + r + l*r**4 = 0.
0
Solve -10/9*q**2 - 4/3*q + 4/9*q**3 + 2/9*q**4 + 0 = 0.
-3, -1, 0, 2
Factor -4*x + 15/2*x**2 - 3/2 - 2*x**3.
-(x - 3)*(x - 1)*(4*x + 1)/2
Let x(d) be the first derivative of -d**6/180 + d**5/180 + d**2/2 - 3. Let h(p) be the second derivative of x(p). Factor h(z).
-z**2*(2*z - 1)/3
Let r(a) be the first derivative of -1 - 1/2*a - 1/3*a**2 - 1/18*a**3. Solve r(u) = 0 for u.
-3, -1
Let v(q) be the third derivative of -q**6/90 - q**5/15 + 2*q**4/9 + 18*q**2. Find y, given that v(y) = 0.
-4, 0, 1
Let r(m) be the first derivative of 1/2*m**2 + 5 + 3/2*m - 1/6*m**3. Factor r(q).
-(q - 3)*(q + 1)/2
Let -d**5 + d + 7*d**3 - d**4 - d**4 - 7*d**3 + 2*d**2 = 0. What is d?
-1, 0, 1
Factor 19*k**4 + 28*k**2 + 61*k**4 - 5*k - 90*k**3 - 24*k**2 - 25*k**5 + 36*k**2.
-5*k*(k - 1)**3*(5*k - 1)
Let f(k) = 21*k**5 - 5*k**4 - 3*k**3 - 16*k**2 + 8*k - 5. Let h(i) = 5*i**5 - i**4 - i**3 - 4*i**2 + 2*i - 1. Let g(m) = 6*f(m) - 26*h(m). Factor g(a).
-4*(a - 1)**2*(a + 1)**3
Let z be 1 + 7/((-70)/6). Suppose -2*k + 0*k = 0. Factor -2/5*l**4 + z - 4/5*l + 4/5*l**3 + k*l**2.
-2*(l - 1)**3*(l + 1)/5
Let r(w) be the first derivative of w**7/700 - 11*w**6/1800 + w**5/150 + w**4/120 + 2*w**3/3 + 3. Let x(f) be the third derivative of r(f). Factor x(a).
(a - 1)**2*(6*a + 1)/5
Let f(z) be the first derivative of 2*z**3/27 + 2*z**2/9 - 15. Factor f(b).
2*b*(b + 2)/9
Suppose 0 = 5*n - 5*b + 10, 3*n + 10 = 2*n + 3*b. Let g = 5 - n. Factor g*a**2 - 4*a**3 - 2*a**2 + 3*a**3.
-a**2*(a - 1)
Factor -1/2 - 5/6*k + 1/6*k**3 - 1/6*k**2.
(k - 3)*(k + 1)**2/6
Let r(t) be the third derivative of -t**5/60 + t**4/3 - 8*t**3/3 - 2*t**2. Suppose r(y) = 0. What is y?
4
Factor 443 - 221 - 3*g**2 + 6*g - 222.
-3*g*(g - 2)
Let y(p) = -p**2 + 4. Let j be y(0). Let z(u) = -u**2 + 6*u - 5. Let k be z(j). Solve 12/7*x**k - 4/7 + 38/7*x**2 + 6/7*x - 16/7*x**4 = 0.
-1, -1/2, 1/4, 2
Let q(g) be the second derivative of g**4/60 - g**3/5 + 9*g**2/10 - 5*g - 2. Suppose q(x) = 0. What is x?
3
Suppose 2*z + 96 = 10*z. Suppose 2*c - 1 = 5. Factor 15*x - 99*x**2 - 2*x**4 - 46*x**4 + z*x + 120*x**c.
-3*x*(x - 1)*(4*x - 3)**2
Let z = 13 + -23. Let x be 4/z - (-4)/10. Suppose -2/3*s**2 + x + 2/3*s = 0. Calculate s.
0, 1
Let i(k) = 7*k**4 + k**3 - 7*k**2 + 7*k. Let x(n) = -15*n**4 - 3*n**3 + 15*n**2 - 15*n. Let f(m) = 9*i(m) + 4*x(m). Determine l, given that f(l) = 0.
-1, 0, 1
Factor -4/7*i**2 + 0 + 4/7*i**3 - 8/7*i.
4*i*(i - 2)*(i + 1)/7
Let c(l) be the second derivative of l**7/180 - l**6/270 - l**3/6 - 3*l. Let n(v) be the second derivative of c(v). Let n(d) = 0. Calculate d.
0, 2/7
Let c(a) be the first derivative of 1 + 0*a**2 + 3*a**2 + 11*a - 2*a - a**3. Determine b so that c(b) = 0.
-1, 3
Let n(l) = 6*l**4 - 3*l**3 - 2*l**2 + l - 1. Let k(a) = a**3 + a - 1. Let b(y) = k(y) - n(y). Factor b(z).
-2*z**2*(z - 1)*(3*z + 1)
Let d(z) = 3*z**2 - z. Let h(o) = -o + 11. Let r be h(12). Let s be d(r). Suppose 0*n + 20/7*n**2 + 30/7*n**s + 40/7*n**3 - 2/7 + 8/7*n**5 = 0. Calculate n.
-1, 1/4
Let f = 15 + -11. Suppose 4*s + 6 = -3*z, 3*s + 2*z = 4*z + f. Factor 2*l**2 + 2 + s + 4*l + 0.
2*(l + 1)**2
Let k be 3 + 1 - (3 + -1). Suppose y**k + y**5 - 7*y + 7*y - y**4 - y**3 = 0. Calculate y.
-1, 0, 1
Let v be 5/(3 + 2)*0. Let k(p) be the first derivative of 1/20*p**5 + 1/8*p**4 + 0*p**2 + 1 + v*p + 1/12*p**3. Suppose k(r) = 0. What is r?
-1, 0
Let q(w) = 2*w**4 - 10*w**3 + 15*w**2 + 5*w - 16. Let z(t) = 6*t**4 - 30*t**3 + 44*t**2 + 16*t - 48. Let g(a) = 8*q(a) - 3*z(a). Suppose g(d) = 0. Calculate d.
-1, 2
Let t(c) = -c**4 - c**3 + c**2 - c + 1. Let z(w) = 4*w**4 - 2*w**2 + 2 - 18*w - 6 - 4 + 24*w + 6*w**3. Let n(x) = -6*t(x) - z(x). Factor n(d).
2*(d - 1)**2*(d + 1)**2
Let c(y) be the first derivative of -y**6/60 + y**5/40 + y**4/24 - y**3/12 + 3*y - 1. Let t(v) be the first derivative of c(v). Factor t(z).
-z*(z - 1)**2*(z + 1)/2
Suppose -2/3*i**5 - 2/3*i + 4/3*i**3 + 4/3*i**2 - 2/3*i**4 - 2/3 = 0. What is i?
-1, 1
Let j(n) be the first derivative of 7*n**4/24 + 3*n**3/4 + n**2/2 + 2*n - 3. Let o(x) be the first derivative of j(x). Suppose o(f) = 0. What is f?
-1, -2/7
Suppose -22*l + 26*l - 24 = 0. Let t(o) be the first derivative of 1/9*o**l + 0*o**2 + 8/15*o**5 + 0*o + 3 + 4/9*o**3 + 5/6*o**4. Solve t(y) = 0.
-2, -1, 0
Factor -46 + 22*k**3 - 54 + 84 + 104*k - 92*k**2.
2*(k - 2)**2*(11*k - 2)
Let f(w) be the third derivative of w**5/150 + w**4/20 + 2*w**3/15 - 11*w**2. Factor f(i).
2*(i + 1)*(i + 2)/5
Let d = 23 - 21. Determine t so that -t + 2/3 + 1/3*t**d = 0.
1, 2
Suppose 8 - 20 = 3*w - 3*l, 4*w = -2*l + 14. Let j = w + 1. Let -2/9*v + 0*v**j + 0 + 2/9*v**3 = 0. What is v?
-1, 0, 1
Let w = -2 + 6. Factor 2*s + w*s**2 + 0*s - s**3 - 5*s**2.
-s*(s - 1)*(s + 2)
Let g(l) be the second derivative of l**7/105 - l**5/50 - 4*l. Let g(b) = 0. Calculate b.
-1, 0, 1
What is v in 0*v**2 + 12 - 8*v - 6*v**2 + 2*v**2 = 0?
-3, 1
Let x(o) be the second derivative of 7*o**5/360 - o**4/72 - 5*o**2/2 + 5*o. Let j(t) be the first derivative of x(t). Factor j(g).
g*(7*g - 2)/6
Let b(k) 