11. Let b be d(8). Determine f so that -4*f - 7*f - 4*f**2 + 2*f - b*f - 8 = 0.
-2, -1
Let s(p) be the second derivative of -49*p**4/30 - 28*p**3/15 - 4*p**2/5 - 4*p. Factor s(j).
-2*(7*j + 2)**2/5
Let z(m) be the third derivative of 0 + 0*m - 1/20*m**6 + 0*m**4 + 0*m**3 + 1/105*m**7 + 0*m**5 + 7*m**2. Factor z(f).
2*f**3*(f - 3)
Suppose 2*c + 24 = 3*s, 5*c + 1 = -2*s - 2. Suppose -3*k + s + 0 = 0. Factor -1/3*l**k + 0 - 2/3*l**3 + 0*l.
-l**2*(2*l + 1)/3
Let k(j) = 2*j**3 + 2*j**2 - 1. Let p be k(1). Factor -1/2*r**p + 0*r + 0 + 1/2*r**2.
-r**2*(r - 1)/2
Let l(r) be the third derivative of -r**5/300 - r**4/30 - 2*r**3/15 + 6*r**2. Factor l(w).
-(w + 2)**2/5
Factor -12*u**2 - 15*u**4 + 8*u - 3*u**4 - 48*u**3 - 10*u**4.
-4*u*(u + 1)**2*(7*u - 2)
Let o(n) be the second derivative of n + 0*n**2 + 0*n**3 + 0*n**4 + 1/15*n**6 + 0 + 1/21*n**7 + 0*n**5. Factor o(z).
2*z**4*(z + 1)
Let v(y) = -12*y**2 + 14*y + 10. Let p(a) = a**2 + a - 1. Let g(c) = 2*p(c) + v(c). Factor g(m).
-2*(m - 2)*(5*m + 2)
Let n(s) be the third derivative of -s**7/2520 + s**6/720 - 5*s**4/24 + 3*s**2. Let p(o) be the second derivative of n(o). Factor p(f).
-f*(f - 1)
Let g = -631/3 + 211. Let f(c) be the second derivative of g*c**3 + c + 1/12*c**4 + 2*c**2 + 0. Solve f(s) = 0.
-2
Let r(j) = 38*j + 195. Let s be r(-5). What is y in 0 + 6/5*y**3 + 12/5*y**2 - 3/5*y - 36/5*y**4 - 27/5*y**s = 0?
-1, 0, 1/3
Suppose -3*y - 3*d + 3 = 0, 4*y + 3*d - 7 = 2*d. Let m be -3 + (y - 0) - -1. Factor -6*s**2 + m*s - 2*s + 0*s.
-2*s*(3*s + 1)
Let k(n) be the second derivative of 10*n**7/189 - 7*n**6/270 - 13*n**5/90 + 7*n**4/108 + n**3/9 + 21*n. Determine o so that k(o) = 0.
-1, -2/5, 0, 3/4, 1
Factor 2*w + 8/5*w**2 + 4/5 + 2/5*w**3.
2*(w + 1)**2*(w + 2)/5
Let n(u) be the first derivative of 5*u**3/9 - 5*u**2/6 - 10*u/3 - 16. Factor n(k).
5*(k - 2)*(k + 1)/3
Let d(x) be the third derivative of 0*x**4 + 1/120*x**5 - 5*x**2 + 0*x + 0*x**3 + 0. Determine r, given that d(r) = 0.
0
Factor 44*l - l**3 + 4*l**3 - 44*l.
3*l**3
Suppose -103*p**2 + 2 + 45*p + 3*p**3 + 25 + 124*p**2 = 0. What is p?
-3, -1
Let k be 0*(-2)/6*-1. Suppose 0*r + 4*r = k. Find p such that r + 1/4*p + 1/4*p**2 = 0.
-1, 0
Let w(l) = l**3 - l**2 - 5*l + 3. Let d be w(3). Find y such that 3 - 1 + d*y**2 + 2*y**2 - 8*y = 0.
1/2
Factor 3*o**2 - 4 - 6*o + 2*o**3 - o**4 - 4*o + 6*o.
-(o - 2)**2*(o + 1)**2
Let i(s) = -s**4 - s**3 - s + 1. Let o(c) = 15*c**3 + 15*c**2 - 15*c - 25. Let a(z) = -5*i(z) - o(z). Let a(l) = 0. Calculate l.
-1, 2
Let f(i) be the first derivative of -i**6/2 + 9*i**5/5 - 9*i**4/4 + i**3 - 14. Factor f(z).
-3*z**2*(z - 1)**3
Let w(c) = c + 7. Let r be w(-6). Let b be -5*1/(-3) - r. Factor b*y - 2/3*y**3 + 0 + 0*y**2.
-2*y*(y - 1)*(y + 1)/3
Suppose 2 = c + m, 0 = -6*c + 3*c - 5*m. Factor -15 - 5*a**4 + a**c + 15 - 4*a**2 + 8*a**3.
a**2*(a - 2)**2*(a - 1)
Suppose 18 = -3*y + d - 4, -d + 16 = -2*y. Let t be ((-32)/12)/(4/y). Let q**3 + 0*q**2 + 0*q**3 + 0*q**2 + 3*q**2 - t = 0. Calculate q.
-2, 1
Let d(f) be the second derivative of -f**6/2520 + f**5/420 - f**3/3 + 6*f. Let x(r) be the second derivative of d(r). Suppose x(p) = 0. What is p?
0, 2
Let v(q) = 4*q + q**2 - 8 + 2 + q**2. Let a(i) = -3*i - 1. Let k(u) = u. Let o(n) = -a(n) - 4*k(n). Let t(w) = 4*o(w) + v(w). Determine r so that t(r) = 0.
-1, 1
Factor 3/2*h + 1/4*h**2 - 7/4.
(h - 1)*(h + 7)/4
Let v(t) be the third derivative of -t**5/25 + 3*t**4/10 - 9*t**3/10 - 5*t**2. Let v(j) = 0. Calculate j.
3/2
Let s be (42/56)/((-1)/132). Let x be 2/3 + (-24)/s. Suppose 4/11 + 8/11*h**2 + x*h + 2/11*h**3 = 0. What is h?
-2, -1
Let k be (-2 + 2)/(1 - 0). Let -x**2 + k*x**4 + 0*x**4 + 2*x**2 - x**4 = 0. Calculate x.
-1, 0, 1
Let z(y) = y**4 + y + 1. Let g(h) = 4*h**5 + 22*h**4 + 31*h**3 + 19*h**2 + 4*h + 1. Let a(n) = 4*g(n) - 12*z(n). Determine k, given that a(k) = 0.
-2, -1, 1/4
Let y(s) be the second derivative of s**5/40 + 7*s**4/12 + 49*s**3/12 - 25*s. What is k in y(k) = 0?
-7, 0
Let z be (-1 - (-12)/3)*(-5)/(-3). Let f(g) be the first derivative of 0*g + 0*g**2 + 7/4*g**4 + 2/3*g**3 + g**z + 2. Factor f(p).
p**2*(p + 1)*(5*p + 2)
Let j(k) be the second derivative of 1/40*k**6 + 0*k**2 + 0 - 4*k + 0*k**3 + 0*k**4 - 3/80*k**5. Find a, given that j(a) = 0.
0, 1
Let n(p) = p**2. Let x(m) = -28*m**2 + 12*m - 8. Let q(o) = -24*n(o) - x(o). Factor q(a).
4*(a - 2)*(a - 1)
Suppose -21 = -4*j - 9. Suppose -5*m = -7 - j. Let -1/2 + 1/4*i**m - 1/4*i = 0. What is i?
-1, 2
Let s = -57 - -57. Let f(g) be the second derivative of -1/6*g**4 - g**3 + s + 2*g - 2*g**2. Solve f(b) = 0 for b.
-2, -1
Let b(m) = 13*m**3 - 13*m**2 - 8*m + 8. Let u(s) = 6*s**3 - 6*s**2 - 4*s + 4. Let l(y) = 2*b(y) - 5*u(y). Factor l(t).
-4*(t - 1)**2*(t + 1)
Let x(y) be the third derivative of -y**5/140 + 5*y**4/7 - 200*y**3/7 + 14*y**2 - 4. Factor x(d).
-3*(d - 20)**2/7
Let t(s) = -2*s + 23. Let k be t(10). Suppose 4 = -k*o + 10. Determine g, given that -o - 5*g + 5/2*g**2 + 45/4*g**3 - 27/4*g**5 + 0*g**4 = 0.
-2/3, 1
Let s(j) be the third derivative of j**6/480 - j**5/240 - j**4/96 + j**3/24 - 2*j**2. Determine m so that s(m) = 0.
-1, 1
Factor 0 - 2/5*o**3 + 0*o - 32/5*o**2.
-2*o**2*(o + 16)/5
Suppose 13*y = 8*y. Suppose -t = 3*z - 4 - 1, y = -t + 5*z - 3. What is j in 7/4*j**4 - 1/2*j + 3/4*j**5 + 3/4*j**3 + 0 - 3/4*j**t = 0?
-1, 0, 2/3
Let n = -116/77 - -22/7. Factor -n + 12/11*m - 2/11*m**2.
-2*(m - 3)**2/11
Let y(r) = 38*r - 187. Let i be y(5). Factor 0*g + 2/11*g**5 - 2/11*g**2 + 0 + 2/11*g**4 - 2/11*g**i.
2*g**2*(g - 1)*(g + 1)**2/11
Suppose -5*g = 2*d - 4, d + 0*d + g - 2 = 0. Suppose 5*c - 9 = d*c. Determine w, given that -6/7*w**5 + 8/7*w**4 - 2/7*w - 12/7*w**2 + 4/7 + 8/7*w**c = 0.
-1, -2/3, 1
Suppose -24*y = -21*y - 6. Suppose 0 = -5*h + 5*f, 0 = -y*h + 5*f - 4*f + 2. Factor 0*o + 2/3*o**h + 2/3*o**3 + 0.
2*o**2*(o + 1)/3
Let n(y) be the third derivative of -y**8/1680 - y**7/280 - y**6/180 - y**3 + 4*y**2. Let i(m) be the first derivative of n(m). Factor i(v).
-v**2*(v + 1)*(v + 2)
Let g(k) = k**3 - 4*k**2 - 6*k + 7. Let q be g(5). Suppose v = q*v - 3. Factor -t + t + t**4 + 3*t**v + 0*t**4 - 4*t.
t*(t - 1)*(t + 2)**2
Let n(x) be the third derivative of -x**7/10 + 19*x**6/40 - 2*x**5/5 - x**4/2 + 2*x**2. Solve n(z) = 0 for z.
-2/7, 0, 1, 2
Let g be (0 + -5)*51/(-85). Let u be 0/(-4*g/(-12)). Suppose u - 1/3*a**2 + 1/3*a - 1/3*a**3 + 1/3*a**4 = 0. What is a?
-1, 0, 1
Let k = 49 + -145/3. Determine j so that 8*j**3 + 0 + 4*j**4 + 16/3*j**2 + k*j**5 + 0*j = 0.
-2, 0
Suppose -25 = -5*o + 5*x, 0 = -3*o - 4*x - 0*x - 20. Let u(j) be the first derivative of 1 + 2/3*j**3 + 0*j - 1/2*j**4 + o*j**2. Factor u(t).
-2*t**2*(t - 1)
Let i(a) be the second derivative of -a**5/80 + 5*a**4/48 - a**3/3 + a**2/2 - 23*a. What is s in i(s) = 0?
1, 2
Suppose 4 = o, -5*h + o + 16 = 5*o. Let z(s) be the second derivative of -1/80*s**5 + h*s**2 + 0*s**3 + 0*s**4 + 1/120*s**6 - s + 0. Factor z(y).
y**3*(y - 1)/4
Factor -16*s**2 - 2*s**2 - 142*s**4 - 2*s**5 - 30*s**3 + 128*s**4.
-2*s**2*(s + 1)*(s + 3)**2
Let n(g) = -31 + 11 + 9 - 3 - 2*g. Let s be n(-8). Solve -2/3*y - 4/9 - 2/9*y**s = 0.
-2, -1
Let 2/9*q**4 - 10/9*q**3 + 2/9*q**5 + 0 + 2/3*q**2 + 0*q = 0. What is q?
-3, 0, 1
Let k be 20/(-50)*(-5 - 0). Factor 12*g**k - 2*g**3 + 4*g**2 - 4*g**2 + 16 - 24*g.
-2*(g - 2)**3
Let y(z) be the third derivative of z**8/12 - 38*z**7/105 + z**6/30 + 23*z**5/15 - 4*z**4/3 - 8*z**3/3 + 33*z**2. Suppose y(w) = 0. Calculate w.
-1, -2/7, 1, 2
Suppose 1 = t - a - 0*a, -5 = 5*t + 5*a. Let j(i) be the first derivative of 1 - 2/5*i**5 + 1/3*i**6 + 2/3*i**3 - 1/2*i**4 + 0*i + t*i**2. Factor j(u).
2*u**2*(u - 1)**2*(u + 1)
Factor 0 - 1/3*y**3 + 4/9*y + 0*y**2 + 1/9*y**4.
y*(y - 2)**2*(y + 1)/9
Let x(b) = b**3 - b**2 + 3*b - 7. Let u(w) = 3*w - 6. Suppose -20 = 7*p - 2*p. Let k(m) = p*u(m) + 3*x(m). Solve k(n) = 0.
-1, 1
Let a be 2/(-3)*3/(-1). Let k(j) be the first derivative of 2/3*j**3 + 0*j - j**2 - a. Factor k(s).
2*s*(s - 1)
Let m be 6/9 - (-1)/(9/(-6)). Factor 0*t + 2*t**3 + m + 2*t**4 + 2/3*t**2 + 2/3*t**5.
2*t**2*(t + 1)**3/3
Let z = 130/203 - 2/29. Let 0 - 8/7*i**4 - 18/7*i**2 + z*i + 24/7*i**3 = 0. Calculate i.
0, 1/2, 2
Find m such that 4*m**3 - 17*m**4 + 31*m**4 - 13*m**4 + 4*m**2 = 0.
-2, 0
Let z(m) be the first derivat