 15. Let b be d/(-2)*-14 + -3. Determine c so that 2*c**5 + 0 + 0*c - 4/3*c**3 - 2/3*c**b + 0*c**2 = 0.
-2/3, 0, 1
Let d be (-1 + (-17)/(-2))*(-26)/(-260). Let c(r) be the first derivative of 2 + d*r**4 + 1/2*r**2 + 4/3*r**3 + 0*r. Factor c(i).
i*(i + 1)*(3*i + 1)
Let j(d) = d - 13. Let h be j(17). Let s(z) be the second derivative of 0*z**5 + 0*z**2 - 1/105*z**7 + 0 + 1/75*z**6 + 0*z**3 + 0*z**h + z. Factor s(a).
-2*a**4*(a - 1)/5
Let a(g) be the third derivative of -g**5/15 + 4*g**4/3 - 32*g**3/3 + 9*g**2. Solve a(l) = 0.
4
Suppose 49*z = 78*z. Factor 4/3*u + 8/3*u**3 + 2/3*u**4 + z + 10/3*u**2.
2*u*(u + 1)**2*(u + 2)/3
Let j be 50/6 - 4/(-6). Let l = j - 6. Determine g so that 8*g**4 + 4 - 22*g + 7*g**l + 42*g**2 - 41*g**3 + 2*g**4 = 0.
2/5, 1
Let d = 8 + -8. Let w(h) be the first derivative of d*h**3 + 1/10*h**4 + 0*h**2 + 0*h + 3. Factor w(o).
2*o**3/5
Let q(f) be the first derivative of -f**3/3 + f + 29. Factor q(j).
-(j - 1)*(j + 1)
Let z(o) be the first derivative of 2*o**3/21 + 2*o**2 + 14*o + 6. Factor z(m).
2*(m + 7)**2/7
Suppose -9*q + 4*q = 0. Let t(w) be the third derivative of -1/240*w**5 + q*w + 0*w**6 + 0 + 0*w**4 - w**2 + 1/840*w**7 + 0*w**3. Suppose t(g) = 0. What is g?
-1, 0, 1
Determine m, given that 1/2*m**2 - 1/2 + 1/2*m**3 - 1/2*m = 0.
-1, 1
Suppose 5*b = -3*d + 16, 4*b + d = 11 - 1. Let n be (-1 - -1)/(b - -1). Factor 0 - 1/2*g**2 - 25/2*g**4 + 5*g**3 + n*g.
-g**2*(5*g - 1)**2/2
Let f(x) be the third derivative of -x**6/120 + x**5/10 - 5*x**4/24 + 2*x**2. Suppose f(s) = 0. What is s?
0, 1, 5
Let a(w) be the second derivative of -1/24*w**3 + 1/16*w**4 + 0 + 0*w**2 + 2*w. What is g in a(g) = 0?
0, 1/3
Let m = -28 + 199/7. Factor 3/7*g - 3/7*g**3 - 3/7 + m*g**2.
-3*(g - 1)**2*(g + 1)/7
Let q(t) be the first derivative of -6*t**3 + 2*t - 8/5*t**5 + t**2 + 2 + 11/2*t**4. Factor q(b).
-2*(b - 1)**3*(4*b + 1)
Let c be (-1 + 1/(-3))*-3. Factor -31 + 31 - 4*j**3 + c*j.
-4*j*(j - 1)*(j + 1)
Let d(i) be the first derivative of -i**7/105 + i**6/120 + i**5/30 - i**4/24 - 3*i**2/2 - 2. Let o(z) be the second derivative of d(z). Factor o(k).
-k*(k - 1)*(k + 1)*(2*k - 1)
Let h = 13 - 7. Suppose h*t = t. Factor 4/3*p**2 + 0 + 8/3*p**4 + t*p + 2/3*p**5 + 10/3*p**3.
2*p**2*(p + 1)**2*(p + 2)/3
Let k(x) be the first derivative of 3*x**4/20 - 9*x**2/10 - 6*x/5 - 2. Factor k(p).
3*(p - 2)*(p + 1)**2/5
Let d(a) be the third derivative of -a**8/1176 + a**7/245 - a**6/210 - a**5/105 + a**4/28 - a**3/21 + 3*a**2. Factor d(i).
-2*(i - 1)**4*(i + 1)/7
Let d be (1 - 0)*-1 - 2. Let g(c) = -c**3 - 4*c**2 - 2*c + 3. Let n be g(d). Solve 3*h**2 - h**2 + n*h**2 - 4*h**2 + 2*h**3 = 0 for h.
0, 1
Suppose -4*u = -3*m - 6, 0*m = -u - 5*m - 10. Factor u - 2/7*x**3 - 2/7*x**2 + 4/7*x.
-2*x*(x - 1)*(x + 2)/7
Let v(l) be the second derivative of l**7/84 - l**6/30 + l**5/40 - 2*l - 7. Factor v(a).
a**3*(a - 1)**2/2
Let i(n) = -2*n + 18. Let m be i(7). Factor 8*w**2 + 1/2 + m*w.
(4*w + 1)**2/2
Let h(a) be the first derivative of a**4/26 - 3*a**2/13 + 4*a/13 - 23. Let h(x) = 0. Calculate x.
-2, 1
Let z(u) = 10*u - 1. Let y be z(1). Factor y*c**4 + 3*c**3 - 24*c**2 + 8 + 12*c - 8.
3*c*(c - 1)*(c + 2)*(3*c - 2)
Let t(f) be the second derivative of -f**3/3 - 9*f**2/2 + 2*f. Let l be t(-6). Find o such that 5 - 2 + l*o - 4*o**3 + o**3 + o**2 - 4*o**2 = 0.
-1, 1
Let c(i) be the first derivative of -5*i**4/4 - 35*i**3/3 - 35*i**2 - 40*i + 43. Factor c(s).
-5*(s + 1)*(s + 2)*(s + 4)
Let k(s) be the third derivative of s**6/540 + s**5/90 + s**4/54 + 37*s**2. Suppose k(h) = 0. What is h?
-2, -1, 0
Let t(q) be the third derivative of -q**7/140 - q**6/80 + 3*q**5/40 + 5*q**4/16 + q**3/2 + 4*q**2. Solve t(m) = 0 for m.
-1, 2
Let n(l) = -5*l**2 + 8*l - 3. Let u(v) = -5*v + 4*v + 1 + 2*v**2 + 3*v - 5*v. Let w(o) = 3*n(o) + 8*u(o). Solve w(h) = 0.
-1, 1
Let f(a) = -a**2 - a + 1. Let k(c) = -8*c**2 + 7*c - 4. Let v(m) = 5*f(m) - k(m). Factor v(b).
3*(b - 3)*(b - 1)
Solve 120/7*d**2 - 6/7*d**5 + 0 + 6*d**4 - 108/7*d**3 - 48/7*d = 0.
0, 1, 2
Suppose 6*w = 11*w - 15. Let k(n) be the third derivative of -4*n**w - 81/40*n**6 + 0*n - 11/2*n**4 - n**2 + 0 - 27/70*n**7 - 9/2*n**5. Factor k(z).
-3*(z + 1)*(3*z + 2)**3
Let b(i) = 51*i**2 - 195*i - 114. Let p(d) = 10*d**2 - 39*d - 23. Let c(x) = -5*b(x) + 24*p(x). Factor c(m).
-3*(m - 3)*(5*m + 2)
Suppose 85 = 2*y + 3*y. Let v be y/4 - 3 - 1. Factor -v*c + 1/4*c**3 - 1/4*c**2 + 1/4.
(c - 1)**2*(c + 1)/4
Let p be -2*-1*(-3)/(-6). Let d(r) be the first derivative of -1/10*r**4 - p + 1/5*r**2 + 4/15*r**3 - 4/5*r. Determine o, given that d(o) = 0.
-1, 1, 2
Let y(m) be the first derivative of -1/2*m + 2 - 1/2*m**2 + 1/2*m**3. Factor y(n).
(n - 1)*(3*n + 1)/2
Determine j, given that -2/11*j**2 - 4/11 + 6/11*j = 0.
1, 2
Let d = 242/63 - 32/9. Determine n, given that 0*n + 0 + 0*n**3 - 2/7*n**4 + d*n**2 = 0.
-1, 0, 1
Factor 0*a**2 - 2/5*a**4 + 0 + 2/5*a**3 + 0*a.
-2*a**3*(a - 1)/5
Factor 0 - 1/2*m**4 - 2*m + 3/2*m**3 + 0*m**2.
-m*(m - 2)**2*(m + 1)/2
Factor 2/3*y**2 + 2/3*y**3 - 2/3*y**4 - 2/3*y + 0.
-2*y*(y - 1)**2*(y + 1)/3
Factor -22*k - 15*k - 5*k + 9*k**2 - 24 + 72*k.
3*(k + 4)*(3*k - 2)
Let g(w) be the first derivative of -4/9*w - 2/15*w**5 + 4 + 5/18*w**4 - 5/9*w**2 + 10/27*w**3. Determine a so that g(a) = 0.
-1, -1/3, 1, 2
Let d(i) = 2*i**2. Let w be d(1). Let 0*z - 17*z**2 + 4*z + 21*z**w = 0. Calculate z.
-1, 0
Factor -488*f**3 + 2*f**5 + 2 + 482*f**3 + 4*f - 2*f**2 + 2*f**4 - 2.
2*f*(f - 1)**2*(f + 1)*(f + 2)
Let p be (6/15 - 0)/(128/480). Factor 0 + 0*a - 3/4*a**3 + p*a**2.
-3*a**2*(a - 2)/4
Let i(x) = -x**2 - 1. Let q(g) = -3*g**3 - 11*g**2 + 3*g + 7. Let t(m) = -2*i(m) + q(m). Let t(c) = 0. What is c?
-3, -1, 1
Let g(n) be the second derivative of -n**6/360 + n**4/24 + n**3/6 - 2*n. Let w(s) be the second derivative of g(s). Factor w(k).
-(k - 1)*(k + 1)
Suppose 5 = -f + 7. Factor 2/7 - 2/7*l**f - 2/7*l + 2/7*l**3.
2*(l - 1)**2*(l + 1)/7
Let j = 0 - -3. Let 3*b**2 - 12 - 2*b**2 - 4 - 2*b**j - 13*b**2 - 24*b = 0. What is b?
-2
Suppose 12 = 8*s - 5*s. Let v(b) be the second derivative of -4/3*b**2 - b + 0 - 16/9*b**3 + 8/15*b**5 - 1/6*b**s + 7/45*b**6. Solve v(x) = 0.
-2, -1, -2/7, 1
Let j(u) be the second derivative of -u**6/60 - u**5/10 - 5*u**4/24 - u**3/6 + 35*u. Factor j(w).
-w*(w + 1)**2*(w + 2)/2
Let r(p) be the first derivative of -p**6/24 - p**5/10 + 3*p**4/16 + 7. Factor r(a).
-a**3*(a - 1)*(a + 3)/4
Let m(v) be the third derivative of v**8/56 - 11*v**7/105 + v**6/10 - 25*v**2. Factor m(a).
2*a**3*(a - 3)*(3*a - 2)
Let q(b) be the second derivative of 0 + 1/60*b**6 + 3*b + 1/84*b**7 + 0*b**3 + 0*b**2 - 1/24*b**4 - 1/40*b**5. Let q(k) = 0. Calculate k.
-1, 0, 1
Let s be (64/(-12) - -5)/(2/(-24)). Factor 0 - 2/7*d**5 - 2/7*d**s + 2/7*d**2 + 0*d + 2/7*d**3.
-2*d**2*(d - 1)*(d + 1)**2/7
Let f(s) = -4*s**2 - 13*s. Let p(x) = -5*x**2 + 3*x + 6. Let o(k) = 9*k**2 - 6*k - 11. Let y(d) = 6*o(d) + 11*p(d). Let q(z) = -2*f(z) + 9*y(z). Factor q(u).
-u*(u + 1)
Let t be (-15)/10 - (-17)/2. Let j(k) be the third derivative of 0 + 0*k + 0*k**3 - 1/336*k**8 + 1/120*k**6 + 0*k**t + k**2 + 0*k**5 + 0*k**4. Factor j(o).
-o**3*(o - 1)*(o + 1)
Suppose 0*n + 0 + 2/5*n**4 - 2/5*n**2 - 2/5*n**3 + 2/5*n**5 = 0. Calculate n.
-1, 0, 1
Let i be ((-28)/4 + 6)/((-3)/9). Factor -2/5 + 2/5*a**2 + 2/5*a**i - 2/5*a.
2*(a - 1)*(a + 1)**2/5
Let d be (-5)/10*(-4)/10. Factor 0*s - d*s**3 + 0 + 1/5*s**2.
-s**2*(s - 1)/5
Let o be (1 + 0/(-2))*-1. Let f(n) = n**2. Let d = 6 + -11. Let t(w) = -3*w**2 + 2*w. Let z(g) = d*f(g) + o*t(g). Factor z(l).
-2*l*(l + 1)
Let n(o) be the second derivative of -o**5/70 + o**4/21 + o**3/21 - 2*o**2/7 - 9*o - 1. Find q such that n(q) = 0.
-1, 1, 2
Let m(w) = w**2 + 2*w + 2. Let p be m(-3). Suppose -5*f + 2*i + 3 = -5, i = p*f - 9. Factor -2/5*g - 4/5 + 2/5*g**3 + 4/5*g**f.
2*(g - 1)*(g + 1)*(g + 2)/5
What is l in 2*l**2 - 3*l - l - 8*l**3 + 8*l**2 + 2*l = 0?
0, 1/4, 1
Let x be 4/(-2) - (26 - 10)/(-4). Factor -4*f**3 + 0*f + 0 - 45/8*f**4 + 81/8*f**5 - 1/2*f**x.
f**2*(f - 1)*(9*f + 2)**2/8
Let a = 4 + 0. Suppose v = -3*l - 2*l + 18, -3*v + a*l - 3 = 0. Find d such that 2/7*d**v - 2/7*d + 2/7*d**4 - 2/7*d**2 + 0 = 0.
-1, 0, 1
Let s(c) = -c**2 + 6*c + 4. Let j be s(6). Let r(a) = 5*a - 17. Let v be r(j). What is x in 0*x**v - 2/3*