33 - 18*i**2/11 + 6*i + 1. Determine k so that z(k) = 0.
-9, 2/5
Factor -1/8*f**5 - 1/4*f**2 + 0 + 0*f - 1/2*f**4 - 5/8*f**3.
-f**2*(f + 1)**2*(f + 2)/8
Let r = -1 + 3. Suppose 2*i = -8*f + 4*f + 16, -5*f - i + 14 = 0. Factor f - 2 - b**r.
-b**2
Suppose -3*s = -10 - 2. Find q, given that -s - 2*q - 6*q**2 - q - 3*q**3 + 4 = 0.
-1, 0
Let l be -2 + (-60)/(-35) - (-24)/21. Factor -2/7*i**2 - l*i - 4/7.
-2*(i + 1)*(i + 2)/7
Let g(l) be the first derivative of -l**4/42 - 2*l**3/21 - l**2/7 + 3*l - 2. Let v(d) be the first derivative of g(d). Suppose v(q) = 0. What is q?
-1
Let u(c) be the second derivative of 5/24*c**4 + 1/8*c**5 + 1/168*c**7 + 3*c + 0 + 5/24*c**3 + 1/24*c**6 + 1/8*c**2. Let u(b) = 0. Calculate b.
-1
Suppose 4*s = -4*v + 8*v + 4, -5*s + 20 = 0. Factor -2*g**3 + v - 3 - 8*g**5 - 10*g**4.
-2*g**3*(g + 1)*(4*g + 1)
Let p(q) be the first derivative of 1/16*q**4 + 0*q + 1/40*q**5 + 0*q**3 - 3 + 3/2*q**2. Let u(k) be the second derivative of p(k). Suppose u(i) = 0. What is i?
-1, 0
Let f = 2086 - 10424/5. Let c be 3/10*(2 + 4). Find k, given that 1/5*k**2 + c - f*k = 0.
3
Let y(o) = 10*o**4 - 6*o**3 - 4*o**2 + 7*o - 7. Let k(q) = 3*q**4 - 2*q**3 - q**2 + 2*q - 2. Suppose -4*p = 4 - 32. Let z(f) = p*k(f) - 2*y(f). Factor z(r).
r**2*(r - 1)**2
Let p(c) be the second derivative of c**6/45 + c**5/30 - c**4/18 - c**3/9 + 3*c. Factor p(h).
2*h*(h - 1)*(h + 1)**2/3
Let x(u) = u + 6. Let z be x(-3). Determine l, given that 7*l - 4*l**2 - l**3 - 3*l + 12*l**2 + 5*l**z = 0.
-1, 0
Let i(h) be the second derivative of 5/72*h**4 + 0*h**2 + h + 1/18*h**3 - 1/36*h**6 + 0 - 1/60*h**5. Suppose i(a) = 0. What is a?
-1, -2/5, 0, 1
Let v(n) be the first derivative of 4*n**3/3 - 2*n**2 + 2. Determine o so that v(o) = 0.
0, 1
Let d = 2 + -2. Let a be (-2)/3*(-18)/4. Solve d + 3*g + 2 - 3 - a*g**2 + g**3 = 0 for g.
1
Let n = -42 + 216/5. Determine k so that -2/5*k**2 - n*k - 4/5 = 0.
-2, -1
Determine r so that -5/12*r + 1/12*r**2 + 0 = 0.
0, 5
Let q be 6*2/12 + (-2)/10. Factor 0*t + 0 + q*t**2 + 2/5*t**3.
2*t**2*(t + 2)/5
Let h(p) be the third derivative of -1/525*p**7 - 2*p**2 + 0 - 1/150*p**5 + 0*p**4 + 0*p + 0*p**3 + 1/150*p**6. Factor h(g).
-2*g**2*(g - 1)**2/5
Let o(k) be the first derivative of k**6/4 + 9*k**5/10 + 9*k**4/8 + k**3/2 + 12. Determine j so that o(j) = 0.
-1, 0
Let i = 3 - 9. Let u = -4 - i. Factor -1/3*m**u - 1/3 + 2/3*m.
-(m - 1)**2/3
Let k be ((-4)/6)/(16/(-6)). Factor 3/4*v + k*v**2 + 1/2.
(v + 1)*(v + 2)/4
Let a(s) be the first derivative of -1/6*s**2 - 4 + 1/3*s + 1/12*s**4 - 1/9*s**3. Factor a(r).
(r - 1)**2*(r + 1)/3
Suppose 0 = 3*w - 2*f - 12, 7*w - 4*w + f = 12. Let j(i) = -i - 4. Let y be j(-7). Solve 0 + 0*p**y + 0*p**2 + 0*p - 1/2*p**w = 0.
0
Factor -1/6*o**2 + 0 - 1/6*o.
-o*(o + 1)/6
Let x(u) be the second derivative of -u**5/5 - u**4 + 6*u**3 - 10*u**2 - 18*u. Factor x(l).
-4*(l - 1)**2*(l + 5)
Let v(d) = -10*d**2 - 6*d - 6. Let s(m) = m**2 - 1. Let a(y) = -5*s(y) - v(y). Let n(p) = -p**2 - p - 2. Let x(w) = -2*a(w) - 11*n(w). Factor x(b).
b*(b - 1)
Let a = -15 - -15. Determine v so that -2/7*v + a + 2/7*v**2 = 0.
0, 1
Let h(p) be the third derivative of p**7/525 + p**6/100 + p**5/50 + p**4/60 + 12*p**2. Solve h(d) = 0 for d.
-1, 0
Let s = 31 + -19. Let v be (3 - 15)*(-4)/s. Let -q**2 + 4/3 + 4/3*q + 1/3*q**v - 2/3*q**3 = 0. Calculate q.
-1, 2
Factor 2/11*j**2 - 8/11*j + 8/11.
2*(j - 2)**2/11
Let h(i) be the third derivative of -i**8/84 + 8*i**7/105 - i**6/5 + 4*i**5/15 - i**4/6 + 7*i**2. Let h(n) = 0. Calculate n.
0, 1
Factor -6/7 - 4/7*b + 2/7*b**2.
2*(b - 3)*(b + 1)/7
Suppose 12*x - 3 = 33. Factor -54*k - 27*k**2 - 1/2*k**4 - 81/2 - 6*k**x.
-(k + 3)**4/2
Let r(j) = -j**2 + 12*j + 5. Let y be r(12). Let l(n) be the second derivative of n + 2/9*n**3 + 1/15*n**y - 1/6*n**4 + 0 - 1/90*n**6 - 1/6*n**2. Factor l(k).
-(k - 1)**4/3
Let g be 7*(-32)/(-392) - (-4)/42. Let w(q) be the first derivative of 0*q**2 + 0*q - 4 - g*q**3 + 0*q**4 + 2/5*q**5. Factor w(h).
2*h**2*(h - 1)*(h + 1)
Let g(q) be the second derivative of 4/15*q**2 + 0 + 1/105*q**7 - 7/150*q**5 - 2*q - 1/45*q**6 + 7/30*q**4 - 16/45*q**3. Find r, given that g(r) = 0.
-2, 2/3, 1
Let m = 12 - 7. Solve 2*y**4 + 4*y + 0*y**5 - 4*y**3 + y**3 + y**m - 4*y**2 = 0 for y.
-2, 0, 1
Let m(b) be the third derivative of 0*b + 1/525*b**7 + 5*b**2 - 1/50*b**5 - 1/12*b**4 + 1/300*b**6 - 2/15*b**3 + 0. Suppose m(f) = 0. Calculate f.
-1, 2
Let b = -149 - -1343/9. Let s(u) be the second derivative of -1/54*u**4 + b*u**2 + 0 - 1/27*u**3 - u. Solve s(m) = 0 for m.
-2, 1
Let b be 32/(-14)*143/212. Let l = -6/53 - b. Determine t so that -2/7 - 8/7*t**2 + l*t = 0.
1/4, 1
Let t(g) be the third derivative of 1/900*g**6 + 7/450*g**5 + 1/5*g**3 + 0 + 2*g**2 + 0*g + 1/12*g**4. Factor t(k).
2*(k + 1)*(k + 3)**2/15
Suppose 0*s + s + 6 = 0. Let n(m) = 7*m**3 + 6*m**2 - 13. Let x(f) = 4*f**3 + 3*f**2 - 7. Let t(w) = s*n(w) + 10*x(w). Solve t(q) = 0 for q.
-2, 1
Let l(d) = -d + 2. Let i be l(-3). Let 2*n**3 + n**2 + n**4 - n**i + 0*n**5 - n**3 - 2*n**4 = 0. Calculate n.
-1, 0, 1
Let h(n) = -n**4 - 3*n**3 + n**2. Let c = -16 + 9. Let p(b) = -3*b**2 + 6*b**3 - 4*b**3 + 5*b**3 + 3*b**4. Let w(f) = c*h(f) - 3*p(f). Factor w(y).
-2*y**2*(y - 1)*(y + 1)
Let v(p) = -2*p**2 - 9*p**2 - p**2 - 3 + 4*p - 5*p**2. Let f(c) = 35*c**2 - 8*c + 5. Let j(l) = -3*f(l) - 5*v(l). Find t such that j(t) = 0.
0, 1/5
Factor -12*m**4 + 24*m**2 - 7*m**3 + 20 + 45*m - 9*m**3 + 3*m.
-4*(m + 1)**3*(3*m - 5)
Let v(x) be the second derivative of 2*x - 3/20*x**5 - 1/6*x**4 + 0*x**2 + 0 + 1/6*x**3 - 7/180*x**6. Let c(u) be the second derivative of v(u). Factor c(m).
-2*(m + 1)*(7*m + 2)
Let j(x) be the second derivative of x**5/70 - x**4/14 + 2*x**3/21 - 3*x. Factor j(t).
2*t*(t - 2)*(t - 1)/7
Suppose 5 = -5*x + 20. Suppose 0*t = -t + x. Factor 0 + 1/3*z**t + z**2 - z**4 + 1/3*z**5 - 2/3*z.
z*(z - 2)*(z - 1)**2*(z + 1)/3
Let w be 4/(-22) + 120/660. Solve w + 1/4*d - 1/4*d**2 = 0.
0, 1
Let i = 5920/11 + -538. Suppose -2/11*u**3 + 0 - 4/11*u**2 - i*u = 0. Calculate u.
-1, 0
Let m(g) be the second derivative of 3*g**5/160 - g**4/8 + 5*g**3/16 - 3*g**2/8 + 9*g. Factor m(q).
3*(q - 2)*(q - 1)**2/8
Factor 15*a**2 + 4*a**4 - 16*a**3 - 4*a**2 - 16 + 20*a + a**2 - 4*a**3.
4*(a - 4)*(a - 1)**2*(a + 1)
Let q(r) be the first derivative of r**2 - 12*r + 1. Let j be q(8). Factor g**j + g**3 - 2*g + 5*g**3 + 3*g**4.
2*g*(g + 1)**2*(2*g - 1)
Let u(l) = 64*l**5 - 352*l**4 + 388*l**3 + 6*l**2 - 90*l - 18. Let z(h) = h**2 - h + 1. Let o(v) = u(v) + 2*z(v). Find y such that o(y) = 0.
-1/4, 1, 4
Let q**2 - 1/3*q**3 + 1/3*q - 1/3*q**4 - 2/3 = 0. Calculate q.
-2, -1, 1
Let u(n) be the first derivative of n**3 - n + 4. Let g = -4 + 0. Let h(p) = -7*p**2 + 2. Let i(a) = g*h(a) - 10*u(a). Find k, given that i(k) = 0.
-1, 1
Determine v, given that 0*v**2 + 0 - 4/5*v + 3/5*v**3 + 1/5*v**4 = 0.
-2, 0, 1
Let i(n) be the second derivative of n**4/2 + 9*n**3/4 + 3*n**2/2 + 3*n. Factor i(f).
3*(f + 2)*(4*f + 1)/2
Let d(k) be the third derivative of -k**8/336 - k**7/105 + k**5/30 + k**4/24 + 9*k**2. Suppose d(i) = 0. Calculate i.
-1, 0, 1
Let a = -51/2 + 26. Let k be 20/9 - (-10)/(-45). Factor 9/2*z**k - 3*z + a.
(3*z - 1)**2/2
Suppose 3*i - 5 = 3*y + 4, 9 = 5*i - 3*y. Let c = -1 + 1. Solve -g - 2 + i*g + 4*g + c*g - g**2 = 0.
1, 2
Let z = 10/7 - 2/7. Determine t so that -146/7*t**3 + 34/7*t**2 - 6*t**4 + 14*t**5 + z + 48/7*t = 0.
-1, -2/7, 1
Let w(k) be the first derivative of k**6/6 - 4*k**5/5 + 5*k**4/4 - 2*k**3/3 + 10. Factor w(h).
h**2*(h - 2)*(h - 1)**2
Factor 468*k**3 + 245*k**5 - 700*k**4 + 242*k**3 - k - 300*k**2 + 46*k.
5*k*(k - 1)**2*(7*k - 3)**2
Let j(s) be the second derivative of -4*s**7/63 + 7*s**6/45 + s**5/15 - 4*s**4/9 + 2*s**3/9 + s**2/3 - 3*s. Let j(d) = 0. What is d?
-1, -1/4, 1
Let b(k) = -k**3 + 2 + 2 + 10*k - 8*k**2 + 8. Let r be b(-9). Factor 0*m - 10/7*m**r + 0 + 4/7*m**2.
-2*m**2*(5*m - 2)/7
Suppose 12 + 48 = 2*p. Let h be 70/4*24/p. Find a such that -16/3*a**3 + 16/3*a + 50/3*a**2 - h*a**4 - 8/3 = 0.
-1, -2/3, 2/7, 1
Let k(a) be the second derivative of -a**4/2 + 7*a**3 - 147*a**2/4 - 17*a. Factor k(d).
-3*(2*d - 7)**2/2
Let g(v) be the second derivative of 0 + 0*v**3 - 1/240*v**5 - 1/2*v**2 - v - 1/48*v**4. Let r(h) be the first deriva