+ 2)
Let w(n) = -2*n**3 + 13*n**2 - 7*n + 8. Let j be w(6). Determine l, given that 24/7*l**j + 12/7*l**3 + 16/7*l + 2/7*l**4 + 0 = 0.
-2, 0
Let i(n) be the second derivative of -n**5/70 + n**4/14 - 2*n**3/21 + 4*n. Suppose i(t) = 0. Calculate t.
0, 1, 2
Let i(m) be the second derivative of -m**6/105 - m**5/35 - m**4/42 + 3*m. Factor i(f).
-2*f**2*(f + 1)**2/7
Let l = -26 + 28. Let y(v) be the second derivative of -1/18*v**3 + 0*v**4 - 2*v + 0 + 0*v**l + 1/60*v**5. Find r, given that y(r) = 0.
-1, 0, 1
Factor -3*h - 4*h**3 + 3*h**2 - 3 + 11*h**3 - 4*h**3.
3*(h - 1)*(h + 1)**2
Let z(l) be the third derivative of -l**6/1320 - l**5/110 - l**4/24 - l**3/11 - 2*l**2 + 12*l. Suppose z(s) = 0. What is s?
-3, -2, -1
Suppose 0 = 8*b + 7 - 23. Solve 0 - 2/3*s - 2/3*s**b + 2/3*s**3 + 2/3*s**4 = 0 for s.
-1, 0, 1
Let r(i) = 4*i**3 + 3*i**2 + 4*i. Let j(n) = -n**3 - 4*n**2 + 8*n**2 - 3*n - 6*n**2 - 2*n**3. Let z(w) = -5*j(w) - 4*r(w). Find d such that z(d) = 0.
-1, 0
Let t(m) = 5*m**2 - 15*m + 8. Let w(p) = -10*p**2 + 30*p - 15. Let c(s) = -5*t(s) - 2*w(s). Let c(n) = 0. What is n?
1, 2
Let v(j) be the first derivative of 3*j**4/4 + j**3 - 3*j**2 - 16. Factor v(a).
3*a*(a - 1)*(a + 2)
Let g(i) = i**2 + 3*i - 2. Let j be g(-4). Let y be j - (-1 + (1 - 3)). Let 2*u + y*u - u**2 - 5*u = 0. What is u?
0, 2
Let w = 18 + -14. Let q be w + -4 + 1 + -1. Suppose -1/2*z**2 + 1/2*z**3 + 0 - 1/2*z**5 + q*z + 1/2*z**4 = 0. What is z?
-1, 0, 1
Let s(m) be the second derivative of m**5/4 + 5*m**4/4 - 5*m**3/6 - 15*m**2/2 + 33*m. Let s(u) = 0. Calculate u.
-3, -1, 1
Let p(k) be the first derivative of 6 - 4/5*k - 3/5*k**2 - 2/15*k**3. Factor p(y).
-2*(y + 1)*(y + 2)/5
Find j, given that 0*j - 1/8*j**3 + 0 + 1/8*j**2 = 0.
0, 1
Suppose -3*v = -2*v. Let j be (v + -4)*(-6)/15. Solve 126/5*u**3 - 8/5*u**2 + 0 - j*u = 0 for u.
-2/9, 0, 2/7
Suppose 18 = 5*u - 2*u. Let k(y) be the third derivative of 0*y**3 + 1/48*y**4 - 1/120*y**5 + 0 + 1/420*y**7 + 0*y + y**2 - 1/240*y**u. Let k(r) = 0. What is r?
-1, 0, 1
Factor -8*y**2 + 31*y**2 - 4 - 19*y**2.
4*(y - 1)*(y + 1)
Let r(i) be the second derivative of i**6/75 + 2*i**5/25 - i**4/15 - 4*i**3/5 + 9*i**2/5 + 12*i. Factor r(a).
2*(a - 1)**2*(a + 3)**2/5
Let u be ((-66)/55)/(-4 + 1). Solve 0 + u*k + 2/5*k**2 = 0.
-1, 0
Let d = -2/31 - -43/186. Suppose 0*i + d*i**2 + 1/2*i**3 + 1/2*i**4 + 0 + 1/6*i**5 = 0. What is i?
-1, 0
Let u(l) be the third derivative of -l**5/15 + 2*l**3/3 - 8*l**2. Find t, given that u(t) = 0.
-1, 1
Let g(t) be the third derivative of t**6/360 - t**4/24 + t**3/2 - 2*t**2. Let z(r) be the first derivative of g(r). Find f, given that z(f) = 0.
-1, 1
Let y = 209/3 + -69. Let j(f) be the third derivative of 1/20*f**6 + 0*f - 1/4*f**4 - 1/30*f**5 + f**2 - 1/105*f**7 + 0 + y*f**3. Suppose j(o) = 0. What is o?
-1, 1, 2
Solve 45 - 25 - 5*m**2 + 0*m**2 = 0 for m.
-2, 2
Let h(r) be the first derivative of r**3/3 - r**2/4 + 30. Determine s so that h(s) = 0.
0, 1/2
Let v(o) be the third derivative of -3*o**6/10 + 4*o**5/3 - 13*o**4/6 + 4*o**3/3 - 2*o**2. Factor v(f).
-4*(f - 1)**2*(9*f - 2)
Determine i so that -3/2*i**2 - 3/2*i**3 + 0*i + 0 = 0.
-1, 0
Let x(p) = 9*p**3 + 27*p**2 + 8*p + 8. Let d(t) = 3*t**3 + 9*t**2 + 3*t + 3. Let j(o) = -8*d(o) + 3*x(o). Solve j(y) = 0 for y.
-3, 0
Determine j, given that j**2 + 0 + 3/4*j**3 + 1/4*j**5 - j**4 - j = 0.
-1, 0, 1, 2
Let z = -11 + 16. Suppose 0 = 4*y + u - z - 6, u = y + 1. Factor -2/3*m**4 + 2*m**3 - 2*m**y + 0 + 2/3*m.
-2*m*(m - 1)**3/3
Let m(g) = 3*g**2 + 10*g + 14. Let b be 12/(-30) + (-8)/5. Let s(f) = 39*f**2 + 129*f + 183. Let w(p) = b*s(p) + 27*m(p). Factor w(k).
3*(k + 2)**2
Let f(v) be the second derivative of v**5/60 + v**4/6 + 2*v**3/3 + 4*v**2/3 + 2*v. Factor f(r).
(r + 2)**3/3
Let j(s) be the second derivative of 0*s**2 + 3*s - 1/2*s**6 + 1/2*s**3 - 9/20*s**5 + 0 + 1/4*s**4 - 1/7*s**7. Let j(q) = 0. Calculate q.
-1, 0, 1/2
Let s be 2/6 - (-10)/(-48). Factor 0 + s*k**2 - 1/4*k.
k*(k - 2)/8
Let n = -5 + 8. What is m in 1 + 2*m**3 + m**3 + 4*m + 2*m**3 + 5*m**2 - n*m**3 = 0?
-1, -1/2
Suppose 0 = 5*w - 72 + 7. Suppose f**4 - 13 + f**2 + w + 2*f**3 = 0. Calculate f.
-1, 0
Let j(a) = 2*a**2 + 2*a + 2. Let u be j(-2). Let k(q) = q**2. Let r(m) = -3*m**3 + 21*m**2 - 9*m - 27. Let z(l) = u*k(l) - r(l). Factor z(t).
3*(t - 3)**2*(t + 1)
Factor -264 - 5*d**2 + 264 - 25*d.
-5*d*(d + 5)
Let j be 2/(-6)*(-5 + 8). Let v = j + 3. Let -4/7*n + 2/7 + 0*n**v - 2/7*n**4 + 4/7*n**3 = 0. What is n?
-1, 1
Let l(f) be the second derivative of -f**5/150 + f**4/90 + 5*f. Factor l(p).
-2*p**2*(p - 1)/15
Let x be 18*(-3 + 6 - 2). Let q be (-3)/2*(-4)/x. What is t in -1/3 + q*t - 1/3*t**3 + 1/3*t**2 = 0?
-1, 1
Let s(u) be the third derivative of 0*u + 0 + 3*u**2 + u**3 - 1/8*u**4 + 1/160*u**5. Determine m so that s(m) = 0.
4
Suppose 37*u + 4 + 25*u**5 - 10*u**2 + 5*u**4 - 50*u**3 - 38*u + 1 + 26*u = 0. What is u?
-1, -1/5, 1
Let c be (-2)/20*(-45)/18. Let y = -9 + 11. Find d, given that 0 + c*d + 1/4*d**3 + 1/2*d**y = 0.
-1, 0
Let p(d) be the first derivative of 3*d**4/2 + 8*d**3/3 - d**2 - 4*d - 6. Factor p(x).
2*(x + 1)**2*(3*x - 2)
Find y, given that -41*y**2 - 7*y + 5*y**2 + y + 21*y**2 = 0.
-2/5, 0
Let g(p) = -1000*p**2 - 1215*p - 270. Let b(h) = -37*h**2 - 45*h - 10. Let o(t) = -55*b(t) + 2*g(t). What is n in o(n) = 0?
-1, -2/7
Suppose 2*h = -o + 12, 0 = -3*o - h + 18 - 2. Factor 21*l - 2*l**3 + 0*l**3 - 21*l + o*l**2.
-2*l**2*(l - 2)
Let b(c) be the second derivative of c**6/50 + 3*c**5/50 + c**4/20 - 7*c. Suppose b(f) = 0. What is f?
-1, 0
Determine g, given that g**2 + 2*g**2 - 3*g - 2*g**2 = 0.
0, 3
Suppose -2/9*f**2 + 0 + 2/9*f = 0. Calculate f.
0, 1
Suppose d**3 - d - 10*d**3 + 5*d**2 - 11*d**2 + 0*d**3 - 4*d**4 = 0. Calculate d.
-1, -1/4, 0
Let l(j) be the second derivative of -j**5/10 + j**3/3 + 12*j. Let l(g) = 0. Calculate g.
-1, 0, 1
Let d(t) = 6*t**5 + 14*t**4 + 4*t**3 - 4*t**2 - 2*t. Let x(a) = -a**5 - a**2 - a. Let m(s) = -d(s) + 2*x(s). Factor m(y).
-2*y**2*(y + 1)**2*(4*y - 1)
Let f = -1 - -1. Suppose 2*c + q + 2*q - 21 = 0, f = 2*q - 10. Factor 2/3*k**c - 14/9*k**2 + 10/9*k - 2/9.
2*(k - 1)**2*(3*k - 1)/9
Let r(f) = f**3 + f**2 - 3*f - 2. Let o be r(-2). Let k be (-28)/21 - (o - 2). Let -2/3*l + k*l**2 + 0 = 0. Calculate l.
0, 1
Let z = 2391/2 - 1191. Suppose 0 + 3/2*b**2 - z*b = 0. What is b?
0, 3
Factor 36 - 18 - z**3 + 5*z**2 - 15 - 7*z.
-(z - 3)*(z - 1)**2
Suppose 2/13*d**2 - 2/13*d + 0 = 0. What is d?
0, 1
Let k(m) be the third derivative of -m**8/280 + m**6/50 - m**4/20 + 7*m**2. Determine b so that k(b) = 0.
-1, 0, 1
Factor 6*a**3 - 15*a - 4 + 4 - 15*a**3 + 3*a**4 - 27*a**2.
3*a*(a - 5)*(a + 1)**2
Determine y so that 0 - 15/2*y**4 - 21/2*y**3 - 3*y**2 + 0*y = 0.
-1, -2/5, 0
Let u(w) be the third derivative of 11*w**6/300 - w**5/50 + 23*w**2. Factor u(q).
2*q**2*(11*q - 3)/5
Let f be (0 - 1) + -1 + 0 - -2. Let 0 + 0*t**2 + 0*t**3 + f*t - 2/5*t**4 + 2/5*t**5 = 0. What is t?
0, 1
Let t(s) = -2*s**5 + 32*s**4 + 58*s**3 + 57*s**2 + 13*s. Let x(y) = -y**5 + y**4 - y**3 - y. Let k(l) = t(l) - 5*x(l). Determine o, given that k(o) = 0.
-6, -1, 0
Let a be 18/2*90/(-27). Let b = a + 92/3. Factor -4/3*f**4 + 0*f + 1/3*f**5 - b*f**2 + 5/3*f**3 + 0.
f**2*(f - 2)*(f - 1)**2/3
Determine j, given that -1425*j + 1425*j + 4*j**4 + 16*j**3 = 0.
-4, 0
Let l(f) = -27*f**3 - f. Let y be l(1). Let z be y/(-6) + (-2)/3. Find s such that -s**3 - 2*s**4 - 3*s**3 + 0*s**z - 2*s**2 = 0.
-1, 0
Factor -2*r**2 - 20*r + 40 + 5*r**3 - 2*r**2 - 6*r**2.
5*(r - 2)**2*(r + 2)
Determine j, given that -8*j**2 + 0 - 8/3*j + 16/3*j**4 - 2*j**5 + 2*j**3 = 0.
-1, -1/3, 0, 2
Suppose 0*j + 5 = j - 5*y, 2*y = -2. Let u(z) be the second derivative of 0*z**2 + 1/12*z**4 - 1/40*z**5 + j - 1/12*z**3 + 3*z. Let u(g) = 0. What is g?
0, 1
Let v(n) be the first derivative of -n**4/12 - n**3 - 9*n**2/2 - 9*n - 2. Factor v(d).
-(d + 3)**3/3
Let r be 1/1 - (-1)/(-1). Suppose 4*t - 8 = -2*k + 3*k, r = -5*k. Solve 1/4*u**3 + 0 + 1/2*u**t + 1/4*u = 0.
-1, 0
Let i(y) be the second derivative of 0*y**2 - 3/20*y**5 - 1/6*y**3 + 0 - 1/30*y**6 + y - 1/4*y**4. Solve i(d) = 0 for d.
-1, 0
Suppose 4*v + 0*v = 16. Let h(p) be the first derivative of -1/12*p**3 + 0*p + 1 - 1/8*p**v + 1/8*p**2. Factor h(t).
-t*(t + 1)*(2*t - 1)/4