 - 12*k + 2. Let b(x) = -x**3 - x**2 + x - 1. Let p(g) = n*b(g) + l(g). Factor p(v).
-2*(v + 1)**4
Let z be 10/18*18/30. Determine b so that -z*b**5 + 0*b + 0*b**2 + 1/3*b**3 + 0*b**4 + 0 = 0.
-1, 0, 1
Suppose -65*v + 37*v - 5*v**3 + 48*v = 0. Calculate v.
-2, 0, 2
Let p(a) be the first derivative of a**5/10 + a**4/4 + a**3/6 + 5. Suppose p(d) = 0. What is d?
-1, 0
Let j be ((-9)/(-12))/(1/8). Let h = j - 3. Factor 8 - 2*q**2 - 4*q**2 - 10*q**3 + 6*q**h + 8*q + 2*q**4.
2*(q - 2)**2*(q + 1)**2
Factor 2/5*f**5 + 0*f + 16/5*f**2 + 24/5*f**3 + 12/5*f**4 + 0.
2*f**2*(f + 2)**3/5
Let j(k) = k**2 + k + 2. Let t be j(0). Let y be -2 + 14*t/6. Factor 4*d**2 + 2/3 + 8/3*d + y*d**3 + 2/3*d**4.
2*(d + 1)**4/3
Let s be (-1 - -1)*(1 - 10/15). Let a(w) be the third derivative of 1/40*w**5 + w**2 + 0 + s*w - 1/8*w**4 + 1/4*w**3. Factor a(u).
3*(u - 1)**2/2
Factor 20/3*w - 20/3 - 5/3*w**2.
-5*(w - 2)**2/3
Suppose 0 = -5*z + 24 + 51. What is f in 6*f**2 + 15/2*f**5 - 3*f**4 + 15/2*f - 3 - z*f**3 = 0?
-1, 2/5, 1
Let r be 9/(-15) - (-326)/10. Let j be ((-6)/(-21))/(r/28). Factor 1/4*c**4 + 1/2*c**3 - 1/4*c - 1/2*c**2 + 1/4 - j*c**5.
-(c - 1)**3*(c + 1)**2/4
Find l, given that 0*l**2 + 48 - 24*l + 3*l**2 + 0*l = 0.
4
Let z be (22/(-77))/(6/(-14)). Suppose -2/3*d - 2/9*d**3 - z*d**2 - 2/9 = 0. What is d?
-1
Let v = 5 - 2. Suppose 3*t - 12 = -v*g, 7*g - 8 = 2*g - 2*t. Factor g + 1/2*m**2 - m.
m*(m - 2)/2
Let x(v) = -5*v**4 + 5*v**3 + 7*v**2 - 5*v + 2. Let u(d) = -d**4 + d**3 + d**2 - d + 1. Let k(g) = -20*u(g) + 5*x(g). Determine j so that k(j) = 0.
-1, 1, 2
Let z(v) be the first derivative of -2/15*v**3 - 1 + 4/5*v**2 - 8/5*v. Factor z(b).
-2*(b - 2)**2/5
Let p(z) be the first derivative of -23*z**3 + 3*z**2 - 12. What is u in p(u) = 0?
0, 2/23
Let j = 92 + -88. Factor 9/4*c**5 + 0*c**2 + 3/2 + 15/2*c**3 - 15/4*c - 15/2*c**j.
3*(c - 1)**4*(3*c + 2)/4
Determine c, given that -1/2 + 5/6*c - 1/6*c**2 - 1/6*c**3 = 0.
-3, 1
Let y be ((-10)/(-3) + -3)*9. Factor 0*b + 0*b**2 + 0 + 2/11*b**y + 0*b**4 - 2/11*b**5.
-2*b**3*(b - 1)*(b + 1)/11
Let k(z) = 5*z + 4. Let i be k(5). Let h = i + -259/9. Factor h*w**5 + 0 - 2/9*w**4 - 2/9*w**3 + 0*w + 2/9*w**2.
2*w**2*(w - 1)**2*(w + 1)/9
Let k(t) be the second derivative of -t**8/2520 - t**7/1575 + t**6/900 + t**5/450 - 3*t**2/2 - 2*t. Let i(d) be the first derivative of k(d). Factor i(s).
-2*s**2*(s - 1)*(s + 1)**2/15
Suppose -2 = -4*x + 2*p, p - 3*p + 19 = 3*x. Let g = x - 1. Factor j**3 + 2 - 2*j**g - 1 - 1.
j**2*(j - 2)
Let k(x) = 4*x**3 + 6*x**2 - 6*x - 10. Let q(i) = -i**2 - i - 1. Let v(f) = k(f) - 2*q(f). Let v(d) = 0. What is d?
-2, -1, 1
Let y be (37 + -36)*2/10. Factor 1/5 + 4/5*t + 4/5*t**3 + 6/5*t**2 + y*t**4.
(t + 1)**4/5
Let c(l) be the third derivative of l**8/56 - l**7/140 - l**6/20 + l**5/40 + 14*l**2. Solve c(h) = 0.
-1, 0, 1/4, 1
Let l(m) = m**3 + 10*m**2 + 9*m + 2. Let b be l(-9). Factor 1/4 + 1/4*n**b - 1/2*n.
(n - 1)**2/4
Let n be 4 - (-2 + 2)/(-3). Suppose 2*j = 4*b - n, -5 = 3*j + 5*b - 21. Suppose -1/2 - 1/2*s**j + s = 0. Calculate s.
1
Let s(j) be the third derivative of j**5/150 - 13*j**2. Solve s(c) = 0 for c.
0
Determine a, given that -150*a**3 + 47 + 45*a**4 - 2 - 91*a - 5*a**5 - 74*a + 124*a**2 + 106*a**2 = 0.
1, 3
Let j be ((-6)/16)/(9/(-6) + 0). Find p, given that -j*p + 1/2 + 1/4*p**3 - 3/4*p**2 + 1/4*p**4 = 0.
-2, -1, 1
Solve -32/5*u + 128/5 + 2/5*u**2 = 0.
8
Let c(y) be the third derivative of -y**8/1176 - 2*y**7/735 - y**6/420 - 4*y**2. Suppose c(i) = 0. Calculate i.
-1, 0
Suppose 0 = 5*t - 30 + 10, 2*k - 3*t = -8. Solve k*h + h - 7*h**3 + h + 4*h**5 - h**3 = 0 for h.
-1, 0, 1
Let s be 2/12*(4 - 8 - -6). Factor 0 - 1/3*z + s*z**2.
z*(z - 1)/3
Factor -3/7*a + 0*a**2 - 2/7 + 1/7*a**3.
(a - 2)*(a + 1)**2/7
Let t(r) be the second derivative of 0*r**2 - 2*r + 1/24*r**4 + 0 + 0*r**3. Factor t(w).
w**2/2
Let z(p) = 5*p**3 + p**2 + p - 1. Let d(s) = -16*s**3 - 4*s**2 - 4*s + 4. Let m(c) = 3*d(c) + 10*z(c). Factor m(h).
2*(h - 1)**2*(h + 1)
Let 9/2*t**3 - 7/2*t**5 - t + 5/2*t**2 + 0 - 5/2*t**4 = 0. Calculate t.
-1, 0, 2/7, 1
Suppose 3*d - 2*d = 1. Let o(x) be the first derivative of -x**3/3 - x**2/2 + 1. Let q(g) = g**3 + 9*g**2 + 6*g - 4. Let b(m) = d*q(m) + 6*o(m). Factor b(p).
(p - 1)*(p + 2)**2
Let o(n) be the third derivative of n**8/1008 + 2*n**7/315 + n**6/120 + 2*n**2. Factor o(q).
q**3*(q + 1)*(q + 3)/3
Let l be (0 + (-2)/(-30))*2. Let h(u) be the first derivative of -l*u**3 - 3/20*u**4 + 1 + 1/10*u**2 + 0*u. Factor h(c).
-c*(c + 1)*(3*c - 1)/5
Let x = -6 - -8. Factor 6*k - 2*k + k + k - x*k**2.
-2*k*(k - 3)
Factor -u + 3/2*u**5 - 1/2*u**3 + 11/4*u**4 - 3*u**2 + 1/4.
(u - 1)*(u + 1)**3*(6*u - 1)/4
Let q(v) = 4*v**3 - 2*v. Let i(h) = -h**3 - h - 2. Let p be i(0). Let z(l) = -l**4 + l**2 - l. Let n(s) = p*z(s) - q(s). Solve n(u) = 0 for u.
-1, 0, 1, 2
Let r(q) = 35*q. Let n be r(0). Factor -1/3*k**2 + 0*k - 1/3*k**3 + n.
-k**2*(k + 1)/3
Let l(q) be the second derivative of -q**4/3 - 2*q**3/3 - 26*q. Factor l(z).
-4*z*(z + 1)
Suppose 5*n = 3*m - 39, 0 = -5*m + 2*n - 0*n + 84. Let y be (-3)/m*(-1 + -3). Factor 2/3 + y*k**2 - 4/3*k.
2*(k - 1)**2/3
Let o(w) be the second derivative of 0 - 4/3*w**3 + 25/12*w**4 - w + 11/5*w**5 - 2*w**2 + 1/2*w**6. Let o(d) = 0. Calculate d.
-2, -1, -1/3, 2/5
Let j(i) be the third derivative of 3*i**2 + 1/60*i**6 - 1/3*i**3 - 1/10*i**5 + 0*i + 1/4*i**4 + 0. Solve j(x) = 0 for x.
1
Let g(j) be the third derivative of -j**9/7560 - j**8/3360 + j**4/12 - j**2. Let f(w) be the second derivative of g(w). Factor f(k).
-2*k**3*(k + 1)
Suppose 2*i + 4*k - 32 + 2 = 0, i - 4*k + 15 = 0. Let o be 27/15 + 1/i. Factor -2*p**2 - 4*p**3 - 4*p + 4*p - o*p**4.
-2*p**2*(p + 1)**2
Suppose -2*i - 4*k = 0, 0 = 3*i + i + k. Factor 5*r**2 + i + r**2 + 0 + 3*r**3 + 3*r.
3*r*(r + 1)**2
Let t be 1 + 2 - 5 - -4. Find q such that -5*q**3 + 27*q**2 + 2*q**3 - 21*q**t = 0.
0, 2
Let c(q) be the second derivative of -q**4/24 - q**3/2 - 9*q**2/4 - 2*q. Factor c(m).
-(m + 3)**2/2
Suppose -3*l + 12 = 3*g + 2*g, -3*g - 8 = -2*l. Factor 2*x**3 + 3*x**4 + 4*x**4 - l*x**4 + 2*x**2 - 5*x**4 - 2*x.
-2*x*(x - 1)**2*(x + 1)
Let t(c) be the third derivative of 0*c**3 + 0*c + 4*c**2 + 0*c**4 - 2/735*c**7 - 1/420*c**6 + 1/210*c**5 + 0. Suppose t(a) = 0. Calculate a.
-1, 0, 1/2
Suppose 3*w - 2*s = -2*w + 61, 2*w + 3*s - 13 = 0. Suppose -5*t + 4*k = 1 - w, t = k + 2. Factor 0 - 7/4*x**3 + 0*x - 1/2*x**t.
-x**2*(7*x + 2)/4
Let k(x) = -2*x**3 - 6. Let z(d) = -3*d**3 - 11. Let i(w) = 11*k(w) - 6*z(w). Find u, given that i(u) = 0.
0
Suppose 0*m**2 - 1/9*m**5 - 1/9*m**4 + 0*m + 0 + 2/9*m**3 = 0. What is m?
-2, 0, 1
Let r be (6/(-8))/(27/(-9)). Find q, given that -1/4*q + r*q**3 + 1/4*q**2 - 1/4*q**4 + 0 = 0.
-1, 0, 1
Let r(b) be the first derivative of b**5/10 + 5*b**4/8 + b**3/2 - 5*b**2/4 - 2*b - 19. Factor r(s).
(s - 1)*(s + 1)**2*(s + 4)/2
Let d(x) be the first derivative of -3*x**5/20 + 9*x**4/4 - 27*x**3/2 + 81*x**2/2 - 6*x - 2. Let r(b) be the first derivative of d(b). What is s in r(s) = 0?
3
Suppose 3*q + q - 16 = 0. Let r(n) be the second derivative of -1/147*n**7 + 0*n**2 + 2/21*n**q + 4/105*n**6 - 3/35*n**5 - 1/21*n**3 + 0 - 2*n. Factor r(z).
-2*z*(z - 1)**4/7
Solve -8/9*l - 2/3 - 2/9*l**2 = 0 for l.
-3, -1
Let q(r) = -r + 1. Let t(v) = 6*v**2 - 17 + 18 + v - 5*v**2. Let z(p) = -p**3 + 3*p**2 - 1. Let b be z(2). Let s(u) = b*t(u) - 3*q(u). Factor s(x).
3*x*(x + 2)
Let n(b) be the first derivative of 1/27*b**6 - 4 + 4/45*b**5 + 0*b**3 + 1/18*b**4 + 0*b + 0*b**2. Factor n(y).
2*y**3*(y + 1)**2/9
Let b be 182/30 - 24/(-40). Let l(a) be the first derivative of 2 + 5*a**4 + 1/3*a**6 + 5*a**2 + 2*a + 2*a**5 + b*a**3. Find t, given that l(t) = 0.
-1
Let m(y) be the second derivative of -3*y**5/70 + 11*y**4/28 - 13*y**3/14 + 6*y**2/7 - 9*y. Solve m(c) = 0 for c.
1/2, 1, 4
Let d = -82 - -82. Determine h, given that d*h + 2/9*h**4 - 4/9*h**3 + 2/9*h**2 + 0 = 0.
0, 1
Let o(q) = q**2 - 3*q + 2. Let d(s) = 3*s**2 - 7*s + 4. Let m(x) = -4*d(x) + 10*o(x). Factor m(j).
-2*(j - 1)*(j + 2)
Suppose -y = -4*u + 6 + 14, 3*u = -5*y + 15. Let w(l) be the first derivative of -2/15*l**3 + 0*l + 1 + y*l**2. Factor w(z).
-2*z**2/5
Factor -4*v + 18*v**2 + v - 12*v**3 + 3 - v + 3*v**4 - 8*v.
3*(v - 1)**4
Factor 0*h**2 - 2/5*h**3 + 0 -