*3 - 9*w**2 + 12*w + 6. Let k(a) = a**4 + a**3 + a**2 + a + 1. Let i(p) = -j(p) + 6*k(p). What is b in i(b) = 0?
0, 1, 2
Suppose 4*c = c. Let s(h) be the second derivative of -1/12*h**4 + c*h**3 + 0 + 0*h**2 - 2*h. Factor s(i).
-i**2
Let w(p) = -p**4 - p**3 - 3*p**2 + 4*p - 2. Let s(t) = -3*t**4 - t**3 - 7*t**2 + 8*t - 4. Let l(q) = 6*s(q) - 14*w(q). Factor l(o).
-4*(o - 1)**3*(o + 1)
Let o(w) be the first derivative of -w + 5 - w**2 + 1/2*w**4 + 1/5*w**5 + 0*w**3. Find r, given that o(r) = 0.
-1, 1
Let q(m) be the third derivative of m**8/43680 + m**7/16380 - m**4/8 - 6*m**2. Let h(n) be the second derivative of q(n). Factor h(z).
2*z**2*(z + 1)/13
Let 16/9 + 2/9*h**4 - 2/3*h**2 + 20/9*h - 8/9*h**3 = 0. Calculate h.
-1, 2, 4
Let r(d) = -21*d**2 + 9*d + 11. Let i(b) = 11*b**2 - 4*b - 6. Let g(p) = 11*i(p) + 6*r(p). Determine f, given that g(f) = 0.
0, 2
Let b(t) be the second derivative of -t**7/21 + t**6/15 + t**5/10 - t**4/6 + 8*t. Determine y so that b(y) = 0.
-1, 0, 1
Solve 0 - 2/7*l**2 + 8/7*l = 0.
0, 4
Let h(z) be the first derivative of -z**6/6 - 2*z**5/5 + z**4/2 + 4*z**3/3 - z**2/2 - 2*z - 12. Factor h(i).
-(i - 1)**2*(i + 1)**2*(i + 2)
Let a(w) = -3*w**5 - 6*w**4 - 3*w**3 + 6*w**2 + 6*w + 3. Let o(v) = -v**3 + v + 1. Let y(g) = a(g) - 3*o(g). Factor y(x).
-3*x*(x - 1)*(x + 1)**3
Let b(s) = -4*s**3 - 7*s**2 + 4*s + 12. Let z(y) = -4*y**3 - 8*y**2 + 4*y + 12. Let k(q) = 4*b(q) - 5*z(q). Solve k(x) = 0 for x.
-3, -1, 1
Let f = 15 + 62. Let p = f + -229/3. Factor 0 + p*w + 2/3*w**2.
2*w*(w + 1)/3
Let l = -1 - -1. Let 2/3*q**4 + 0*q + l - 2/3*q**2 + 0*q**3 = 0. Calculate q.
-1, 0, 1
Suppose -4*c - 6 = 2*j - 0*c, -4*j = 3*c - 3. Factor -f - f**j - 2*f**2 + 7*f**2 + 0*f - 3*f**2.
-f*(f - 1)**2
Let i(j) be the second derivative of j**3 + 0 + 2*j**2 + 1/6*j**4 - 3*j. Factor i(z).
2*(z + 1)*(z + 2)
Let q(d) be the second derivative of -d**7/21 - d**6/15 + d**5/5 + d**4/3 - d**3/3 - d**2 - 5*d. Factor q(y).
-2*(y - 1)**2*(y + 1)**3
Let n(k) = 4*k - 3 + 0 - 5*k. Let g be n(-6). What is j in 3*j**4 + j**2 + 3*j**3 - 2*j**4 - 2*j**3 - 3*j**g = 0?
0, 1
Let l(v) be the first derivative of v**3/3 - v**2 + v - 11. Suppose l(n) = 0. Calculate n.
1
Suppose 0 = -4*f + 3*b - 0*b + 17, -2*f + 2*b = -10. Let c(u) be the second derivative of 1/9*u**3 - 1/18*u**4 + 0*u**2 - f*u + 0. Factor c(l).
-2*l*(l - 1)/3
Let k(l) be the second derivative of -5*l**4/12 + 25*l**3/6 - 10*l**2 - 27*l. Determine n, given that k(n) = 0.
1, 4
Factor 3/2*k - 3/2*k**2 + 3.
-3*(k - 2)*(k + 1)/2
Let u(g) be the first derivative of 0*g + 3 - 2/3*g**3 - 1/2*g**2. Factor u(b).
-b*(2*b + 1)
Let v(o) = -o**2 - 6*o + 4. Let x be v(-6). Let z be 1 + 2/(x/2). Determine s, given that 4/3*s**z - 1/3 + 2/3*s**3 - s**4 - 2/3*s = 0.
-1, -1/3, 1
Let o(z) be the first derivative of -2*z**3/17 - 7*z**2/17 - 4*z/17 - 30. Factor o(r).
-2*(r + 2)*(3*r + 1)/17
Let m = 211/60 + -17/20. Solve -10/3*n - 2/3*n**3 + 4/3 + m*n**2 = 0 for n.
1, 2
Suppose -3*y = -0*y - 15. Let 8/5*o**3 + 4/5 - 8/5*o**4 + 4/5*o**2 + 2/5*o**y - 2*o = 0. Calculate o.
-1, 1, 2
Let l(w) be the second derivative of w**5/5 - 2*w**4/3 - 2*w**3 + 9*w. Find a such that l(a) = 0.
-1, 0, 3
Let r be 2/((-10)/15)*(-4)/6. Factor 0 + 4/3*f**3 + 0*f - 2/3*f**4 - 2/3*f**r.
-2*f**2*(f - 1)**2/3
Factor 242/9*j**3 - 8/9 - 154/9*j**2 - 80/9*j.
2*(j - 1)*(11*j + 2)**2/9
Let u(t) be the second derivative of -5*t**4/4 - 3*t**3/2 + 4*t**2 - 2*t. Let r(c) = -195*c**2 - 117*c + 105. Let n(k) = -2*r(k) + 27*u(k). Factor n(j).
-3*(j + 1)*(5*j - 2)
Let d = 26021/246 - 9/82. Let k = d - 1567/15. Factor -4/5 + k*p - 2/5*p**2.
-2*(p - 2)*(p - 1)/5
Factor 28/9*t**3 + 4/9*t**4 + 52/9*t + 20/3*t**2 + 16/9.
4*(t + 1)**3*(t + 4)/9
Factor -3/4*t**2 - 3/4*t**3 + 3/4 + 3/4*t.
-3*(t - 1)*(t + 1)**2/4
Factor -20*n**3 + 4*n**4 + 0*n**4 - 12*n - 655*n**2 + 683*n**2.
4*n*(n - 3)*(n - 1)**2
Solve 2*p - 15/2*p**3 + 6*p**2 + 2*p**4 + 0 = 0 for p.
-1/4, 0, 2
Determine s so that -6 + 4 + 5*s**5 + 2 + 4*s**2 + 16*s**3 + 17*s**4 = 0.
-2, -1, -2/5, 0
Let r(h) be the second derivative of h**5/60 + 3*h**4/2 + 54*h**3 + 972*h**2 + 2*h - 5. Factor r(m).
(m + 18)**3/3
Let k be -2 - 1/2*-5. Let f be (-2)/15 - 8/(-60). Suppose f + 1/4*n**3 + k*n**2 + 1/4*n = 0. Calculate n.
-1, 0
Let n(i) = -i**2 + 23*i - 86. Let z(y) = -y**2 + 22*y - 85. Let o(h) = 4*n(h) - 5*z(h). Factor o(t).
(t - 9)**2
What is w in -4/3*w**3 - 4/3 - 17/3*w**2 - 20/3*w = 0?
-2, -1/4
Let p = 3 + -3. Suppose -2*b + 8 = -p*b. Factor 2*o**2 - 6 + o - o**2 + b.
(o - 1)*(o + 2)
Factor 2*y**3 + 2*y**2 - 6*y**2 - 4*y**2 - 9*y**3 + y**4.
y**2*(y - 8)*(y + 1)
Let r(s) be the second derivative of 0*s**2 + 8*s + 0 + 1/4*s**4 + 1/10*s**6 + 0*s**3 - 3/10*s**5. What is c in r(c) = 0?
0, 1
Let u(z) be the second derivative of 0 + 2/45*z**6 - 5/9*z**4 + 0*z**2 + 1/15*z**5 + 2/3*z**3 + 8*z. Factor u(y).
4*y*(y - 1)**2*(y + 3)/3
Let c(f) be the third derivative of 3/8*f**4 - 1/40*f**6 - f**2 + f**3 + 0*f**5 + 0 + 0*f. Find k such that c(k) = 0.
-1, 2
Suppose 0 = -2*m - 3*m. What is q in 0 - 2*q - 3*q**2 + m*q**4 + 0 + q**4 = 0?
-1, 0, 2
Let b(w) be the second derivative of -w**6/15 - 3*w**5/10 - w**4/6 + w**3 + 2*w**2 - 7*w. Determine j, given that b(j) = 0.
-2, -1, 1
Factor 33 - 34 + 0*z**2 + z**2.
(z - 1)*(z + 1)
Let n(t) be the third derivative of t**6/210 - 2*t**5/35 + 2*t**4/7 - 16*t**3/21 + 12*t**2. Let n(q) = 0. What is q?
2
Let s(j) be the second derivative of 7*j**6/15 + 8*j**5/5 + 2*j**4/3 + j. Suppose s(f) = 0. Calculate f.
-2, -2/7, 0
Suppose 0 = -4*m + 5*z + 36, -3*m + 2*m + 5*z + 24 = 0. Factor o**3 - o**5 - 3*o**3 + 3*o**3 + 2*o**5 - 2*o**m.
o**3*(o - 1)**2
Suppose 4*y + 3 = 3*d - 6*d, d + 14 = 3*y. Determine t so that 0*t + 0 - 2/5*t**y + 0*t**2 = 0.
0
Let x be (-3)/(-6) + (-10)/(-4). Factor 2*u + 6*u**2 + 20 - 20 + 6*u**x + 2*u**4.
2*u*(u + 1)**3
Let d(g) = -g**2 - 44*g - 396. Let z(o) = -o + 1. Let h(v) = d(v) - 4*z(v). Let h(l) = 0. Calculate l.
-20
Suppose 3/4*r**2 - 3/2*r**3 + 0 + 3/2*r - 3/4*r**4 = 0. What is r?
-2, -1, 0, 1
Let o(f) be the third derivative of 2*f**2 + 0 - 1/90*f**5 + 0*f + 1/36*f**4 - 1/27*f**3 + 1/540*f**6. Let o(l) = 0. Calculate l.
1
Let s = -122 + 126. Factor -5/3*z**5 + 8/3*z**2 - 4*z**3 + 0*z - 6*z**s + 0.
-z**2*(z + 2)**2*(5*z - 2)/3
Let f = 24 + -17. Let q(i) be the third derivative of -2*i**2 + 0*i**4 + 1/105*i**f + 0*i**6 + 0 - 1/30*i**5 + 0*i + 0*i**3. Solve q(w) = 0 for w.
-1, 0, 1
Let o(i) = -3*i - 61. Let p be o(-21). Factor -1/2*u**4 + u**p + 0*u + 0 + 1/2*u**3.
-u**2*(u - 2)*(u + 1)/2
Let u(i) be the first derivative of -16/5*i**5 + 0*i + i**2 + 5*i**3 + 3 + 6*i**4. Let u(d) = 0. What is d?
-1/4, 0, 2
Let i(q) be the second derivative of -q**4/3 - 4*q**3 + 14*q**2 + 23*q. Suppose i(v) = 0. Calculate v.
-7, 1
Let t be 10 - (-7)/(231/(-6)). Let q = -712/77 + t. Solve 0*p + q*p**3 + 6/7*p**2 - 2/7 = 0.
-1, 1/2
Suppose 3*p + p = 4*q - 28, 5*q + 5*p = 5. Let u(n) = -n + 1. Let j(o) = -o**2 - 8. Let x(k) = q*u(k) + j(k). Suppose x(t) = 0. What is t?
-2
What is d in 3*d - 5*d - 2*d - d**3 + 5*d**3 = 0?
-1, 0, 1
Let k(a) be the second derivative of -a**9/22680 + a**8/10080 + 5*a**4/12 + 4*a. Let n(o) be the third derivative of k(o). Factor n(r).
-2*r**3*(r - 1)/3
Let r(k) be the first derivative of -4*k**3/3 + 2*k**2 + 4. Find h, given that r(h) = 0.
0, 1
Let 6*i**2 - 10/3*i**3 - 2/3 - 2*i = 0. Calculate i.
-1/5, 1
Let q = -9 - -15. Let c be q/(-3) - (-5 + 3). What is g in -4*g**3 - 2 + 4*g**3 - 3*g**2 + c*g**3 + g**4 + 5*g - g**3 = 0?
-2, 1
Let u(i) be the third derivative of 0 + 0*i + 0*i**4 + 1/80*i**5 - 1/8*i**3 - 4*i**2. Factor u(p).
3*(p - 1)*(p + 1)/4
Let k(d) be the first derivative of -d**4/36 - d**3/9 + d**2/2 - 4*d + 1. Let g(a) be the first derivative of k(a). Factor g(n).
-(n - 1)*(n + 3)/3
Let o = 12 + -8. Determine l so that -2 + 2*l**3 + o*l**3 - 5*l**3 - 3*l = 0.
-1, 2
Let j(g) be the first derivative of -8*g**5/15 - g**4/2 + 2*g**3/9 - 6. What is n in j(n) = 0?
-1, 0, 1/4
Let i(z) = 15*z**2 - 11*z - 4. Suppose -4 = m + 2. Let k(q) be the first derivative of -7*q**3/3 + 5*q**2/2 + 2*q - 1. Let n(y) = m*i(y) - 13*k(y). Factor n(g).
(g - 1)*(g + 2)
Suppose -46 = 5*z - 136. Let 21*a**2 + z*a**4 + 3*a**2 - 42*a**3 + 6*a**3 - 3*a**5 = 0. Calculate a.
0, 2
Let d = 1 + 1. 