 + 1)**2/3
Let k be (3 - 2) + -3 - 65/(-30). Suppose 1/6*o - 1/6 - k*o**3 + 1/6*o**2 = 0. Calculate o.
-1, 1
Determine i, given that -i - 3*i + 19*i**4 - 13*i**3 - 19*i**2 + 7*i**5 + 10*i = 0.
-3, -1, 0, 2/7, 1
Suppose -1/3*h - h**2 + 0 - h**3 - 1/3*h**4 = 0. What is h?
-1, 0
Let j be 1*(-3 - -1)*-2. Let i be (-48)/(-20)*j/8. What is d in 4/5*d**4 + i*d**3 - 8/5*d**2 - 8/5*d - 2/5*d**5 + 0 = 0?
-1, 0, 2
Let v(c) = -2*c**2 - 4*c + 4. Let u(x) = -5*x**2 - 9*x + 9. Let a(m) = m**3 + 8*m**2 + 7*m - 4. Let p be a(-7). Let w(h) = p*u(h) + 9*v(h). Factor w(z).
2*z**2
Let y(q) be the first derivative of -2*q**6/15 + 4*q**5/25 + q**4/5 - 4*q**3/15 + 31. Suppose y(t) = 0. Calculate t.
-1, 0, 1
Let h(b) = b**4 + b**3 + 1. Let x(u) be the first derivative of 6*u**5/5 + 3*u**4 - 2*u**3/3 + 8*u - 3. Let i(o) = -8*h(o) + x(o). Factor i(w).
-2*w**2*(w - 1)**2
Let f(s) be the first derivative of s**5/5 - s**4/2 - s**3 + 4*s**2 - 4*s + 6. Determine h, given that f(h) = 0.
-2, 1, 2
Let s(x) = -x**2 - 7*x - 2. Let u be s(-7). Let d(k) = -k**3 + k**2 + 3*k + 1. Let h be d(u). Suppose -2*q**3 - h*q**4 - 1 + q**2 + 1 - 4*q**5 = 0. What is q?
-1, 0, 1/4
Let r be (-6)/(-21) + (-8)/28. Let o(a) be the second derivative of -1/36*a**4 + 0*a**3 + r - 3*a - 1/10*a**6 + 0*a**2 + 1/10*a**5. Factor o(p).
-p**2*(3*p - 1)**2/3
Let t be (-3)/(-4) + 0/(-2). Let q be (-8 - -8)*(-4)/24. Factor t - 3/4*o**2 + q*o.
-3*(o - 1)*(o + 1)/4
Find u, given that 0*u**3 - 10*u - 4*u**3 - 12*u**2 + 12*u**4 - 3 - 13*u**4 - 2*u**3 = 0.
-3, -1
Let d(l) be the third derivative of -l**7/42 + l**6/12 + l**5/3 - 5*l**4/3 + 13*l**2. Factor d(i).
-5*i*(i - 2)**2*(i + 2)
Let b(d) be the second derivative of -d**4/72 - d**3/18 - d**2/12 - 4*d. Factor b(r).
-(r + 1)**2/6
Let q(n) = 3*n + 1. Let y be q(2). Let r(a) = -a**3 + 7*a**2 + a - 7. Let u be r(y). Factor u - 1/3*t**5 + 4/3*t**4 - 2*t**3 - 1/3*t + 4/3*t**2.
-t*(t - 1)**4/3
Let p(w) = -6*w**3 + 154*w**2 - 306*w + 226. Let x(v) = -v**3 + 31*v**2 - 61*v + 45. Let q(f) = 3*p(f) - 14*x(f). Determine l, given that q(l) = 0.
2, 3
Let z(c) be the first derivative of 4*c**5/5 + 7*c**4/4 + 2*c**3/3 - c**2/2 - 17. Let z(w) = 0. What is w?
-1, 0, 1/4
Let a(m) be the third derivative of m**5/30 + m**4/6 + m**3/3 + 10*m**2. Factor a(n).
2*(n + 1)**2
Let t(b) be the third derivative of b**7/12600 - b**6/1800 + b**4/24 - 7*b**2. Let d(f) be the second derivative of t(f). Let d(m) = 0. What is m?
0, 2
Suppose -2*m + 10 = -0. Factor m*i**2 - 6*i**2 - 5*i**2 + 2*i**3 + 0*i**3 + 4*i.
2*i*(i - 2)*(i - 1)
Suppose -2/3 + 2/3*s**3 + 2*s - 2*s**2 = 0. What is s?
1
Factor 9 - 1 + 2*y**2 + 8 - 8 - 8*y.
2*(y - 2)**2
Let n(y) be the third derivative of -y**8/672 - y**7/70 - 13*y**6/240 - y**5/10 - y**4/12 - 41*y**2. Factor n(p).
-p*(p + 1)**2*(p + 2)**2/2
Let c(q) = -7*q**5 - 8*q**4 - 7*q**3 - 11. Let u(i) = 2*i**5 + 2*i**4 + 2*i**3 + 3. Let h(z) = -6*c(z) - 22*u(z). Factor h(r).
-2*r**3*(r - 1)**2
Let c(h) be the first derivative of 1/12*h**2 - 1/24*h**4 + 3 + 0*h**3 + 0*h. Factor c(n).
-n*(n - 1)*(n + 1)/6
Let m(j) = -j**3 + j + 7. Let c be m(0). Factor 0*b + c*b - b**2 - 8*b.
-b*(b + 1)
Let l(w) be the third derivative of 5*w**8/1344 - w**7/105 - w**6/120 + w**5/24 - w**4/96 - w**3/12 + 8*w**2. Factor l(q).
(q - 1)**3*(q + 1)*(5*q + 2)/4
Let g(n) = -n - 4. Let p be g(-9). Let j = -3 + p. Find u such that 4*u**j - u**4 - 2*u**2 - u**4 = 0.
-1, 0, 1
Let y(r) = 4*r**2 + r + 1. Let s(j) = -3*j**2 - j. Suppose -4*p + 5 = -3. Let k(u) = p*y(u) + 3*s(u). Factor k(b).
-(b - 1)*(b + 2)
Let a(d) be the second derivative of 2*d**7/63 - 4*d**6/45 - d**5/5 - 34*d. Factor a(m).
4*m**3*(m - 3)*(m + 1)/3
Let u = 17 - 14. Suppose 7*h + 4 = g + 3*h, u*h + 3 = 4*g. What is q in -4/7*q**3 - 2/7*q**2 + g*q + 0 - 2/7*q**4 = 0?
-1, 0
Let c(m) be the third derivative of 0*m - 4*m**2 + 0 + 1/110*m**5 + 0*m**3 + 1/660*m**6 + 1/66*m**4. Determine g, given that c(g) = 0.
-2, -1, 0
Let w = 1/26 - -461/182. Factor -2/7*q**5 - w*q**3 + 0 - 4/7*q + 2*q**2 + 10/7*q**4.
-2*q*(q - 2)*(q - 1)**3/7
Suppose -5*i + 17 - 137 = 0. Let k be (6/i)/((-6)/8). Solve 1/3 + 2/3*w + k*w**2 = 0 for w.
-1
Let v = 141/20 - 7. Let i(n) be the third derivative of -v*n**6 + 0*n + 0*n**4 - 4*n**2 + 0 + 1/20*n**5 + 1/70*n**7 + 0*n**3. Determine p so that i(p) = 0.
0, 1
Suppose 2*n + 18 = -2*z, 6*n + 15 = -z + 2*n. Let v = z - -7. Factor 1/2*x**2 + 3/4*x**4 + v + 0*x - 5/4*x**3.
x**2*(x - 1)*(3*x - 2)/4
Factor 2*k**2 + 33 - 7*k - 10*k - 11*k + 65.
2*(k - 7)**2
Suppose 1/4*m**2 + 1/2 - 3/4*m = 0. What is m?
1, 2
Let g(l) = 1. Let z(y) = -4*y**2 + 4*y + 4. Let m(b) = 4*g(b) - z(b). Factor m(f).
4*f*(f - 1)
Let w be ((-2 - 0) + 3)*3. Factor 1 + 1 - 6 - 6*s**w + 6*s + 2*s**4 + 2*s**2 + 0*s**4.
2*(s - 2)*(s - 1)**2*(s + 1)
Let q be (6/(-4))/((-7)/14). Let -14 - 4 - 48*j**2 + 64*j**q - 30*j - 18*j**5 - 66*j + 30*j**4 - 14 = 0. What is j?
-1, -2/3, 2
Let c(p) be the first derivative of -p**4/22 - 2*p**3/33 + 5*p**2/11 - 6*p/11 + 14. Determine o so that c(o) = 0.
-3, 1
Let q(i) be the second derivative of 0 + 0*i**2 - 4*i + 0*i**3 + 1/14*i**7 + 0*i**4 + 1/5*i**6 + 3/20*i**5. Suppose q(h) = 0. What is h?
-1, 0
Let j = -13 + 15. Solve -3*m**3 + 4 - 4 + 7*m**2 - 4*m**j = 0 for m.
0, 1
Let v(z) be the third derivative of 0*z + 5*z**2 - 3/7*z**3 + 0 - 1/210*z**5 + 1/14*z**4. Factor v(f).
-2*(f - 3)**2/7
Let m(t) = -5*t**2 - 7*t - 8. Let l(s) = 6*s**2 + 6*s + 9. Let j(g) = -2*g + 3. Let f be j(3). Let z(q) = f*m(q) - 2*l(q). Factor z(b).
3*(b + 1)*(b + 2)
Factor -4/5*i**3 + 0*i**2 + 2/5 + 4/5*i - 2/5*i**4.
-2*(i - 1)*(i + 1)**3/5
Let r(z) = -4*z**5 - 4*z**4 + 4*z**3 + 6*z**2 - 2*z + 2. Let d(h) = -h**2 + h - 1. Let c(s) = 2*d(s) + r(s). Find t, given that c(t) = 0.
-1, 0, 1
Let y(c) be the second derivative of c**4/4 - 3*c**3 - 21*c**2/2 + 3*c + 3. Factor y(f).
3*(f - 7)*(f + 1)
Let b(l) be the second derivative of -l**4/48 + l**3/24 + 8*l. Solve b(t) = 0.
0, 1
Suppose 4*c - a - 18 = 14, 4*c + a = 32. Let l be -14*(2 + (-18)/c). Factor -l*o**3 - o**2 + 7/2*o + 1.
-(o - 1)*(o + 1)*(7*o + 2)/2
Let j(p) be the first derivative of 3 + 1/3*p**3 + p + p**2. Factor j(k).
(k + 1)**2
Let x(g) be the second derivative of g**6/45 - g**5/60 - g**4/12 + g**3/18 + g**2/6 + g. Factor x(c).
(c - 1)**2*(c + 1)*(2*c + 1)/3
Let f(o) = -3*o - 5. Let m be f(-5). Let i be 4/m - (-36)/10. Factor s**2 - i*s - 4 - s**2 - s**2.
-(s + 2)**2
Factor -4*a**2 - 2*a + 0*a**2 + 0*a**3 - 2*a**3 + 0*a.
-2*a*(a + 1)**2
Suppose -q - 1 = -3*p + 8, 0 = -4*q - 12. Suppose 3*h**2 - 199*h + 202*h + 0*h**p = 0. What is h?
-1, 0
Let d(w) be the third derivative of 0 + 0*w**4 - 3*w**2 + 0*w + 0*w**6 - 1/1344*w**8 + 0*w**5 + 0*w**3 + 1/840*w**7. Find t such that d(t) = 0.
0, 1
Factor -19*w**2 + 22*w**2 + 0*w**4 - 3*w**4.
-3*w**2*(w - 1)*(w + 1)
Suppose 4*q + q = 0. Suppose q*c + 3*c - 9 = 0. Solve 6*u**3 + u + 12*u**3 - 2*u**c - 8*u**2 = 0 for u.
0, 1/4
Let n(y) be the second derivative of -y**3/6 + 11*y**2/2 + 2*y. Let f be n(9). Let 4 - z**2 + z**2 + 2*z - f*z**2 = 0. Calculate z.
-1, 2
Let h be ((-6)/(-1))/((-39)/(-26)). Find j, given that 4*j + 6*j**2 - 10*j**2 + h + 4 = 0.
-1, 2
Let n(b) = -b**2 - 5*b + 5. Let y be n(-6). Let q(r) = 4*r**2. Let w be q(y). Solve -w*d + 5*d - 2*d**2 + d = 0 for d.
0, 1
Factor -5 - 21*q + 21*q + 12*q**2 - 4*q**3 - 11.
-4*(q - 2)**2*(q + 1)
Let i(v) be the first derivative of v**4/4 - v**3/3 - v**2/2 + 2*v + 1. Let l be i(2). Suppose -4*t**4 + t**l - 4*t**3 - 6*t**2 - 5*t**3 = 0. Calculate t.
-2, -1, 0
Let v(u) be the third derivative of u**7/70 - u**6/60 + u**5/120 + u**4/24 + 4*u**2. Let z(q) be the second derivative of v(q). Factor z(r).
(6*r - 1)**2
Let b(l) = -l**3 + 6*l**2 + 8*l - 3. Suppose u - 17 = 2*m, 3*u - 5*m = 11 + 35. Let s be b(u). Factor -1/2*h**5 + 0 + 0*h**2 - 1/2*h + 0*h**s + h**3.
-h*(h - 1)**2*(h + 1)**2/2
Let s(c) be the first derivative of -c**7/560 + 7*c**6/720 - c**5/120 - 2*c**3/3 + 5. Let r(m) be the third derivative of s(m). Find v such that r(v) = 0.
0, 1/3, 2
Let u(h) be the third derivative of -5*h**8/168 - 13*h**7/105 + h**6/10 + 2*h**5/3 - 2*h**4/3 - 6*h**2. Let u(l) = 0. What is l?
-2, 0, 2/5, 1
Let a = 25/132 - -2/33. Factor 0*f + 0 + a*f**2 - 1/4*f**3.
-f**2*(f - 1)/4
Let s(n) = 3*n - 3*n**2 + 10*n - 15*n - 6. Let y