/(-18) + (-24)/108. Factor -4*w + 0 + m*w**2 - 1 - 1 - 4.
2*(w - 3)*(w + 1)
Determine k so that 1/3*k + 0 - 1/3*k**2 = 0.
0, 1
Suppose -4 = 4*o - 16. Suppose 19 = o*i + 4. Factor -1/2*d**4 + 1/2*d**2 + 0 + 1/4*d - 1/4*d**i + 0*d**3.
-d*(d - 1)*(d + 1)**3/4
Let r(k) = -3*k**3 + 2*k**2 - k - 2. Let t(o) = o**3 + o. Suppose z - 2*j - 9 - 3 = 0, -21 = -2*z + 3*j. Let v(i) = z*t(i) + 3*r(i). Solve v(q) = 0 for q.
-1, 1, 2
Let d(y) be the third derivative of -y**7/35 + y**6/60 + y**5/18 + y**4/36 + 36*y**2. Factor d(a).
-2*a*(a - 1)*(3*a + 1)**2/3
Suppose -w = 1 - 5. Factor 5*n**3 + n**3 - w*n**3 - 2*n**2.
2*n**2*(n - 1)
Suppose -u + 4*h + 5 = 0, 5*u + 3*h + 2*h = 0. Let t be u - (-3)/(3/(-1)). Factor t - 4/9*s**2 - 2/9*s**3 - 2/9*s.
-2*s*(s + 1)**2/9
Suppose 5*i - 2*i = 0. Let j be (i + 2/(-4))*-6. Factor -6/5*m - 2/5*m**j + 2/5 + 6/5*m**2.
-2*(m - 1)**3/5
What is l in -1/2 - 2*l**2 - 5/2*l = 0?
-1, -1/4
Factor 0*w**3 - w**2 + w**3 + 3*w**2 - 2*w**3 - w**4.
-w**2*(w - 1)*(w + 2)
Suppose -3 + 0 = -f. Suppose f*o + 2*m - 4 - 4 = 0, -2*o = -2*m - 12. Factor -5*l**4 - 4*l**5 - 32*l**3 + 2 + 23*l**o + 28*l**2 - 4*l - 8*l.
-2*(l - 1)**4*(2*l - 1)
Let u(k) be the second derivative of 5/6*k**4 + 0 + k + 2/5*k**5 + 0*k**2 + 1/3*k**3. What is h in u(h) = 0?
-1, -1/4, 0
Factor 15*b**3 - 3*b**2 - 3*b**5 - 83*b**4 + 59*b**4 + 15*b**5.
3*b**2*(b - 1)*(2*b - 1)**2
Let r(k) = -5*k**3 - 9*k**2 - 4*k - 3. Let g(q) = -4*q**3 - 8*q**2 - 4*q - 2. Let s(n) = -3*g(n) + 2*r(n). Solve s(u) = 0.
-2, -1, 0
Let b = 55/96 + 3/32. Factor b*z + 0 - 2/3*z**2.
-2*z*(z - 1)/3
Let l(p) be the first derivative of -p**3 + 1 + 3/2*p**4 - 3*p**2 + 0*p + 3/5*p**5. Solve l(f) = 0.
-2, -1, 0, 1
Let m(c) be the first derivative of c**4/12 - c**3 + 9*c**2/2 + 4*c + 9. Let b(l) be the first derivative of m(l). Suppose b(y) = 0. What is y?
3
Let p(a) be the third derivative of -1/8*a**4 + 0 + 0*a**3 + 0*a + 7*a**2 - 1/20*a**5. Factor p(z).
-3*z*(z + 1)
Let g(z) = z**4 - z**3 - 4*z**2 + z - 3. Let m = 17 + -9. Let b = m + -11. Let f(x) = -x**2 - 1. Let i(s) = b*f(s) + g(s). Factor i(h).
h*(h - 1)**2*(h + 1)
Let l(q) = -6*q**4 + 2*q**3 + 10*q**2 + 2*q - 16. Let i(z) = -13*z**4 + 5*z**3 + 19*z**2 + 4*z - 33. Let b(c) = -4*i(c) + 9*l(c). Suppose b(r) = 0. What is r?
-3, -1, 1, 2
Suppose 2*w = -2*w + 10*w. Solve -2*j**3 - 4/7*j**2 - 4/7*j**4 + 0 + 6/7*j**5 + w*j = 0 for j.
-1, -1/3, 0, 2
Let z be 1 - (2 - (-15)/(-5)). Factor 6/7*u - 3/7 - 3/7*u**z.
-3*(u - 1)**2/7
Let r(p) be the first derivative of 5*p**6/33 - 16*p**5/55 - 2*p**4/11 + 20*p**3/33 - p**2/11 - 4*p/11 + 34. Suppose r(h) = 0. What is h?
-1, -2/5, 1
Let r(v) = v**2 + v. Let g(i) = -i**2 - 21*i. Let d(t) = 2*g(t) + 6*r(t). Factor d(b).
4*b*(b - 9)
Let w(y) be the first derivative of -2 - y - y**2 - 1/3*y**3. Factor w(j).
-(j + 1)**2
Let o(i) be the second derivative of -i**6/6 + i**5/4 + 5*i**4/12 - 5*i**3/6 + 62*i. Factor o(t).
-5*t*(t - 1)**2*(t + 1)
Let a(q) = -q**2 + 8*q - 9. Let f be a(7). Let l(p) = p**2 + 7*p + 1. Let b(g) = 6*g. Let y(d) = f*l(d) + 3*b(d). Factor y(c).
-2*(c - 1)**2
Factor 1/3*c**2 + 1/3*c - 2/3.
(c - 1)*(c + 2)/3
Let c(w) = 3*w**3 + 6*w**2 - 3*w - 3. Let o(m) = -m**4 + 2*m**3 + 7*m**2 - 4*m - 4. Let h(u) = -4*c(u) + 3*o(u). Let h(f) = 0. What is f?
-1, 0
What is f in 2 - 1818*f + 1812*f - 10*f**2 + 2 = 0?
-1, 2/5
Let a be ((-36)/(-48))/(1/4). Let i(g) be the first derivative of 1/15*g**3 + 1/10*g**2 - a + 0*g. Factor i(p).
p*(p + 1)/5
Let f(d) be the third derivative of -d**5/30 - d**4/6 + d**3 - d**2. Factor f(v).
-2*(v - 1)*(v + 3)
Let i = -633 + 1903/3. Solve -4/3*b**3 + 2/3*b + 2/3 - i*b**2 + 2/3*b**5 + 2/3*b**4 = 0 for b.
-1, 1
Factor -1/2*p**2 + 1/4*p + 1/2*p**4 - 1/4*p**5 + 0*p**3 + 0.
-p*(p - 1)**3*(p + 1)/4
Let t be 12/5 + (-12)/30. Suppose -4*w = -t*i - 16, 5*i + 3*w - 28 = -3. Find l such that -2*l + 3*l**4 - 3*l**3 - 5*l**2 + i*l**2 + 5*l = 0.
-1, 0, 1
Let n(w) be the third derivative of w**5/12 + w**4/6 - w**3/6 - 48*w**2. Factor n(h).
(h + 1)*(5*h - 1)
Let y be ((81/20)/27)/((-1)/(-5)). What is u in -3/2*u - 3/4*u**2 - y = 0?
-1
Let o(h) = 8*h**2 + 10*h - 37. Let l(v) = v**2 + 1. Let y(d) = 3*l(d) - o(d). Suppose y(i) = 0. What is i?
-4, 2
Suppose -3*s = -s - 6. Let p(m) = 72*m**3 - 80*m**2 - 108*m + 100. Let y(u) = 8*u**3 - 9*u**2 - 12*u + 11. Let h(c) = s*p(c) - 28*y(c). Solve h(l) = 0.
-1, 1/2, 2
Let h(d) be the third derivative of d**6/420 - d**4/84 - 3*d**2. Factor h(a).
2*a*(a - 1)*(a + 1)/7
Factor -18*r - 6*r**2 - 18 - 2/3*r**3.
-2*(r + 3)**3/3
Suppose 2*p - 42 = -2*t + 4*p, -36 = -t + 4*p. Let x be t/9 - 4/(-18). Find o, given that -x*o**2 - o - o + 0*o**2 + 0*o = 0.
-1, 0
Let h be 7/2*12/2. Determine c, given that -10*c**4 + 24*c**2 - h*c**3 + 0*c**4 + 2*c**4 - 7*c**4 + 12*c = 0.
-2, -2/5, 0, 1
Factor 0 - 6/5*o - 6/5*o**3 - 3*o**2.
-3*o*(o + 2)*(2*o + 1)/5
Let d(n) be the third derivative of -n**7/945 - n**6/270 - n**5/270 - 15*n**2. Factor d(g).
-2*g**2*(g + 1)**2/9
Determine p, given that -16/11 - 12/11*p**2 - 2/11*p**3 - 24/11*p = 0.
-2
Let k(q) = 8*q**4 + 27*q**3 - 27*q**2 - 8*q + 17. Let y(s) = 3*s**4 + 9*s**3 - 9*s**2 - 3*s + 6. Let l(c) = -6*k(c) + 17*y(c). Factor l(t).
3*t*(t - 1)**3
Let l(j) be the first derivative of 2*j**3/3 - 4*j**2 + 8*j + 2. Let l(n) = 0. Calculate n.
2
Let l(j) be the second derivative of -j**8/2240 - j**7/1260 + j**4/6 - 4*j. Let d(r) be the third derivative of l(r). Find o, given that d(o) = 0.
-2/3, 0
Suppose 4*k + 8 = 5*o, 2*k + 0*k = -4. Let 0*g**2 + o + 1/2*g**3 - 1/4*g + 0*g**4 - 1/4*g**5 = 0. What is g?
-1, 0, 1
Let k(m) = -m - 4*m**2 + 4*m + 7*m - 2*m. Let d(a) = 3*a**2 - 8*a - 1. Let b(n) = 6*d(n) + 5*k(n). Factor b(c).
-2*(c + 1)*(c + 3)
Let h(v) be the first derivative of -1/6*v**4 + 1 - 4/9*v**3 + 0*v - 1/3*v**2. Find g, given that h(g) = 0.
-1, 0
Let p be (11 - 203/21)*6/4. Determine t so that 0 - 8/7*t - 60/7*t**3 + 44/7*t**4 - 12/7*t**5 + 36/7*t**p = 0.
0, 2/3, 1
Suppose -32 = -2*c + 5*q, c - 3*q + q = 16. Let w = c + -110/7. What is x in 0 + w*x - 2/7*x**3 + 2/7*x**4 - 2/7*x**2 = 0?
-1, 0, 1
Let g(q) = q**3 - 15*q**2 - 17*q + 16. Let k be g(16). Let d(o) be the first derivative of 1 + k*o + 1/5*o**3 + 3/5*o**2. Factor d(i).
3*i*(i + 2)/5
Let z = -2 + 2. Let j be (6/(-5))/((-12)/80). Factor 2*t**4 + j*t**3 + z*t + 2*t + 12*t**2 + 6*t + 2.
2*(t + 1)**4
Let q(b) be the first derivative of 1/4*b**4 + 4/3*b**3 - 9/10*b**5 + 1/2*b + 1/3*b**6 - 3/2*b**2 + 1. Determine y so that q(y) = 0.
-1, 1/4, 1
Let n be 4/3*12/8. Let s = n + 1. Solve -v**3 - 40*v - 16 - 2*v**4 - 36*v**2 - 6*v**3 - 7*v**s = 0.
-2, -1
Suppose 4/5*y**4 + 0 + 0*y**2 - 6/5*y**3 + 2/5*y = 0. Calculate y.
-1/2, 0, 1
Let x(t) be the second derivative of 2*t**6/9 + 9*t**5/5 + 5*t**4/9 - 6*t**3 - 20*t**2/3 - 32*t. Let x(a) = 0. Calculate a.
-5, -1, -2/5, 1
Let x(a) be the second derivative of a**4/12 - a**2/2 - a. Factor x(v).
(v - 1)*(v + 1)
Let s be 12/4 + (-5 - -2). Let x(u) be the second derivative of 1/2*u**2 + 1/6*u**3 + s - 1/20*u**5 - u - 1/12*u**4. Factor x(n).
-(n - 1)*(n + 1)**2
Let w(u) be the first derivative of 1/10*u**5 + 9/2*u + 11/3*u**3 + 4 - u**4 - 6*u**2. Factor w(z).
(z - 3)**2*(z - 1)**2/2
Let m(t) be the third derivative of -t**6/90 - 4*t**3/3 + 5*t**2. Let i(f) be the first derivative of m(f). Let i(x) = 0. What is x?
0
Factor 12/5 - 2/5*l**3 + 16/5*l**2 - 26/5*l.
-2*(l - 6)*(l - 1)**2/5
Let o be (-1)/90*(-48)/64. Let w(l) be the third derivative of -1/36*l**4 + 0 + 1/36*l**5 + 0*l - o*l**6 - 3*l**2 + 0*l**3. Factor w(z).
-z*(z - 1)*(3*z - 2)/3
Suppose 0*z + 4/7 - 1/7*z**2 = 0. What is z?
-2, 2
Let k(t) be the first derivative of 3*t + 0*t**2 + 1/6*t**3 + 1/12*t**4 - 1. Let g(l) be the first derivative of k(l). Factor g(a).
a*(a + 1)
Let r(w) be the third derivative of -w**6/1080 - w**5/180 + w**3/3 + 3*w**2. Let z(y) be the first derivative of r(y). Factor z(k).
-k*(k + 2)/3
Determine r so that 90*r**4 + 6 - 84*r**4 + 3*r**3 + 3*r**5 - 9*r**3 - 12*r**2 + 3*r = 0.
-2, -1, 1
Let c(l) be the second derivative of l**4/3 + 2*l**3/3 - 4*l**2 - 3*l. Suppose c(u) = 0. What is u?
-2, 1
Suppose -4*q + 33 = 5*m, 0*m = 3*m - 15. Factor -3/5*s - 3*s**3 - 24/5*s**q + 6/5.
-3*(s + 1)**2*(5*s - 2)/5
Let j(w) be the first derivative of -w**5/25 + 3*w**4/20 - w**3/5 + w**2/10