**6/2 + 3*k**4/2 - 3*k**2/2 - 3. Suppose l(h) = 0. What is h?
-1, 0, 1
Suppose -2*z + 3*z = -54. Let v be 2/(-9) + (-174)/z. Factor 0*m**v + 1/6*m**2 + 1/3*m**5 + 0 + 0*m - 1/2*m**4.
m**2*(m - 1)**2*(2*m + 1)/6
Let y(u) = -u**2 - 4*u + 4. Let t be y(-4). Factor -s**3 + s - 11*s**4 - t*s**2 + 7*s**4 + s**5 + 7*s**3.
s*(s - 1)**4
Suppose -5*r - 33 = -4*p - 10, r = 2*p - 7. Solve -4/3*k**3 + 0*k - 2*k**4 + 2/3*k**p + 0 = 0 for k.
-1, 0, 1/3
Let l = 78 - 76. Factor 1/4*c**l - 1/2 - 1/4*c.
(c - 2)*(c + 1)/4
Let d be ((-1)/(-12))/((-40)/(-160)). Factor -1/3 + 0*j + d*j**2.
(j - 1)*(j + 1)/3
Let x(i) = 2*i**4 - 22*i**3 + 42*i**2 + 32*i - 22. Let n(t) = -4*t**4 + 43*t**3 - 83*t**2 - 65*t + 45. Let c(y) = -3*n(y) - 5*x(y). Solve c(u) = 0.
-1, 1/2, 5
Let f(m) be the second derivative of -9*m**5/20 + 7*m**4/8 - 3*m**2/4 + 14*m. Determine t so that f(t) = 0.
-1/3, 1/2, 1
Let n(h) = -h**3 + h. Let q be n(1). Factor 0*g**2 + 0*g**2 - g**5 + q*g**3 + g**3.
-g**3*(g - 1)*(g + 1)
Determine d so that -14/9*d**2 - 4/3 - 46/9*d = 0.
-3, -2/7
Factor 16*q**3 - 32*q**3 + 18 + 0*q**3 - q**4 + 3*q**4 - 48*q + 44*q**2.
2*(q - 3)**2*(q - 1)**2
Suppose 3*d - 20 = -5*b, 0 = b - 2*d - 1 - 3. Factor 1/2*s + 1/4*s**5 + 0 + 1/4*s**b - 1/4*s**2 - 3/4*s**3.
s*(s - 1)**2*(s + 1)*(s + 2)/4
Let f(b) be the first derivative of 0*b**2 - 1/4*b**4 + 0*b + 1/15*b**5 - 2 + 2/9*b**3. Factor f(o).
o**2*(o - 2)*(o - 1)/3
Let m(u) = -9*u - 162. Let b be m(-18). Factor -1/3*s**2 + 1/3*s**3 + 0 + b*s.
s**2*(s - 1)/3
Let k(v) be the second derivative of -1/5*v**2 + 0 - 1/5*v**4 - 2/25*v**5 - 2*v - 1/75*v**6 - 4/15*v**3. Solve k(a) = 0.
-1
Suppose 4*h - 45 = -h + 5*b, 0 = 2*h - b - 14. Factor -l**4 - l**4 + 2*l**2 - 6*l**3 - l**4 - h*l**2.
-3*l**2*(l + 1)**2
Factor 1/3*i**4 - 1/3*i**5 + 0*i**3 + 0*i + 0 + 0*i**2.
-i**4*(i - 1)/3
Let o(r) be the first derivative of -2*r**5/45 - r**4/9 + 2*r**3/27 + 2*r**2/9 + 43. Factor o(t).
-2*t*(t - 1)*(t + 1)*(t + 2)/9
Let k = 2/157 - -916/2041. Let -2/13*m**2 + 4/13*m**4 - 6/13*m**3 - 2/13 + k*m = 0. Calculate m.
-1, 1/2, 1
Let r(a) be the second derivative of a**8/2240 - a**7/420 + a**6/240 - a**4/6 - 2*a. Let p(q) be the third derivative of r(q). Let p(g) = 0. What is g?
0, 1
Let y(k) be the second derivative of 1/90*k**4 + 0 + 2/15*k**3 + 3/5*k**2 + 8*k. Suppose y(n) = 0. What is n?
-3
Factor -2/5*y**2 - 4/5*y + 2/5*y**3 + 0.
2*y*(y - 2)*(y + 1)/5
Let f = 239/90 + -13/5. Let y(n) be the second derivative of -f*n**4 - 2/27*n**3 + n + 0 + 0*n**2 + 0*n**5 + 1/135*n**6. Factor y(p).
2*p*(p - 2)*(p + 1)**2/9
Let f(t) = t - 3. Let d(g) = -2*g + 6. Let a(z) = 4*d(z) + 7*f(z). Let w be a(3). Solve 2 - y**3 + w - 2 = 0 for y.
0
Let w be ((-44)/(-1815)*11)/((-2)/(-5)). Solve -w*h**2 + 0 + 2/3*h = 0.
0, 1
Let o(h) be the first derivative of 0*h**2 - 3/8*h**4 + 5 + 0*h + 0*h**3 + 1/4*h**6 + 0*h**5. Factor o(p).
3*p**3*(p - 1)*(p + 1)/2
Let o(d) be the third derivative of d**6/24 - d**5/6 + 5*d**4/24 + 3*d**2 - 5*d. Factor o(n).
5*n*(n - 1)**2
Let r(o) = 21*o**3 - 35*o**2 + 6*o + 8. Let m(l) = 7*l**3 - 12*l**2 + 2*l + 3. Let d(w) = -8*m(w) + 3*r(w). Find t such that d(t) = 0.
0, 2/7, 1
Suppose -5*z + 100 = 30. Factor 24*k + 3*k**3 - z*k**2 - k**2 - 9 - 3.
3*(k - 2)**2*(k - 1)
Let z(f) be the second derivative of -f**8/8960 + f**7/2520 + f**6/2880 - f**5/240 - f**4/12 - 2*f. Let i(c) be the third derivative of z(c). Factor i(w).
-(w - 1)**2*(3*w + 2)/4
Find p such that -2/9 - 6*p**4 + 8/3*p**2 - 4/9*p + 4*p**3 = 0.
-1/3, 1/3, 1
Let q(w) be the first derivative of -w**4 - 5. Factor q(v).
-4*v**3
Suppose 5*v**2 - 4*v**2 + 4*v**2 - 4*v - 3*v**2 = 0. What is v?
0, 2
Let q be 3 + 4/(-12) + -2. Determine w, given that 8/15*w - q*w**2 + 2/15 = 0.
-1/5, 1
Factor -2*y**2 - 6*y**3 + 3*y**4 - 6*y**4 - 6*y**2 + 5*y**2.
-3*y**2*(y + 1)**2
Let x(k) = -10*k**3 + 13*k**2 + 3*k - 13. Let w(p) = -3*p**3 + 4*p**2 + p - 4. Let g(r) = -7*w(r) + 2*x(r). Factor g(q).
(q - 2)*(q - 1)*(q + 1)
Factor -12 + 22*x**4 + 9*x - 2*x**4 - 8*x**2 - 4*x**5 + 10*x**3 - 34*x**3 + 19*x.
-4*(x - 3)*(x - 1)**3*(x + 1)
Let s(n) be the second derivative of -1/10*n**6 - 1/2*n**4 + 13/40*n**5 - n + 0*n**2 + 1/84*n**7 + 0 + 1/3*n**3. Find d, given that s(d) = 0.
0, 1, 2
Suppose -h + 13 = 4*w - 2*h, -2*w - 21 = 5*h. Let l be (-18)/(-14) - 4/4. Factor -2/7*m**3 - 2/7*m**w + 2/7 + l*m.
-2*(m - 1)*(m + 1)**2/7
Let b = 4 + -2. Let x be (-52)/(-16) - b/8. Factor r**4 - r**x + 3*r**2 + r**2 + r + 0*r - 5*r**2.
r*(r - 1)**2*(r + 1)
Let k(c) = c**2 - 11*c - 22. Let r = -19 + 32. Let q be k(r). Suppose 0*i**2 - 1/4*i**q - 1/2*i + 1/4 + 1/2*i**3 = 0. Calculate i.
-1, 1
Let g = -28891/4 - -7284. Let h = g + -61. Factor h*j**4 + 3/4*j**3 + 1/4*j + 3/4*j**2 + 0.
j*(j + 1)**3/4
Factor 0*n + 9/2*n**2 + 0 - 1/2*n**3.
-n**2*(n - 9)/2
Let q(h) = -27*h + 108. Let a be q(4). Suppose -2/7*w**3 + 0*w - 3/7*w**4 + 1/7*w**2 + a = 0. What is w?
-1, 0, 1/3
Let o(u) be the first derivative of -2 + 1/6*u**2 - 2/3*u + 1/9*u**3. Factor o(s).
(s - 1)*(s + 2)/3
Let k(r) be the second derivative of r**6/10 - 3*r**5/20 - 7*r - 3. Suppose k(j) = 0. What is j?
0, 1
Let c = 61381/240 + -1023/4. Let v(q) be the third derivative of 0 - 2*q**2 + 1/480*q**6 + 0*q + 0*q**4 + 0*q**3 + c*q**5. Suppose v(i) = 0. What is i?
-1, 0
Suppose k - 2*i = 0, -4*k - 3*i - 6 = -50. Let q be (-6)/(-3) + k/(-5). Factor -6/5*p - q*p**2 - 4/5.
-2*(p + 1)*(p + 2)/5
Let g(m) be the third derivative of 0*m + 0*m**4 + 0 + 0*m**5 - 4*m**2 + 0*m**3 - 1/540*m**6 - 1/945*m**7. Factor g(o).
-2*o**3*(o + 1)/9
Let w = 47/40 - 17/40. Factor 1/2*a**5 + 0*a + 1/4 - 1/2*a**3 - a**2 + w*a**4.
(a - 1)*(a + 1)**3*(2*a - 1)/4
Let r(j) be the second derivative of -1/39*j**3 - 3*j - 1/13*j**2 + 1/130*j**5 + 1/78*j**4 + 0. Let r(f) = 0. What is f?
-1, 1
Let m be (-3)/18*(-16)/1. Suppose 102*n - 92*n = 20. Factor 2/3 - 10/3*b + m*b**n.
2*(b - 1)*(4*b - 1)/3
Let n(u) be the first derivative of 1/4*u**4 - 1 - 2*u - 3/2*u**2 + 0*u**3. Find f such that n(f) = 0.
-1, 2
Let u(m) be the second derivative of -7/18*m**3 + 0 - m + 1/3*m**2 + 1/4*m**4 - 1/12*m**5 + 1/90*m**6. Determine j so that u(j) = 0.
1, 2
Let d be (3 - 1)*3/(-2). Let b(y) = y + 5. Let k be b(d). Let -2/5*n**k + 2/5*n + 0 = 0. What is n?
0, 1
Let f(d) be the third derivative of -d**7/280 - d**6/40 - 3*d**5/80 + 27*d**2. Factor f(w).
-3*w**2*(w + 1)*(w + 3)/4
Let n(v) be the third derivative of 0*v + 1/14*v**3 - 3*v**2 + 0*v**4 + 0 - 1/140*v**5. Solve n(k) = 0.
-1, 1
Let w(h) be the first derivative of 0*h + 3/2*h**2 + h**3 + 10. Find g, given that w(g) = 0.
-1, 0
Suppose 0*y + 0 - 2/3*y**4 - 2/3*y**2 - 4/3*y**3 = 0. Calculate y.
-1, 0
Let 8*m + 16 + 16*m**2 - 7*m**2 - 2*m**2 - 6*m**2 = 0. What is m?
-4
Factor -6*w + 3 + 6*w**3 - 6*w**4 - 2*w**4 + 5*w**4.
-3*(w - 1)**3*(w + 1)
Let j = 2894/3655 - -6/731. What is k in 24/5*k + j*k**2 + 36/5 = 0?
-3
Suppose 3*r - 362 = r - 4*m, -163 = -r + 4*m. Let k be 6/(-33) - r/(-55). Factor 2/7*x**k + 2/7 - 2/7*x**2 - 2/7*x.
2*(x - 1)**2*(x + 1)/7
Let f(t) = -t**2 + 5*t - 1. Let a(b) = 3*b**2 - 19*b + 5. Let q(i) = 6*a(i) + 22*f(i). Factor q(o).
-4*(o - 1)*(o + 2)
Suppose t - 4 = -0*t. Solve 12*s**2 + s**t + 6*s**4 - 3*s**5 - 18*s**3 - 3*s + 5*s**4 = 0 for s.
0, 1
Let j(x) be the second derivative of -2*x**2 - x**3 - x + 0 - 1/6*x**4. Suppose j(y) = 0. What is y?
-2, -1
Suppose -4*s = 3*y + 8 - 0, -4*s = 8. Factor h**2 + y*h**2 - h + 1 + 3*h.
(h + 1)**2
Factor 20*t**3 + 8*t**2 - 82 + 82 - 28*t**4.
-4*t**2*(t - 1)*(7*t + 2)
Determine z, given that -2/3 + 1/3*z**5 + 2/3*z**4 - 2/3*z**3 - 7/3*z - 8/3*z**2 = 0.
-1, 2
Let b = 9128 - 730231/80. Let k(p) be the second derivative of b*p**5 - 1/12*p**3 - 7/48*p**4 + 0*p**2 + p + 0. Factor k(d).
d*(d - 1)*(9*d + 2)/4
Let a(j) = 5*j**2 - 150*j + 1125. Let n(x) = 20*x**2 - 600*x + 4500. Let b(c) = 25*a(c) - 6*n(c). Factor b(r).
5*(r - 15)**2
Determine d, given that -69*d + 63*d - 4*d**3 + 56*d**2 - 190*d = 0.
0, 7
Let i(v) = -v - 2. Let h be i(-5). Let j be h/((0 - -1)/1). Let 3*u**3 - u**4 + 0*u**2 - 2*u**j + u**2 - u = 0. What is u?
-1, 0, 1
Let v(w) be the second derivative of 2*w**7/21 - 2*w**6/15 - w**5/5 + w**4/3 + 8*w. Factor v(s).
4*s**2*(s - 1)**2*(s + 1)
Suppose -3*d = -z - 41, -4*d - d - 2*z = -83. Suppose -6*p + d = -p. Factor 6 + 0*q**4 + p*q**