r - 6. Let y(q) = -m(q) - 6*s(q). What is u in y(u) = 0?
0, 1
Let h(b) = 0 + b + 4 - 3. Let a be h(2). Factor 0 - 1/2*r**a - 1/2*r**2 + 0*r.
-r**2*(r + 1)/2
Factor 2/5*p**2 + 4/5*p + 2/5.
2*(p + 1)**2/5
Let n(y) be the first derivative of y**6/24 + y**5/20 - y**4/16 - y**3/12 + 11. Factor n(z).
z**2*(z - 1)*(z + 1)**2/4
Let u be (-74)/76 + (4 - 3). Let q = 87/418 - u. Factor 0 + 0*v**2 + 0*v - q*v**3 + 2/11*v**4.
2*v**3*(v - 1)/11
Let y(a) be the third derivative of -1/3*a**3 - 1/2160*a**6 + 0*a + 3*a**2 + 0 - 1/36*a**4 - 1/180*a**5. Let d(f) be the first derivative of y(f). Factor d(q).
-(q + 2)**2/6
Let x(i) be the first derivative of 0*i**2 + 6/25*i**5 + 1 + 0*i + 3/10*i**4 + 2/15*i**3 + 1/15*i**6. Factor x(d).
2*d**2*(d + 1)**3/5
Suppose 4 = -4*j + 5*j. Let y be j/8*12/2. Suppose 3 - 2*h**2 - 3 + 2*h - y*h + 2*h**4 + h**5 = 0. What is h?
-1, 0, 1
Suppose 0 = -2*d + d - 3*v + 11, -v + 3 = 0. Solve p - 3 + 3*p**4 - p**d + 3 - p**3 - 2*p**4 = 0.
-1, 0, 1
Let v = 7 + -5. Suppose v = l + 1. What is b in l - b + 1/4*b**2 = 0?
2
Let r(w) be the first derivative of -w**7/420 - w**6/45 - w**5/15 + w**3/3 - 2. Let o(k) be the third derivative of r(k). Factor o(a).
-2*a*(a + 2)**2
Suppose -11*y + 4 = -10*y. Let a(o) be the first derivative of -7/20*o**y - 2/15*o**3 + 7/10*o**2 + 2/5*o + 2. Factor a(u).
-(u - 1)*(u + 1)*(7*u + 2)/5
Let c(s) = 5*s**5 + s**4 - 5*s**3 + 5*s**2 + 3*s + 3. Let x(f) = -9*f**5 - f**4 + 9*f**3 - 9*f**2 - 5*f - 5. Let k(v) = 5*c(v) + 3*x(v). Factor k(p).
-2*p**2*(p - 1)**2*(p + 1)
Let q(j) = 65*j. Let i be q(1). Let c = -193/3 + i. Find s such that 2/3*s**4 - 1/3*s**5 + 0 - c*s**2 + 0*s**3 + 1/3*s = 0.
-1, 0, 1
Suppose -3*j = 2*k - 128, -2*k + 128 = -j - j. Suppose 19 - k = -3*w. Factor -2*x - 4*x**2 + w*x**3 - x**2 - 19*x**4 + 4*x**2 + 7*x**5.
x*(x - 1)**3*(7*x + 2)
Factor -29*f**4 + 25*f**4 - 8*f**3 + 0*f**2 - 2*f**2 - 2*f**2.
-4*f**2*(f + 1)**2
Let c(r) be the second derivative of -r**7/28 - r**6/10 + r**4/4 + r**3/4 - 19*r. Factor c(l).
-3*l*(l - 1)*(l + 1)**3/2
Let s be (-12)/3*3/6. Let v(u) = -5*u**4 - 14*u**3 - u**2 + 4*u + 2. Let r(z) = 9*z**4 + 29*z**3 + z**2 - 9*z - 5. Let o(x) = s*r(x) - 5*v(x). Factor o(p).
p*(p + 1)**2*(7*p - 2)
Suppose 14*s = 3*s + 22. Let u(p) be the second derivative of 0 + 16/3*p**3 - 4*p + s*p**2 - 81/20*p**5 + 15/4*p**4. Factor u(w).
-(w - 1)*(9*w + 2)**2
Let b(q) be the first derivative of -4/3*q**3 - 6/5*q**5 + 5/2*q**4 - 4 + 0*q**2 + 0*q. Solve b(c) = 0 for c.
0, 2/3, 1
Let a(c) = -c**3 + c**2 + 2*c + 2. Let j = 8 + -1. Let z(u) = -4*u**3 + 2*u**2 + 6*u + 7. Let q(p) = j*a(p) - 2*z(p). What is d in q(d) = 0?
-2, -1, 0
Let g be 2/(-3) + (-248)/(-93). Solve 0 + 1/3*o**g - 1/3*o = 0.
0, 1
Let z = -3 + 5. Suppose 5*u + 3*y - 30 = 0, -4*y = -u - 19 + z. Factor b**u + 0*b**3 + 2*b**4 + 2*b**2 - 5*b**3.
2*b**2*(b - 1)**2
Let l be ((-2)/4)/(8/(-48)). Let w(m) be the first derivative of 3/7*m**2 - 2 + 4/7*m + 2/21*m**l. Suppose w(y) = 0. Calculate y.
-2, -1
Let l = -90 + 90. Factor l + 0*o + 2/3*o**2.
2*o**2/3
Determine d, given that 4/7*d**3 - 2/7*d - 4/7*d**2 - 2/7*d**5 + 2/7*d**4 + 2/7 = 0.
-1, 1
Let h be 6/14 - 3298/(-63). Let l = 53 - h. What is i in 2/9 - 2/9*i - l*i**2 + 2/9*i**3 = 0?
-1, 1
Let r = -2 - -8. Let x = r + -4. Suppose b**x + 1/3 + 1/3*b**3 + b = 0. Calculate b.
-1
Let s(a) be the second derivative of -2*a**5/5 - 3*a**4/2 - 2*a**3 - a**2 + 2*a. Factor s(b).
-2*(b + 1)**2*(4*b + 1)
Factor -1 - c + c**3 + 1/4*c**4 + 3/4*c**2.
(c - 1)*(c + 1)*(c + 2)**2/4
Let v(o) be the second derivative of -o**5/50 + o**4/30 + 4*o**3/15 - 4*o**2/5 + 8*o. Factor v(p).
-2*(p - 2)*(p - 1)*(p + 2)/5
Let y(z) be the first derivative of -z**4/24 + z**3/9 - z**2/12 - 24. Factor y(n).
-n*(n - 1)**2/6
Let w(r) = -3*r**4 + 3*r**3 + 10*r**2 - 4. Let a(f) = -f**2 + 1. Let g(b) = -4*a(b) - w(b). Solve g(c) = 0.
-1, 0, 2
Suppose -q = 34 - 38. What is o in 6/11*o**2 - 2/11*o + 2/11*o**q - 6/11*o**3 + 0 = 0?
0, 1
Factor -1/5*u**5 + 3/5*u**4 + 0 - 3/5*u**3 + 0*u + 1/5*u**2.
-u**2*(u - 1)**3/5
Let r = -4998 + 359863/72. Let m(q) be the third derivative of 0*q - 1/9*q**3 + 1/90*q**5 - r*q**4 + 7/360*q**6 - q**2 + 0. Determine g so that m(g) = 0.
-1, -2/7, 1
Let w = 7/36 + -8/45. Let r(j) be the third derivative of 0*j - w*j**5 - 2*j**2 - 1/6*j**3 + 0 - 1/12*j**4. Let r(m) = 0. What is m?
-1
Let o be 2 - 0/(-4 + 3). Factor 3 - 6*h + 4*h - h**o - 4.
-(h + 1)**2
Let s(n) = -n**2 - 2*n - 1. Let y be s(-1). Let l(m) be the second derivative of -m + y - 1/27*m**3 + 2/9*m**2 - 1/18*m**4. Factor l(u).
-2*(u + 1)*(3*u - 2)/9
Let g = 7 - 4. Suppose -16*y + 37 + 27 = 0. Suppose h**g + 0*h**2 - 1/2*h + 0 - 1/2*h**5 + 0*h**y = 0. What is h?
-1, 0, 1
Let r(l) = -2*l**2 - 14 - l**2 + 7*l**2 - 10*l. Let g(v) be the second derivative of -v**4/12 + v**3/3 + 3*v**2/2 + v. Let z(y) = 14*g(y) + 3*r(y). Factor z(j).
-2*j*(j + 1)
Let n(z) = z**2 - z + 1. Let g(d) = -2*d**2 - 9*d - 3. Let s(m) = 4*g(m) - 4*n(m). Suppose s(b) = 0. What is b?
-2, -2/3
Let k(z) = z**3 + 22*z**2 + 18*z - 59. Let h be k(-21). What is y in -2/9*y**h + 0 - 2/3*y**2 + 10/9*y**3 - 2*y = 0?
-1, 0, 3
Let m = 4 + -3. Factor -2*x**4 - m + 7*x**4 - 6*x**4 + 2*x**2.
-(x - 1)**2*(x + 1)**2
Let i(x) be the second derivative of x**4/12 - x**3/15 + 29*x. Factor i(d).
d*(5*d - 2)/5
Solve -7*l - 4*l**2 - 18*l**3 - 6*l**2 + 2*l + 13*l**3 = 0.
-1, 0
Let z(y) = 2*y**2 + 43*y - 36. Let w(s) = -12*s**2 - 216*s + 180. Let o(x) = 3*w(x) + 16*z(x). Let o(d) = 0. What is d?
1, 9
Let b(w) be the third derivative of w**6/30 - w**5/15 + w**4/24 - 2*w**2. Let b(m) = 0. Calculate m.
0, 1/2
Let b(x) be the first derivative of x**6/36 - x**5/10 + x**4/12 + 2*x**3/3 - 1. Let y(o) be the third derivative of b(o). Factor y(p).
2*(p - 1)*(5*p - 1)
Let s(t) be the third derivative of -t**7/420 - t**6/240 + t**5/60 - 2*t**2. Find c such that s(c) = 0.
-2, 0, 1
Let m(z) be the third derivative of -z**5/36 + 5*z**4/18 - 5*z**3/6 + 26*z**2 + 1. Solve m(r) = 0 for r.
1, 3
Let q(o) be the third derivative of -o**8/40320 + o**7/5040 - o**6/1440 + o**5/20 - 4*o**2. Let z(r) be the third derivative of q(r). Factor z(j).
-(j - 1)**2/2
Let s be ((-1)/(-1) + -2)*-3. Suppose -c - s*f + 8 = 0, -5*c + 2*f + 14 = 4*f. Determine p so that 6*p**c - p**4 - 2*p**3 - 3*p**2 + p**3 + 5*p + 2 = 0.
-1, 2
Let b(g) be the third derivative of g**8/6720 + g**7/1680 + g**6/1440 + g**3/3 + 4*g**2. Let z(j) be the first derivative of b(j). Factor z(t).
t**2*(t + 1)**2/4
Let x(q) be the third derivative of 0*q**7 + 0*q - 1/10*q**6 + 0 + 1/112*q**8 + 3/8*q**4 - q**2 - 1/10*q**5 + q**3. Factor x(p).
3*(p - 2)*(p - 1)*(p + 1)**3
Suppose -3*z + 9 = -0*z. Let o be ((-12)/(-18))/(1/z). Factor 0*d**3 + 0*d + 2/7*d**4 - 2/7*d**o + 0.
2*d**2*(d - 1)*(d + 1)/7
Let h(b) be the first derivative of b**5/20 + b**4/8 - b**3/12 - b**2/4 + 5. Determine i, given that h(i) = 0.
-2, -1, 0, 1
Solve 20*r**2 + 47*r**3 + 4*r - 24*r**3 - 7*r**3 = 0.
-1, -1/4, 0
Let o be 5/((-2)/(-2 + 0)). Suppose 2*y - w = 4*w + 26, 0 = o*w + 20. Factor -n**3 + 2*n + 4*n**2 + 0*n**3 + y*n**3.
2*n*(n + 1)**2
Determine i, given that -1/11*i**3 + 0*i + 0 - 1/11*i**2 = 0.
-1, 0
Let b(a) = -a**2 + 2. Let n = 8 - 8. Let g be b(n). Let g*p - 14 - p**3 + 14 - p**5 - 3*p**2 + 3*p**4 = 0. What is p?
-1, 0, 1, 2
Let h(s) be the third derivative of s**8/50400 - s**7/3150 + s**6/450 - s**5/20 - s**2. Let b(a) be the third derivative of h(a). Factor b(d).
2*(d - 2)**2/5
Factor -16/17 + 2/17*l**2 - 4/17*l.
2*(l - 4)*(l + 2)/17
Let g(x) be the second derivative of x**7/168 + x**6/120 - x**5/40 - x**4/24 + x**3/24 + x**2/8 + 14*x. Factor g(f).
(f - 1)**2*(f + 1)**3/4
Let q be (7 - (-3)/(-1)) + -3. Suppose -5*i - 3*p = -5, p + 0 = -i - q. Let -5/2*x**2 + 3/2*x - 3/2*x**3 + 1/2 + 2*x**i = 0. What is x?
-1, -1/4, 1
Let x = 643/86 - -1/43. Factor -1/2*h + 7/2*h**4 - 19/2*h**3 - 1 + x*h**2.
(h - 1)**3*(7*h + 2)/2
Let y(o) be the second derivative of -o**7/17640 + o**5/840 - o**4/3 + 7*o. Let d(x) be the third derivative of y(x). Solve d(h) = 0 for h.
-1, 1
Solve -21*i - 3*i**2 + 3*i**3 + 23 + 6*i**3 - 8 = 0 for i.
-5/3, 1
Let r(m) = -m**4 - m - 1. Let b(i) = -3*i**4 - 4*i**3 - 6*i**2 + 3*i + 3. Let h(n) = b(n) - 5*r(n). Solve h(p) = 0 for p.
-1, 2
Suppose 5*x - 30 = 8*a - 3*a, -5*x - 3