e w, given that 4/3*w**3 - 2/3*w**g + 0*w + r = 0.
0, 1/2
Let g(r) be the second derivative of r**7/21 - r**6/15 - 3*r**5/10 + 5*r**4/6 - 2*r**3/3 - 8*r. Determine p so that g(p) = 0.
-2, 0, 1
Factor -3*a + 9/2 + 1/2*a**2.
(a - 3)**2/2
Let v be 3*(8/12 + 0). Factor -3*t**v - 4*t + 5*t - 3*t - t.
-3*t*(t + 1)
Let l(s) be the first derivative of -1/80*s**5 - 1/4*s**2 - 5/24*s**3 - 3*s - 3 - 1/12*s**4. Let y(o) be the first derivative of l(o). What is h in y(h) = 0?
-2, -1
Let m(x) be the first derivative of 3/5*x**4 - 6/5*x**2 + 4 - 12/5*x + 3/5*x**3 + 3/25*x**5. Let m(s) = 0. What is s?
-2, -1, 1
Suppose 0 = j - 4*z + 1 + 10, 7 = j + 2*z. Let u be (j/(-4))/(1 + -2). Solve 0*s - 1/4*s**2 + u = 0.
-1, 1
Factor 1/4*r**3 + 0 - 1/4*r + 0*r**2.
r*(r - 1)*(r + 1)/4
Suppose 7*t = 3*t + 4*b + 4, 5*b = t - 21. Let j(h) = -h**3 - 3*h**2 + 4*h + 1. Let s be j(t). Solve -1 + y**2 + s + 0 = 0 for y.
0
Let a(k) be the first derivative of -6/5*k**5 + 1/3*k**6 + k**4 + 4/3*k**3 - 2 + 2*k - 3*k**2. Factor a(n).
2*(n - 1)**4*(n + 1)
Let b(r) = -r**2 - 3*r + 10. Let h be b(-5). Let x(k) be the first derivative of 1 - 5/2*k**4 + 0*k**2 + h*k + 4/3*k**3. Factor x(a).
-2*a**2*(5*a - 2)
Let d be ((-4)/(-8))/(-2 + 4). Suppose -1/4*k**2 + 0*k**3 + 0 + 0*k + d*k**4 = 0. What is k?
-1, 0, 1
Suppose z - 4*z = -6. Suppose -3*i - z = s - 7*i, -5*s + 15 = 5*i. Factor 2*m - 2*m**3 + 5*m**3 - 2*m**s - 5*m**3 - 6 + 8.
-2*(m - 1)*(m + 1)**2
Suppose -4*p - 7 = 1. Let z be (-3)/6 + (-7)/p. Factor -2*v**2 + v**z - v**2 - 3*v + v**5 + 3*v**4 + v.
v*(v - 1)*(v + 1)**2*(v + 2)
Suppose -6*u - 4 = -16. Let p(o) be the third derivative of 1/180*o**5 + 0 + 1/210*o**7 - 1/120*o**6 - 1/1008*o**8 + 0*o + 0*o**3 + 0*o**4 + o**u. Factor p(w).
-w**2*(w - 1)**3/3
Let n(f) = f + 7. Let m be n(-4). Suppose 5*p**2 - 18 + 0*p**3 + 9 + m*p + p**3 = 0. What is p?
-3, 1
Let h(r) = r. Let o(i) = -i**3 - 3*i**2 - 3*i - 3. Let k be o(-2). Let b(m) = m**3 + m**2 - 7*m - 1. Let x(c) = k*b(c) - 6*h(c). Factor x(q).
-(q - 1)*(q + 1)**2
Let q(h) be the first derivative of -6/35*h**5 + 0*h - 2 + 0*h**2 - 5/14*h**4 - 4/21*h**3. Factor q(y).
-2*y**2*(y + 1)*(3*y + 2)/7
Let v(r) = 50*r**4 + 35*r**3 + 13*r**2 - 5. Let a(u) = 75*u**4 + 53*u**3 + 19*u**2 - 7. Let m(l) = -5*a(l) + 7*v(l). Determine g so that m(g) = 0.
-2/5, 0
Let x(s) be the first derivative of 2*s**5/5 + 4*s**4/3 + 4*s**3/3 - 2*s/3 + 2. What is w in x(w) = 0?
-1, 1/3
Let m(c) = -3*c**4 - 3*c**3 - 2*c**2 + 3*c + 5. Let t(y) = -3*y**4 - 3*y**3 - y**2 + 3*y + 4. Let b(o) = 4*m(o) - 5*t(o). Factor b(d).
3*d*(d - 1)*(d + 1)**2
Let l(p) be the first derivative of 3*p**6/5 - 186*p**5/25 + 177*p**4/5 - 396*p**3/5 + 81*p**2 - 162*p/5 + 17. Suppose l(x) = 0. Calculate x.
1/3, 1, 3
Let z(r) be the first derivative of r**6/30 - 2*r**5/15 + 7*r**4/36 - r**3/9 + 10*r + 2. Let f(u) be the first derivative of z(u). Let f(x) = 0. What is x?
0, 2/3, 1
Let m(i) = -7*i**4 - i**3 + 6. Let f(u) = -u**4 + 1. Let r(s) = -30*f(s) + 5*m(s). Suppose r(d) = 0. What is d?
-1, 0
Let q(j) be the third derivative of -j**7/840 - j**6/240 - j**5/240 - 16*j**2. Factor q(n).
-n**2*(n + 1)**2/4
Let r = -97/84 - -31/12. Factor -r*f - 4/7 + 2/7*f**4 + 2/7*f**3 - 6/7*f**2.
2*(f - 2)*(f + 1)**3/7
Let q(z) = -z**2 - 10*z - 6. Let y be q(-9). Suppose 0 = v + 3*c - 3 - 12, -3*c = -y*v - 15. Factor -15/4*j**3 - 1/4*j**2 - 7/4*j**5 - 19/4*j**4 + 1/2*j + v.
-j*(j + 1)**3*(7*j - 2)/4
Let f(g) be the first derivative of -15*g**4/4 - g**3 + 15*g**2/2 + 3*g - 6. Factor f(i).
-3*(i - 1)*(i + 1)*(5*i + 1)
Factor -32/7*s - 4*s**2 - 4/7*s**3 + 64/7.
-4*(s - 1)*(s + 4)**2/7
Find z, given that 14/9*z**2 - 4/9*z - 2/9*z**5 + 10/9*z**4 + 0 - 2*z**3 = 0.
0, 1, 2
Let k(m) be the third derivative of -m**8/672 + m**7/210 + m**6/120 - m**5/30 - m**4/48 + m**3/6 + 9*m**2. What is x in k(x) = 0?
-1, 1, 2
Suppose 5*x = x + 32. Let c = x + -5. Determine t, given that 7*t + 5*t**2 + 0*t**2 - 1 + c = 0.
-1, -2/5
Let j(d) be the third derivative of d**8/1512 - d**7/945 - d**6/270 + d**5/135 + d**4/108 - d**3/27 - d**2. Find u such that j(u) = 0.
-1, 1
Let f = 2841/5 + -567. Factor -3/5*v**2 - f + 9/5*v.
-3*(v - 2)*(v - 1)/5
Let a = 17/56 - 1/56. Let s be (-15)/21 + -1 - -2. What is x in 0 + 2/7*x**4 - a*x**2 + 2/7*x**3 - s*x = 0?
-1, 0, 1
Let z = -119 - -365/3. Let c be 4/8 + (-6)/(-4). Factor 2/3*f**c - 8/3*f + z.
2*(f - 2)**2/3
Let r = 4 + -2. Factor 6*s**r + 3*s + 9*s**3 + 3*s - 7*s**3 + 2.
2*(s + 1)**3
Suppose -11 = 8*g - 27. Let i(p) be the third derivative of 0*p + 0 + 0*p**5 - 1/24*p**4 + 0*p**3 + 1/120*p**6 + g*p**2. Find x such that i(x) = 0.
-1, 0, 1
Let m(o) be the first derivative of 9*o**3 + 18*o**2 + 12*o + 11. Let m(p) = 0. What is p?
-2/3
Let d = -9 - -13. Let q be (-10)/d*(-56)/70. Factor 1/4 + 1/2*s - 1/2*s**3 + 0*s**q - 1/4*s**4.
-(s - 1)*(s + 1)**3/4
Suppose -2*t - 3*k = -15, -3 = 3*t - k - 20. Let i be -3*(-2)/t + 1. Factor 0*o + i*o**2 - 4*o + 0 + 1 + 1.
2*(o - 1)**2
Let r be ((-5)/(-15) + 11/(-6))/(-3). Factor -1/2*x**2 - x - r.
-(x + 1)**2/2
Find t such that t**5 - t**4 - 1 + t**2 - 2*t**3 + t + 0*t + t**2 = 0.
-1, 1
Let k(b) be the second derivative of b**5/6 - b**4/36 - 4*b**3/9 + b**2/2 + 25*b. Factor k(j).
(j + 1)*(2*j - 1)*(5*j - 3)/3
Let p = 2/141 + 133/564. Factor -i**2 - 5/4*i - p.
-(i + 1)*(4*i + 1)/4
Factor 6/5*f - 16/5*f**2 - 2/15 + 32/15*f**3.
2*(f - 1)*(4*f - 1)**2/15
What is m in -5*m**5 + 3*m**4 - 2*m**5 + 4*m**5 = 0?
0, 1
Let m(w) be the third derivative of 5*w**2 + 1/180*w**6 + 1/1008*w**8 + 1/18*w**3 - 1/210*w**7 + 0*w - 1/24*w**4 + 1/90*w**5 + 0. Determine i so that m(i) = 0.
-1, 1
Let q(j) be the first derivative of 4*j**3/3 + 2*j**2 + 3. Determine a so that q(a) = 0.
-1, 0
Let y(v) be the first derivative of -4 + 1/12*v**3 - 1/8*v**2 + 0*v. Factor y(n).
n*(n - 1)/4
Suppose -6*z**2 - 4 + 3*z**2 + 4 = 0. What is z?
0
Let t(l) = -2*l**3 - 3*l**2 - l - 1. Let k be t(-2). Factor 3*w**4 - w**4 + w**k - w**4.
w**4*(w + 1)
Let b(l) = -l**2 + 2*l + 4. Let n be b(0). Let -7*a**5 + 4*a**5 - 188*a**n - 27*a**3 + 206*a**4 = 0. What is a?
0, 3
Let v = -4 + 6. Let o be 140/147 - v/7. Let -2/3*s**4 + o*s**2 + 0*s + 2/3*s**5 - 2/3*s**3 + 0 = 0. Calculate s.
-1, 0, 1
Suppose 13 = 5*z + 3. Suppose -z*v + 15 = -1. Factor -j - 6*j**3 - j**4 + v*j**3 - j**2 + j.
-j**2*(j - 1)**2
Let l(a) be the third derivative of 1/70*a**7 - 3*a**2 + 0 - 1/10*a**5 + 0*a**6 + 0*a**4 + 0*a + 1/2*a**3. Factor l(h).
3*(h - 1)**2*(h + 1)**2
Let p(s) = s**4 - s**3 - s**2 + s + 1. Let d(k) = -15*k**4 + 12*k**3 + 18*k**2 - 12*k - 21. Let r(v) = d(v) + 18*p(v). What is z in r(z) = 0?
-1, 1
Let b = 55 - 51. Let x(m) be the second derivative of 0*m**2 + 1/25*m**6 - 2*m + 1/50*m**5 - 1/15*m**b + 0*m**3 + 0. Determine u, given that x(u) = 0.
-1, 0, 2/3
Let z(m) be the first derivative of 1 + 1/36*m**4 + 3*m - 1/18*m**3 + 0*m**2. Let r(a) be the first derivative of z(a). Suppose r(x) = 0. Calculate x.
0, 1
Let r(f) = -53*f**4 + 96*f**3 - 25*f**2 + 15*f - 11. Let s(h) = -13*h**4 + 24*h**3 - 6*h**2 + 4*h - 3. Let k(o) = -6*r(o) + 22*s(o). Factor k(w).
2*w*(w - 1)*(4*w - 1)**2
Let a(u) = -u + 8. Let z be a(4). Suppose z*g + 0*g - 16 = 0. Determine h, given that 2*h**3 + h**4 + 4*h**g - 5*h**2 - 3*h + h = 0.
-1, -2/5, 0, 1
Let v(q) = q**2 - q + 2. Let i be (0/(-2))/(0 + 3). Let b be v(i). Factor -1/3*s**b - 1/3 - 2/3*s.
-(s + 1)**2/3
Let w(u) be the third derivative of -u**5/6 + 11*u**4/36 - 2*u**3/9 + 13*u**2. Determine o so that w(o) = 0.
1/3, 2/5
Factor -1/3*s**2 + 0 + 0*s.
-s**2/3
Suppose 12 = 4*y, -2*l + 13 = 4*y + y. Let q = 5 + l. Factor -q*v + v**2 - v**3 + v**3 - 1 + 4*v**3.
(v - 1)*(v + 1)*(4*v + 1)
Let p(x) = -x**2 - 18*x - 32. Let d be p(-16). Determine l, given that 8/9*l**5 + 4/9*l**3 - 2/9*l**2 + 14/9*l**4 + d + 0*l = 0.
-1, 0, 1/4
Let r = 116/7 - 320/21. Let i(z) be the second derivative of -1/15*z**6 + z + r*z**3 + 0 - z**4 + 2/5*z**5 - z**2. Find b such that i(b) = 0.
1
Let y(s) be the first derivative of -1/8*s**2 + 1/16*s**4 - 2 + 1/12*s**3 - 1/4*s. Factor y(f).
(f - 1)*(f + 1)**2/4
Let t = -73 - -73. Factor t*i - 4*i**3 + 2/3*i**2 + 6*i**4 + 0.
2*i**2*(3*i - 1)**2/3
Let g(d) be the second derivative of 0*d**3 + 0*d**2 - 1/10*d**6 + 0 + 4*d + 1/4*d**4 + 0*d**5. Find o, given that g(o) = 0.
-1, 0, 1
Let x be