/4
Let h(f) = -8*f + 170. Let j be h(21). Factor -4/9 - 2/9*a**j + 2/3*a.
-2*(a - 2)*(a - 1)/9
Suppose -5*g + 2*g = -6. Factor 2*w**5 - g*w + 5*w - 5*w**3 - w**3 + w**5.
3*w*(w - 1)**2*(w + 1)**2
Let s(d) be the second derivative of -7*d**4/6 + 4*d**3 + 4*d**2 - 33*d. Suppose s(f) = 0. Calculate f.
-2/7, 2
Factor 3*j**3 + 8*j**3 + 10*j**2 - j**3 - 5*j - 5*j**5 - 5 - 5*j**4.
-5*(j - 1)**2*(j + 1)**3
Let n(v) be the third derivative of v**7/5880 - v**6/840 - v**4/24 - 2*v**2. Let q(o) be the second derivative of n(o). Determine c, given that q(c) = 0.
0, 2
Let t = -2/37 + 80/111. Let d be (6 + -4)*(5/2 - 1). Factor t*f**d - 2/3 - 2/3*f + 2/3*f**2.
2*(f - 1)*(f + 1)**2/3
Let -6*q - 2*q**2 + 1 - 9*q - q**5 + 2*q**3 - 6*q + 20*q + q**4 = 0. What is q?
-1, 1
Let b(i) = 4*i**2 - 1. Let w be b(-1). Determine v, given that v**4 - 4*v**w + v**3 - v**3 + 3*v**3 = 0.
0, 1
Let y(j) be the first derivative of 3*j**5/5 - j**3 - 8. Let y(q) = 0. Calculate q.
-1, 0, 1
Let p(j) = j**4 - j. Suppose 57 - 147 = -5*v. Let n(a) = 10*a**4 - 9*a. Let w(k) = v*p(k) - 2*n(k). Suppose w(h) = 0. What is h?
0
Let o(g) be the third derivative of g**7/135 - g**6/18 + 43*g**5/270 - 2*g**4/9 + 4*g**3/27 - 26*g**2. Find s such that o(s) = 0.
2/7, 1, 2
Factor -1 + 1/2*g + 1/2*g**2.
(g - 1)*(g + 2)/2
Let f(u) be the first derivative of 2*u**2 - 3*u - 1/10*u**5 - 1 + 0*u**4 + u**3. Let b(d) be the first derivative of f(d). Factor b(a).
-2*(a - 2)*(a + 1)**2
Let o be (-4)/14 - 44/(-7). Let s be (-9)/o - 28/(-8). Factor 0*v + 2/9*v**5 - 2/9*v**4 + 0*v**s + 0 - 4/9*v**3.
2*v**3*(v - 2)*(v + 1)/9
Factor 4/7*r**2 - 4/7*r**3 + 0*r + 0.
-4*r**2*(r - 1)/7
Let o be ((-5)/(-60))/(1/10). Let t(q) be the first derivative of 0*q + 4/3*q**3 + 23/5*q**5 + 2 + 15/2*q**4 + o*q**6 - 4*q**2. Factor t(h).
h*(h + 1)*(h + 2)**2*(5*h - 2)
Let u be 10/3 + 6 + -9. Factor -u - 1/2*s - 1/6*s**2.
-(s + 1)*(s + 2)/6
Let a(v) be the second derivative of -v**7/1680 + v**6/720 + v**5/240 - v**4/48 + v**3/2 + 2*v. Let o(b) be the second derivative of a(b). Factor o(x).
-(x - 1)**2*(x + 1)/2
Let w be -1 - 7 - (-26)/3. Factor 4/9*k + w - 2/9*k**2.
-2*(k - 3)*(k + 1)/9
Let z(u) be the first derivative of u**5/10 - u**4/2 + u**3 - u**2 - 3*u - 9. Let y(j) be the first derivative of z(j). Factor y(t).
2*(t - 1)**3
Let x(m) = m**3 + 5*m**2 - m - 5. Let f(i) = -i**3 - i**2 + i + 1. Let k(z) = -f(z) + x(z). Find t such that k(t) = 0.
-3, -1, 1
Factor -59*y + 0*y**2 + 53*y - 8 + 2*y**2.
2*(y - 4)*(y + 1)
Let o(g) = -2*g**2 + 10*g - 6. Let u be o(4). Let x(z) = 3*z**2 + 2*z + 1. Let k be x(-1). Factor u*q**4 + 7*q**4 - 5*q**3 + 12*q**5 + k*q**3 + 0*q**4.
3*q**3*(q + 1)*(4*q - 1)
Let j(g) be the first derivative of -2*g**3/27 - 2*g**2/9 - 2*g/9 + 5. Find x such that j(x) = 0.
-1
Factor 0 + 6/13*q**2 + 2/13*q**4 - 8/13*q**3 + 0*q.
2*q**2*(q - 3)*(q - 1)/13
Let r(k) = 4*k**3 - 2*k**2 + k. Let c be r(1). Suppose 0 = -c*q + q + 6. Factor 0*t**2 + 2*t - t**2 + q*t**2.
2*t*(t + 1)
Let t be 0 - -1 - 58/(-4). Let y = -15 + t. Factor -1/2*k**2 - k - y.
-(k + 1)**2/2
Let q(i) be the second derivative of -i**7/231 + i**5/55 - i**3/33 + 48*i. Find o such that q(o) = 0.
-1, 0, 1
Let v(g) be the first derivative of -g**6/75 - g**5/25 - g**4/30 - g - 1. Let y(h) be the first derivative of v(h). Factor y(i).
-2*i**2*(i + 1)**2/5
Let p(o) be the second derivative of o**6/6 + 7*o**5/4 + 65*o**4/12 - 5*o**3/2 - 45*o**2 + 27*o. Let p(z) = 0. What is z?
-3, -2, 1
Suppose 7 = 2*f - 1. Let q be (-68)/(-3)*(-7)/(-56). Let 9/2*w**3 - q*w**2 - 3/2*w**f - 1/2*w + 1/3 = 0. Calculate w.
-1/3, 1/3, 1, 2
Let k(j) be the third derivative of j**6/360 - j**5/60 + 2*j**3/9 - 20*j**2. Suppose k(v) = 0. Calculate v.
-1, 2
Factor 0 + 18/5*w + 12/5*w**2 + 2/5*w**3.
2*w*(w + 3)**2/5
Let p(g) be the first derivative of 1/15*g**5 - 2 + 1/6*g**4 + 0*g**3 - 1/3*g - 1/3*g**2. Solve p(s) = 0 for s.
-1, 1
Solve -1/3*d**2 - 4/3*d - 4/3 = 0 for d.
-2
Let m(r) = 7*r**2 + 6*r - 4. Let f(s) = -15*s**2 - 13*s + 8. Let k(i) = -6*f(i) - 13*m(i). Let k(g) = 0. Calculate g.
-2, 2
Let d = -1 + 5. Factor -d*y**2 + 0*y**3 + 3*y**3 + y**2 - y**4 + y.
-y*(y - 1)**3
Let r(b) be the first derivative of b**3/5 - 9*b**2/10 + 16. Factor r(d).
3*d*(d - 3)/5
Let v = -4 - -12. Suppose 3*i = v - 2. Factor -8*x**3 - 6*x**2 - 2*x**3 - x**5 - 5*x**4 - 5*x - 1 - 4*x**i.
-(x + 1)**5
Let h be -1*2 - 24/(-12). Let a(w) be the second derivative of 3*w + h*w**4 + 0*w**2 + 1/130*w**5 + 0 - 1/39*w**3. Factor a(r).
2*r*(r - 1)*(r + 1)/13
Let r(i) be the first derivative of 250*i**6/3 - 160*i**5 + 5*i**4 + 328*i**3/3 - 8*i**2 - 32*i - 3. Let r(j) = 0. What is j?
-2/5, 2/5, 1
Let z be 0/((6/27)/(4/36)). Find v such that 2/7*v - 4/7*v**2 + z + 2/7*v**3 = 0.
0, 1
Let t(k) be the first derivative of 5*k**6/24 + 9*k**5/20 - k**4/8 - 7. Factor t(v).
v**3*(v + 2)*(5*v - 1)/4
Solve 0 - 2/5*g**2 + 14/5*g = 0.
0, 7
Let d = 9 - 7. Determine r so that -2/3*r**d + 4/3*r - 2/3 = 0.
1
Let j be (-588)/270 + 2 + (-2)/(-5). Determine s so that 4/9 + 10/9*s**3 + j*s**4 + 14/9*s + 2*s**2 = 0.
-2, -1
Let l(y) be the second derivative of 0 - 4/5*y**5 - 11/12*y**4 - 7/30*y**6 + 0*y**2 - 1/3*y**3 + 6*y. Factor l(d).
-d*(d + 1)**2*(7*d + 2)
Factor 2/5*q**2 + 0 - 2*q.
2*q*(q - 5)/5
Let i = 12 + -8. Let f(s) be the second derivative of 3*s + 0*s**2 + 0*s**3 + 1/18*s**i + 0 + 1/63*s**7 + 1/15*s**6 + 1/10*s**5. Factor f(y).
2*y**2*(y + 1)**3/3
Let d(k) = 7*k + 2. Let l be d(-4). Let w be l*(-3)/(-30) + 3. Factor 0*t + 2/5*t**3 - w*t**2 + 0.
2*t**2*(t - 1)/5
Let h(f) be the first derivative of -f**4/4 - 2*f**3/3 + f**2/2 + 2*f + 4. Suppose h(o) = 0. Calculate o.
-2, -1, 1
Let o(b) be the second derivative of -5*b**7/42 + 7*b**6/30 - b**5/10 - 21*b. Find w, given that o(w) = 0.
0, 2/5, 1
Let j be 5 - 2 - 3370/1325. Let p = -3/53 + j. Let -p*s**5 - 2*s - 4*s**2 - 2*s**4 - 2/5 - 4*s**3 = 0. Calculate s.
-1
Determine p, given that 0*p + 0 + 2/3*p**2 = 0.
0
Let s(y) be the first derivative of y**3 - 15*y**2 + 75*y + 3. Factor s(t).
3*(t - 5)**2
Let a(x) be the first derivative of -3*x**5/10 - 5*x**4/8 - x**3/6 + x**2/4 - 12. Determine g, given that a(g) = 0.
-1, 0, 1/3
Let w(b) be the first derivative of -b**5/35 + b**4/28 + b**3/7 - b**2/14 - 2*b/7 + 3. Let w(m) = 0. Calculate m.
-1, 1, 2
Let j(h) be the third derivative of -h**5/270 + 5*h**4/18 - 25*h**3/3 + 45*h**2. Factor j(s).
-2*(s - 15)**2/9
Suppose 6*n**2 - 6*n**3 - 2*n**3 - 4*n + 4*n**2 + 2*n**4 = 0. Calculate n.
0, 1, 2
Let g(t) = -4*t**2 + 1. Let h(d) = d**2 + d + 1. Let s(u) = -5*g(u) - 15*h(u). Factor s(z).
5*(z - 4)*(z + 1)
Factor -2*c**3 - 3*c**2 - 8*c**4 + 7*c**2 + 11*c**4 + 10*c**3.
c**2*(c + 2)*(3*c + 2)
Let t(a) = 2*a**2 + 3. Let u be t(0). Suppose -u + 6 = q. Factor 0 - b + 3/2*b**2 - 1/2*b**4 + 0*b**q.
-b*(b - 1)**2*(b + 2)/2
Let z(n) = -n**3 - 2*n**2 - n + 6. Let x(k) = -1. Let l(p) = 6*x(p) + z(p). Factor l(c).
-c*(c + 1)**2
Let u be (-1)/1 + 0 + (0 - -4). Factor 0*y - 1/2*y**u - 1/4*y**2 + 0.
-y**2*(2*y + 1)/4
Solve -36*m**2 + 0*m**2 - 28*m + 2*m**3 - 8 - 4*m**4 - 22*m**3 = 0.
-2, -1
Let p(f) be the first derivative of -7 + 0*f + 16/3*f**3 - f**4 - 8*f**2. Find h, given that p(h) = 0.
0, 2
Suppose h + h = 2. Let m be (h/10)/((-3)/(-12)). Suppose 0 - 2/5*x + m*x**2 = 0. What is x?
0, 1
Let r = 29 - 27. Find d such that -2/7*d**4 + 0*d + 2/7*d**3 + 0*d**r + 0 = 0.
0, 1
Let y(s) = 8*s**5 + 4*s**3 - 4*s**2 - 12*s - 2. Suppose 3*a + 42 = -3. Let g = 9 + a. Let r(h) = h**5 - h**4 - h. Let i(p) = g*r(p) + y(p). Factor i(v).
2*(v - 1)*(v + 1)**4
Let p(m) be the first derivative of 0*m**2 - 1/30*m**6 + 0*m**4 + m + 1/40*m**5 - 1 + 1/84*m**7 + 0*m**3. Let v(k) be the first derivative of p(k). Factor v(u).
u**3*(u - 1)**2/2
Let q(z) = z**3 - 7*z**2 - z - 9. Let y be q(7). Let j be -4 - -2 - y/7. Determine n so that 0 - j*n - 2/7*n**2 = 0.
-1, 0
Let g(a) be the second derivative of a**7/14 - 3*a**5/20 + 8*a. Factor g(b).
3*b**3*(b - 1)*(b + 1)
Suppose 5*s + 15 = m, -4*m + 2*m - 5*s - 15 = 0. Factor m*p**3 + 6*p - 2*p**3 - 5 + 1.
-2*(p - 1)**2*(p + 2)
Let n be 2/(-8) + (0 - (-18)/8). Let 16/7 + 24/7*r + 12/7*r**n + 2/7*r**3 = 0. Calculate r.
-2
Let w(j) be the first derivative of -1/40*j**6 - 1/8*j**4 - 1/10*j**5 + 1/2*j**2 - 1 + 0*j**3 + 0*j. Let i(v) be the second derivati