
Let a(d) = d**2 + d. Let o(g) = -25*g**3 + 154*g**2 + 109*g - 70. Let m(f) = 6*a(f) + o(f). Factor m(b).
-5*(b - 7)*(b + 1)*(5*b - 2)
Let n be 29/(-5) - (-4)/(-20). Let c be n/18 - (-7)/3. Factor -2*r**4 - r**2 - 6*r**c + r**5 - r + 9*r**2.
r*(r - 1)**3*(r + 1)
Let v(k) be the second derivative of -3/20*k**5 + 0 - 3*k - 1/2*k**4 + 0*k**2 + 0*k**3. Factor v(g).
-3*g**2*(g + 2)
Let k be (-3)/(6/(-4)) - 1. Suppose 0 = -2*w + k + 7. Factor 3*x**2 - x**2 - w*x**2 - x**4 - 3*x**3.
-x**2*(x + 1)*(x + 2)
Suppose 19*h = 12*h. Let k(w) be the second derivative of 1/36*w**4 + h + 4*w + 2/9*w**3 + 2/3*w**2. Factor k(p).
(p + 2)**2/3
Let o(n) = n**2 - 8*n - 6. Let v be o(8). Let x be (v/(-30))/((-1)/(-2)). Factor -2/5*r**2 + 0 + 0*r - x*r**3.
-2*r**2*(r + 1)/5
Let n(t) = 16*t**3 - 8*t - 32. Let l(p) = p**3 + p**2 + p - 1. Let r(x) = -20*l(x) + n(x). Find d such that r(d) = 0.
-3, -1
Let h(c) be the third derivative of -c**6/720 - c**5/80 - c**4/24 + c**3/2 - 9*c**2. Let y(b) be the first derivative of h(b). Factor y(w).
-(w + 1)*(w + 2)/2
Let s(q) = 2*q - 8. Let p be s(6). Suppose 3*j = -l, 2*l + 4*j = 3*j. Suppose -8*x**3 + x**4 + l*x + x**4 + 10*x**2 - p*x = 0. What is x?
0, 1, 2
Let w(n) be the second derivative of -3*n + 4/15*n**3 + 2/25*n**5 + 0 - 1/75*n**6 - 1/5*n**2 - 1/5*n**4. Solve w(f) = 0.
1
Factor 2/15*r - 2/15*r**2 + 0.
-2*r*(r - 1)/15
Let a(p) be the second derivative of 3/5*p**5 + 0 + 10/3*p**3 + 2*p**4 + 1/15*p**6 + 3*p**2 + 3*p. What is v in a(v) = 0?
-3, -1
Let a = -1 + -1. Let r be a/(-3)*3/8. Suppose 0*j - r + 1/4*j**2 = 0. Calculate j.
-1, 1
Let s(z) be the first derivative of z**7/1050 + z**6/150 + z**5/50 + z**4/30 + z**3/30 - z**2 - 5. Let l(c) be the second derivative of s(c). Factor l(r).
(r + 1)**4/5
Let u = 21 - 11. Let h(y) = -4*y**2 - 5 - u*y - 3*y**2 + 15*y**3 - 5*y - 2*y**2. Let z(s) = 7*s**3 - 4*s**2 - 7*s - 2. Let j(g) = 3*h(g) - 7*z(g). Factor j(a).
-(a - 1)*(a + 1)*(4*a - 1)
Let t(h) = 17*h**3 - 13*h**2 - 43*h + 60. Let b(v) = 9*v**3 - 6*v**2 - 21*v + 30. Let g(i) = 7*b(i) - 4*t(i). Factor g(n).
-5*(n - 3)*(n - 1)*(n + 2)
Let m be (-3 - 4)/28 + (-2)/(-8). Let i(v) be the second derivative of 0 + 2/5*v**5 + 0*v**3 + 1/15*v**6 + m*v**2 - v + 2/3*v**4. Solve i(x) = 0.
-2, 0
Factor -10*f**5 - 2*f**3 + f**2 - 4*f**4 + 18*f**5 + 3*f**2 - 6*f**5.
2*f**2*(f - 2)*(f - 1)*(f + 1)
Let x(r) = 7*r**3 - 2*r**2 - 2*r - 3. Let a(m) = 4*m**3 - m**2 - m - 2. Let s(v) = -5*a(v) + 3*x(v). Factor s(z).
(z - 1)**2*(z + 1)
Suppose 0 = 2*i + 3*i - 10. What is n in -n + 0*n + 2*n**2 - n**2 - i*n**2 = 0?
-1, 0
Factor -343/6*i**5 + 0 - 14*i**3 + 0*i + 49*i**4 + 4/3*i**2.
-i**2*(7*i - 2)**3/6
Let k(c) be the second derivative of -1/126*c**7 + 0*c**3 + c + 0 + 0*c**2 + 0*c**6 + 0*c**4 + 1/60*c**5. Suppose k(f) = 0. Calculate f.
-1, 0, 1
Factor 2/9*a**2 + 2/9 + 4/9*a.
2*(a + 1)**2/9
Solve 114*a**4 + 2*a**3 - 54*a**4 - 52*a**4 = 0.
-1/4, 0
Let i(d) be the first derivative of 5*d**7/168 + d**6/120 - d**5/16 - d**4/48 - 4*d + 3. Let t(o) be the first derivative of i(o). Find u such that t(u) = 0.
-1, -1/5, 0, 1
Let n(r) = -6*r**2 + 9*r - 1. Let k(q) = -30*q**2 + 45*q - 4. Let c(b) = -2*k(b) + 11*n(b). Factor c(u).
-3*(u - 1)*(2*u - 1)
Let t be ((-4)/(-6) - 0) + (-30)/(-45). Factor 4/3*l**4 - 4/3 - 14/3*l - t*l**3 - 16/3*l**2 + 2/3*l**5.
2*(l - 2)*(l + 1)**4/3
Let w = -6 - 0. Let i = w - -8. Factor 0 + 0*p + 0*p**4 + 2/7*p**5 - 2/7*p**3 + 0*p**i.
2*p**3*(p - 1)*(p + 1)/7
Let r(j) = 44*j**2 - 14*j + 6. Let u(w) = 9*w**2 - 3*w + 1. Let b(g) = 3*r(g) - 14*u(g). Let f(v) = -5*v**2 - v - 3. Let m(i) = -3*b(i) - 4*f(i). Factor m(d).
2*d*(d + 2)
Let l(o) be the first derivative of 5*o**4/4 + 10*o**3/3 + 5*o**2/2 + 8. Factor l(h).
5*h*(h + 1)**2
Let o(q) = q + 13. Let j be o(-11). Suppose 3*w - 8 = -j*d, -2*d + 8 + 0 = 5*w. Let 7*m + 2*m**2 + 1 + 1 - d - 7*m**3 = 0. Calculate m.
-1, 2/7, 1
Let v be 3 + 0/(-2) + 0. Let w(x) be the second derivative of 27/2*x**2 - 3*x**v - 2*x + 0 + 1/4*x**4. Determine a so that w(a) = 0.
3
Let o(h) = h**3 - 5*h**2 - 6*h + 4. Let y be o(6). Factor 128 + 8*t**3 + y*t**4 - 128.
4*t**3*(t + 2)
Let g(q) be the second derivative of 0 + 1/12*q**4 + 2/5*q**2 - 4*q + 4/15*q**3 + 1/100*q**5. Determine a, given that g(a) = 0.
-2, -1
Let u be 1/(-2) + 17/2. Let l be 1 + 2/u - 1. Solve -1/4*g**2 + l + 0*g = 0.
-1, 1
Let p(b) be the first derivative of 14*b**5/75 - 3*b**4/10 - 2*b**3/9 + 3*b**2/5 - 4*b/15 - 8. Find u such that p(u) = 0.
-1, 2/7, 1
Let x(k) = -k + 1. Let i be x(-6). Suppose -5 = -4*w + i. Suppose 0*m**5 - 2*m**w + 0*m**3 + 2*m**5 = 0. What is m?
-1, 0, 1
Let l be ((-4)/3)/(150/27 - 6). Factor 13/2*i**l + 0 + 2*i + 8*i**2 + 3/2*i**4.
i*(i + 2)**2*(3*i + 1)/2
Let j(w) be the second derivative of w**5/20 + w**4/4 + w**3/3 - 7*w. Let j(p) = 0. What is p?
-2, -1, 0
Factor -6*s - 26*s**4 + 6*s**3 + 23*s**4 - 18*s + 12*s**2.
-3*s*(s - 2)**2*(s + 2)
Find f such that 2*f**5 + 0*f - 4/3*f**2 + 0 + 14/3*f**3 - 16/3*f**4 = 0.
0, 2/3, 1
Let z(r) = 4*r**2 - 4*r + 11. Let a(w) = w**2 - w + 2. Let q(x) = 11*a(x) - 2*z(x). Suppose q(u) = 0. What is u?
0, 1
Let o be (1/(-5) - 0) + 26/5. Factor 3/5*s**2 - 3/5*s**4 + 3/5*s**3 + 0*s - 3/5*s**o + 0.
-3*s**2*(s - 1)*(s + 1)**2/5
Let f(h) = -65*h**2 - 117*h - 18. Let g(z) = -22*z**2 - 39*z - 6. Let a(w) = -4*f(w) + 11*g(w). Factor a(x).
3*(x + 2)*(6*x + 1)
Let u(s) be the first derivative of -6 + 0*s + 2/7*s**2 - 4/7*s**3 - 4/35*s**5 + 3/7*s**4. Factor u(i).
-4*i*(i - 1)**3/7
Let o(y) = 2*y - 6. Let t be o(4). Let a(w) be the third derivative of 1/48*w**4 - w**t + 0*w - 1/240*w**5 + 0 - 1/24*w**3. Suppose a(g) = 0. What is g?
1
Let s(g) be the second derivative of g**6/900 - g**4/180 - 2*g**2 - 5*g. Let t(z) be the first derivative of s(z). Factor t(m).
2*m*(m - 1)*(m + 1)/15
Let n = 202 - 2220/11. Suppose -n*g**2 + 0*g + 0 = 0. Calculate g.
0
Let a(l) = l**3 - l**2 + l + 2. Let w be a(0). Determine o so that -w*o**4 + o**5 + 2*o**5 + 5*o**4 = 0.
-1, 0
Determine r, given that 2/5*r - 7/5*r**2 + r**3 + 0 = 0.
0, 2/5, 1
Let h(j) be the first derivative of -5/4*j**2 - 3/8*j**4 - 3 - 7/6*j**3 - 1/2*j. Suppose h(r) = 0. What is r?
-1, -1/3
Let g(u) be the second derivative of -6*u**7/7 - u**6/5 + 2*u**5/5 + u**4/6 + 9*u. Find p, given that g(p) = 0.
-1/3, 0, 1/2
Let y(i) = 31*i - 183. Let p be y(6). Factor 0 + 0*k - 40/3*k**4 + 26/3*k**p - 4/3*k**2 + 6*k**5.
2*k**2*(k - 1)**2*(9*k - 2)/3
Let l be (-36)/(-17) - (-48)/(-408). Solve -4/3*z + 2*z**l - 2/3 = 0 for z.
-1/3, 1
Suppose -2*g = -2 + 2. Let q(y) be the second derivative of -4*y + 6*y**2 + 2*y**3 - 1/10*y**6 - 3/4*y**4 + g - 3/5*y**5. Solve q(w) = 0 for w.
-2, -1, 1
Let n(y) be the first derivative of -y**3/3 - 7*y**2/2 - 6*y - 5. Factor n(l).
-(l + 1)*(l + 6)
Let q(p) be the third derivative of -p**6/320 + 3*p**5/160 - p**4/32 + 11*p**2. Factor q(i).
-3*i*(i - 2)*(i - 1)/8
Let g = -50 + 56. Let b(v) be the third derivative of -1/630*v**7 + 0*v**3 - 1/360*v**g + 0*v**5 + 0*v + 0 + 0*v**4 + v**2. Factor b(f).
-f**3*(f + 1)/3
Suppose -3*m = -0*b - 2*b - 15, 5*m + 3*b = 25. Let t(l) be the second derivative of 59/6*l**4 + 4*l**2 - l + 28/3*l**3 + 7/2*l**m + 0. Factor t(q).
2*(q + 1)*(5*q + 2)*(7*q + 2)
Let l(o) be the second derivative of -3*o**5/50 - 2*o**4/15 + o**3/15 + 2*o**2/5 + 9*o + 4. Factor l(j).
-2*(j + 1)**2*(3*j - 2)/5
Let k be (1/2)/((-6)/(-4)). Solve 0 - k*u - 1/6*u**3 - 1/2*u**2 = 0.
-2, -1, 0
Let m(c) be the first derivative of -c**6/300 - c**5/30 - 2*c**4/15 - 4*c**3/15 + 2*c**2 + 2. Let q(r) be the second derivative of m(r). Factor q(n).
-2*(n + 1)*(n + 2)**2/5
Let m(o) be the first derivative of 45*o**4/4 - 20*o**3 + 10*o**2 + 10. Find b such that m(b) = 0.
0, 2/3
Factor -2/3*w + 1/2 + 1/6*w**2.
(w - 3)*(w - 1)/6
Suppose 0*v - 2*v - 8 = 0, 2*s - 4*v = 22. Let b be 7/3 + s/(-9). Let -3*h - 3*h**b + 6*h - 2 + h**3 + 1 = 0. What is h?
1
Let r be -1 + 2 + (-52)/60. Let l(s) be the first derivative of 2/5*s**2 - r*s**3 + 0*s + 3. Factor l(o).
-2*o*(o - 2)/5
Let q(y) be the second derivative of -y**8/1008 - y**7/630 + y**6/180 + 2*y**2 + 3*y. Let p(c) be the first derivative of q(c). Factor p(j).
-j**3*(j - 1)*(j + 2)/3
Suppose -s = 3*s - 28. Find m, given that s*m**5 + 7*m**4 - 3*m**4 - 2*m**4 = 0.
-2/7, 0
Let g(y) be the first deriva