q). Factor p(j).
-4*(j - 1)**3*(7*j + 2)
Let q(j) = -j + 8. Let i be q(8). Let g(t) be the first derivative of 2 + i*t - 2/9*t**3 + 1/3*t**4 - 1/3*t**2. Let g(s) = 0. Calculate s.
-1/2, 0, 1
Suppose -o = -2*c, -2*o - c - 2*c + 21 = 0. Let y be (-6)/15 + o/15. Factor 0 - 1/2*q**4 + y*q**2 + 0*q + 1/2*q**3.
-q**3*(q - 1)/2
Let m(q) be the second derivative of 0 - 4*q + 0*q**3 + 1/15*q**6 + 0*q**2 + 0*q**4 + 1/5*q**5. Find w such that m(w) = 0.
-2, 0
Factor -4/3 - 4/3*u - 1/3*u**4 + 2/3*u**3 + u**2.
-(u - 2)**2*(u + 1)**2/3
Solve -s**3 + 21*s + 25*s + 30*s - 75*s = 0 for s.
-1, 0, 1
Suppose -15*j + 23*j = 24. Factor -7/3*s**5 + 2/3*s**2 + 0*s - 11/3*s**j + 16/3*s**4 + 0.
-s**2*(s - 1)**2*(7*s - 2)/3
Let l(a) be the third derivative of 1/48*a**4 + 8*a**2 - 1/240*a**6 + 1/420*a**7 + 0*a**3 - 1/120*a**5 + 0*a + 0. Factor l(n).
n*(n - 1)**2*(n + 1)/2
Let f = 3665/4 - 911. Factor 3/2 - 15/4*p - f*p**2.
-3*(p + 1)*(7*p - 2)/4
Let z(b) be the third derivative of 4*b**7/105 + b**6/4 + 23*b**5/60 - b**4/2 - 2*b**3/3 - 5*b**2. Solve z(y) = 0 for y.
-2, -1/4, 1/2
Let p(q) be the second derivative of 1/33*q**6 + 7/22*q**4 - 1/3*q**3 - 4*q - 17/110*q**5 + 0 + 2/11*q**2. Find r such that p(r) = 0.
2/5, 1
Let z(k) be the second derivative of 7*k**5/50 - 19*k**4/30 + 8*k**3/15 + 4*k**2/5 + 14*k. Factor z(c).
2*(c - 2)*(c - 1)*(7*c + 2)/5
Let o(r) = -r**2 + r + 5. Suppose -4*h = -10 - 6. Let v(k) = k**2 - k - 4. Let t(f) = f + 5. Let u be t(0). Let g(z) = h*o(z) + u*v(z). Factor g(a).
a*(a - 1)
Let g(q) be the second derivative of -q**5/30 - q**4/6 - q**3/3 - q**2/3 + 3*q. Factor g(h).
-2*(h + 1)**3/3
Let g(u) be the first derivative of 0*u - 2/15*u**3 - 1/10*u**4 + 0*u**2 + 5. Determine s so that g(s) = 0.
-1, 0
Let n(h) be the first derivative of 3 + 0*h + h**2 - 3/2*h**4 + 2/5*h**5 - 2/3*h**3 + 2/3*h**6. What is w in n(w) = 0?
-1, 0, 1/2, 1
Suppose 6 = -z + 4*z. Factor 3*j - j**2 - j - z*j + j.
-j*(j - 1)
Suppose -2 = -m, -4*p + 3*m + 2*m = -6. Suppose -4*c = p*x - 2*c - 30, 4*c - 5 = 3*x. Solve 4/5*y**4 + 0 + 0*y**3 + 2/5*y**x - 2/5*y - 4/5*y**2 = 0 for y.
-1, 0, 1
Let w(r) = -3*r**4 + 21*r**3 - 3*r**2 - 57*r + 60. Let q(h) = -6*h**4 + 43*h**3 - 6*h**2 - 113*h + 121. Let y(p) = 6*q(p) - 13*w(p). Solve y(a) = 0 for a.
-2, 1, 3
Factor 5*s**2 + 10*s + 44 - 44.
5*s*(s + 2)
Let o(s) be the first derivative of 3*s**4/16 + 5*s**3/4 + 9*s**2/8 - 27*s/4 + 1. Find l such that o(l) = 0.
-3, 1
Let x(n) = 4*n**5 + 5*n**4 + n**3 + 3*n**2 - 3*n + 3. Let j(k) = -k**5 - k**4 - k**2 + k - 1. Let i(a) = 3*j(a) + x(a). Factor i(g).
g**3*(g + 1)**2
Suppose 2*t + 16 = -5*d - 0*t, 5*t + 7 = 4*d. Let m be (2 - 2)/d - -3. Factor 9 - 2*g**m - 9 + 2*g.
-2*g*(g - 1)*(g + 1)
Let j(r) = -12*r**3 + 57*r**2 + 9*r. Let v(b) = -3*b**3 + 14*b**2 + 2*b. Let g(k) = -2*j(k) + 9*v(k). Solve g(z) = 0.
0, 4
Suppose 2/3*d**2 + 4/3 + 3*d = 0. What is d?
-4, -1/2
Let 0 + 2*g**2 - 8/5*g**3 - 4/5*g + 2/5*g**4 = 0. Calculate g.
0, 1, 2
Let -12/5*q**3 - 15*q**2 - 18/5*q + 0 = 0. What is q?
-6, -1/4, 0
Let j(q) be the second derivative of 0 + 1/150*q**5 + 1/30*q**4 + 1/15*q**3 - 3/2*q**2 - 3*q. Let g(l) be the first derivative of j(l). Factor g(m).
2*(m + 1)**2/5
Let k(z) be the first derivative of 1/2*z**4 + 3 + z**2 - 4/3*z**3 + 0*z. Factor k(f).
2*f*(f - 1)**2
Let p = 2 + 1. Factor -2*a**2 + 6*a**2 + 2*a + p*a**3 - a**3.
2*a*(a + 1)**2
Let w(n) = n**2 - 4*n + 4. Let s be w(4). Let z = 4 - s. Factor 1/2*o**2 - o + z.
o*(o - 2)/2
Let w(a) be the third derivative of a**6/1800 - a**5/600 - a**3/6 + 5*a**2. Let f(b) be the first derivative of w(b). Factor f(x).
x*(x - 1)/5
Let p(o) be the first derivative of -o**4/2 + 4*o**3 - 12*o**2 + 16*o + 6. Find d, given that p(d) = 0.
2
Suppose 20*f = 19*f. Factor 0*v**2 + 2/3*v**3 - 2/3*v + f.
2*v*(v - 1)*(v + 1)/3
Let u(v) be the third derivative of 1/160*v**5 + 0*v + 0 + 0*v**3 + 1/64*v**4 - 8*v**2. Solve u(a) = 0 for a.
-1, 0
Let u be 0 + (-1)/(3/(-6)). Suppose 0 = -y + 6 - u. Solve -b**y + 4*b**4 - b**4 + 2*b**3 = 0.
-1, 0
Let a be 0/1 - (-9 + 1). Let j(t) = 3*t**2 + 14*t - 5. Let z = -5 + 10. Let w(y) = -2*y**2 - 9*y + 3. Let g(s) = a*w(s) + z*j(s). Factor g(f).
-(f + 1)**2
Let w(a) be the second derivative of 2*a - 1/24*a**4 + 1/4*a**2 + 0*a**3 + 0. Let w(b) = 0. What is b?
-1, 1
Factor -10*z**3 - z - 5*z + 15*z**2 - 10*z**4 - 2*z**3 + 13*z**4.
3*z*(z - 2)*(z - 1)**2
Find c such that -3*c + c**2 + 7*c + 6 - 9*c = 0.
2, 3
Let a(z) be the first derivative of 2/15*z**3 + 4/5*z**2 + 8/5*z - 3. Suppose a(o) = 0. What is o?
-2
Find k, given that -8/5 + 0*k + 2/5*k**2 = 0.
-2, 2
Factor 2/9*y**3 + 2*y - 4/3*y**2 - 8/9.
2*(y - 4)*(y - 1)**2/9
Let p = -307/3 - -103. Find h, given that p*h**3 - 2/3*h + 0 + 2/3*h**4 - 2/3*h**2 = 0.
-1, 0, 1
Factor 0 + 1/2*s**2 - 3/2*s.
s*(s - 3)/2
Factor -h + 0*h**3 - 4 - h**2 - 2 + h**3 + 7.
(h - 1)**2*(h + 1)
Let j(x) be the second derivative of 3/50*x**5 + 0 + 1/75*x**6 - 2*x + 1/15*x**3 + 1/10*x**4 + 0*x**2. Let j(o) = 0. Calculate o.
-1, 0
Let m(b) = -b**5 + b**4 + b**3 + b**2 + b + 1. Let s(k) = -4*k**5 + 6*k**4 + 3*k**3 - k**2 + 3*k + 3. Let n(a) = 6*m(a) - 2*s(a). Suppose n(z) = 0. Calculate z.
-1, 0, 2
Suppose 45 = 5*a + 5*s, 0 = 2*a - 6*s + 3*s - 3. Let l be 3/5 - a/30. Solve 0 + 0*z**4 + 0*z**2 + l*z**3 - 1/5*z - 1/5*z**5 = 0 for z.
-1, 0, 1
Let t = 34 - 30. Let z(g) be the third derivative of 7/72*g**t + 1/60*g**5 + 0 + 1/9*g**3 - 1/126*g**7 + 0*g - 7/360*g**6 + g**2. Solve z(u) = 0.
-1, -2/5, 1
Let r(n) be the second derivative of n**8/252 + n**7/70 + n**6/60 + n**5/180 - n**2/2 - 2*n. Let q(t) be the first derivative of r(t). Factor q(x).
x**2*(x + 1)**2*(4*x + 1)/3
Let m = 135/92 + -5/23. Factor 1/2*h + 13/4*h**4 - 1/4*h**2 - 9/4*h**3 + 0 - m*h**5.
-h*(h - 1)**3*(5*h + 2)/4
Let b(y) be the third derivative of -y**6/120 + y**5/40 + 2*y**3/3 - 3*y**2. Let l(o) be the first derivative of b(o). Determine t, given that l(t) = 0.
0, 1
Let j be 0 + 2 - (-2 + 1). Suppose -20 = d + 3*o - 9, -4*d + 16 = -j*o. Factor -2*r**3 + r - d + 5*r**3 - 4*r**3 + r**2.
-(r - 1)**2*(r + 1)
Let r(d) be the third derivative of -d**5/15 + d**4/12 + 2*d**2. Let l(f) = 5*f**2 - 2*f. Let g(u) = -2*l(u) - 3*r(u). Let g(x) = 0. What is x?
0, 1
Let o(g) = -7*g**4 + 11*g**3 - g**2 + 3*g. Let v(w) = 20*w**4 - 32*w**3 + 4*w**2 - 9*w. Let a(u) = -17*o(u) - 6*v(u). Determine l, given that a(l) = 0.
0, 1, 3
Factor 8/9*i**3 + 4/9*i**2 - 8/9*i**4 - 10/9*i + 2/9*i**5 + 4/9.
2*(i - 2)*(i - 1)**3*(i + 1)/9
Let u(n) be the first derivative of 3*n**5/5 - 15*n**4/4 + 7*n**3 - 9*n**2/2 - 1. Solve u(c) = 0 for c.
0, 1, 3
Let c(d) = 4*d**3 + 12*d**2 + 4*d. Let b(x) = x**2 + x. Let y(l) = 4*b(l) - c(l). Factor y(n).
-4*n**2*(n + 2)
Let o(a) = 24*a**4 - 60*a**3 + 36*a**2 + 12*a - 33. Let v(j) = 6*j**4 - 15*j**3 + 9*j**2 + 3*j - 8. Let k(u) = -5*o(u) + 21*v(u). Solve k(h) = 0.
-1/2, 1
Let x(z) = 10*z**2 + 0*z - 31*z**2 - 51*z - 29. Let d(w) = 4*w**2 + 10*w + 6. Let s(b) = 11*d(b) + 2*x(b). Suppose s(k) = 0. What is k?
-2
Let f = 239/70 - -3/35. Factor -f*m**5 - 10*m**3 - 4*m**2 + 13*m**4 + 0 + 0*m.
-m**2*(m - 2)**2*(7*m + 2)/2
Let h(g) be the third derivative of -g**8/168 + 2*g**7/105 - g**6/60 - 2*g**2. Factor h(f).
-2*f**3*(f - 1)**2
Suppose -o - 16 = o. Let d = -6 - o. What is y in 2/7*y**d + 0 + 0*y = 0?
0
Let w(r) be the second derivative of 1/9*r**3 - 4*r - 2/45*r**6 + 0*r**5 + 1/9*r**4 + 0*r**2 + 0 - 1/63*r**7. Factor w(j).
-2*j*(j - 1)*(j + 1)**3/3
Let q be (-3)/(-4) - (-45)/36. Factor -2/5*c**q - 2/5*c + 4/5.
-2*(c - 1)*(c + 2)/5
Let l(i) = -8*i**3 + 3*i**2 + 5. Let u be (-5)/((3/(-3))/(-1)). Let t(k) = -9*k**3 + 3*k**2 + 6. Let a(p) = u*t(p) + 6*l(p). Suppose a(x) = 0. What is x?
0, 1
Factor -2*d**2 + 2/3*d**4 + 2/3*d + 4/3 - 2/3*d**3.
2*(d - 2)*(d - 1)*(d + 1)**2/3
Let g(s) be the first derivative of 4*s**5/15 - s**4 + 4*s**3/3 - 2*s**2/3 - 18. Suppose g(i) = 0. Calculate i.
0, 1
Suppose 0*j + 12*j = 7*j. Let 1/3*i + 0 - 1/3*i**3 + j*i**2 = 0. What is i?
-1, 0, 1
Suppose 0*p - 1/9*p**3 + 2/9*p**2 + 0 = 0. Calculate p.
0, 2
Factor 1/3*f**2 + 2/3*f - f**3 + 0 - 1/3*f**4 + 1/3*f**5.
f*(f - 2)*(f - 1)*(f + 1)**2/3
Let f(j) = 2*j**4 - 2*j**3 + 5*j**2 + 5. Let v = 8 - 3. Let b(r) = -6*r**4 + 6*r**3 - 16*r**2 - 16. Let k(w) = v*b(w) + 16*f(w). Solve k(c) = 0 for c.
0,