hat 1/3*r + 1/3*r**2 - v = 0.
-2, 1
Let d = -12 + 15. Let r(s) = -s**5 + s**4 + s**3 - s**2 - s. Let b(v) = -6*v**5 + 6*v**3 - 3*v. Let t(j) = d*r(j) - b(j). Factor t(f).
3*f**2*(f - 1)*(f + 1)**2
Determine a, given that 3/2*a**3 + 0*a + 0 - a**2 = 0.
0, 2/3
Let r(a) = -2*a - 2 - a**2 + 3*a**2 - 3*a. Let f(n) = n**2 - 5. Let t be f(0). Let i(m) = m**2 - 2*m - 1. Let o(y) = t*i(y) + 2*r(y). Factor o(z).
-(z - 1)*(z + 1)
Let p(y) be the third derivative of -y**8/23520 - y**7/8820 + y**6/1260 + y**4/6 + 5*y**2. Let k(f) be the second derivative of p(f). Factor k(d).
-2*d*(d - 1)*(d + 2)/7
Let y(q) be the second derivative of q**7/21 - 2*q**6/15 - q**5/10 + q**4/3 + 6*q. Suppose y(x) = 0. What is x?
-1, 0, 1, 2
Let s be -5 + (-345)/(-50) + (-2)/5. Factor -3/2*z**2 - s + 3*z.
-3*(z - 1)**2/2
Let v be (-1)/2*42/(-28). What is u in 1/4 + 1/4*u**3 + 3/4*u**2 + v*u = 0?
-1
Let k = -7 - -7. Let j(c) be the third derivative of k + 1/630*c**7 + 0*c**6 + 0*c - 1/180*c**5 + 0*c**4 + 0*c**3 - 3*c**2. Factor j(w).
w**2*(w - 1)*(w + 1)/3
Factor 3*q**2 - 10*q**3 + 22*q**2 + 10*q**3 + 10*q + 15*q**3 - 5*q**5 - 5*q**4.
-5*q*(q - 2)*(q + 1)**3
Determine z, given that -z**4 + 1/3*z**5 + 2/3*z**3 + 1/3 - z + 2/3*z**2 = 0.
-1, 1
Let o(u) be the first derivative of 0*u + 1/4*u**3 - 1 + 3/4*u**2. Factor o(n).
3*n*(n + 2)/4
Let u be 0/(3 + -5 + 4). Let i(s) be the third derivative of 1/300*s**6 + 0 + 0*s**4 - 3*s**2 + u*s + 0*s**3 - 1/150*s**5. Factor i(n).
2*n**2*(n - 1)/5
Let v(l) be the second derivative of l**7/7560 - l**4/4 + 3*l. Let i(o) be the third derivative of v(o). Factor i(g).
g**2/3
Suppose 3*w**4 + 3*w**4 + 2*w**3 - 8*w**4 = 0. What is w?
0, 1
Let m = -23 - -19. Let v be -1*1/2*m. Determine p, given that 0 + 0*p - 2/3*p**v = 0.
0
Let r be 30/42 - (-2)/7. Let u be 18/60 + r/5. Factor -1/2*q + u*q**3 - 1 + q**2.
(q - 1)*(q + 1)*(q + 2)/2
Let u be (-10)/(-15)*(-1 + 2). Factor -2/3*m**2 + u*m**3 - 2/3*m + 0 + 2/3*m**4.
2*m*(m - 1)*(m + 1)**2/3
Let w = -4 - -5. Suppose -4*h = w - 9. Factor -c**3 - c**3 + 0*c**2 - 2*c**h.
-2*c**2*(c + 1)
Suppose -2 = -0*j + 2*j. Let v be (j/(-3))/(4/16). Solve 2/3*g**5 - 2/3*g - 4/3*g**2 + 0 + 0*g**3 + v*g**4 = 0.
-1, 0, 1
Let l(o) be the first derivative of o**6/14 + 3*o**5/35 - 3*o**4/28 - o**3/7 + 7. Factor l(w).
3*w**2*(w - 1)*(w + 1)**2/7
Let g(b) be the third derivative of -b**8/42 + 13*b**7/105 - b**6/4 + 7*b**5/30 - b**4/12 - 27*b**2. Factor g(w).
-2*w*(w - 1)**3*(4*w - 1)
Let -30*p**2 - 3*p**4 - 30*p**2 + 66*p**2 + 3*p**3 = 0. What is p?
-1, 0, 2
Let j(m) = -29*m**3 - 40*m**2 + 21*m. Let p(d) = -44*d**3 - 60*d**2 + 32*d. Let r(o) = -8*j(o) + 5*p(o). Factor r(c).
4*c*(c + 2)*(3*c - 1)
Suppose 0 = -h + 5*h. What is n in -1/4*n**4 + 1/2*n**3 + 0 - 1/4*n**5 + h*n**2 + 0*n = 0?
-2, 0, 1
Let v(y) be the third derivative of -y**5/40 + y**4/16 + y**3/2 + 25*y**2. Suppose v(h) = 0. What is h?
-1, 2
Let i be (-3 - -4 - 1)/1. Let y(m) be the first derivative of 2 + 1/3*m**6 + 2/5*m**5 - 1/2*m**4 + 0*m - 2/3*m**3 + i*m**2. Suppose y(t) = 0. What is t?
-1, 0, 1
Let i be 38/84 + (-13)/78. Factor 6/7*t - i - 6/7*t**3 + 2/7*t**2.
-2*(t - 1)*(t + 1)*(3*t - 1)/7
Determine o, given that 2*o**4 - 2*o**2 - 2*o**3 + 3*o**3 - o**4 + 0*o**2 = 0.
-2, 0, 1
Suppose -2*y + 0*y = n - 12, -5*n - 3*y + 25 = 0. Determine k, given that 0 - 2*k**n - 3 + 3 = 0.
0
Let p = -245/2 - -1723/14. Let -p - 10/7*h + 2*h**2 = 0. What is h?
-2/7, 1
Let d(w) be the first derivative of 2/3*w**6 + 4*w - 2 + 2*w**2 - 2*w**4 + 4/5*w**5 - 8/3*w**3. Let d(j) = 0. Calculate j.
-1, 1
Let b(s) be the third derivative of -s**6/1140 - s**5/570 - 12*s**2. Suppose b(t) = 0. What is t?
-1, 0
Factor -2/13*t + 0 + 2/13*t**2.
2*t*(t - 1)/13
Suppose 2*g = 5*g. Factor 3*v - 8*v**2 + 6*v**2 + 3*v**4 + g*v**3 - 1 - 2*v**3 - v**5.
-(v - 1)**4*(v + 1)
Let w(l) be the first derivative of l**6/24 + l**5/5 + 3*l**4/16 - l**3/3 - l**2/2 - 21. Factor w(y).
y*(y - 1)*(y + 1)*(y + 2)**2/4
Let v(d) be the second derivative of -5*d**4/12 - d**3/2 - 3*d**2/2 - 2*d. Let p(r) = 26*r**2 + 16*r + 16. Let k(j) = 3*p(j) + 16*v(j). Factor k(i).
-2*i**2
Let u be 1 + -4 + 1860/(-14). Let j = u - -137. Factor 8/7 - j*w + 2/7*w**2.
2*(w - 2)**2/7
Let v(f) be the first derivative of -2/27*f**3 - 2 - 1/3*f**2 - 4/9*f. Find t, given that v(t) = 0.
-2, -1
Let j(r) be the third derivative of 0*r**3 - 1/140*r**8 + 6*r**2 + 13/350*r**7 - 3/40*r**6 + 0 + 7/100*r**5 - 1/40*r**4 + 0*r. Factor j(c).
-3*c*(c - 1)**3*(4*c - 1)/5
Let q(v) = v**2 + 5*v + 3. Let o be q(-5). Suppose -o*m - 4*d = -26, -3*m = -d + 1 - 2. Factor -w + 3*w - w - w**3 - w**m + w.
-w*(w - 1)*(w + 2)
Let c be (6/(-4))/((-2)/(-12)). Let m be (12/c)/(-4)*0. Factor m*f - 2*f**4 + 0*f + f**3.
-f**3*(2*f - 1)
Let b(r) be the second derivative of r**5/20 + r**3/6 + 2*r. Let p(q) = -q**3 + q**2 - 2*q. Let z(k) = -2*b(k) - p(k). Factor z(c).
-c**2*(c + 1)
Let k(d) be the third derivative of -d**5/4 + 5*d**4/6 + 10*d**3/3 + 16*d**2. Suppose k(i) = 0. Calculate i.
-2/3, 2
Suppose v**2 + v**2 - 7*v**2 - 5*v**3 = 0. Calculate v.
-1, 0
Let b(g) be the third derivative of 3*g**2 + 1/7*g**3 - 1/210*g**5 + 1/42*g**4 + 0*g + 0. Find f such that b(f) = 0.
-1, 3
Let v(h) be the second derivative of -h**4/9 + h**3/18 + h. Suppose v(q) = 0. Calculate q.
0, 1/4
Let h(z) be the third derivative of 0 - 3*z**2 - 1/3*z**3 + 7/60*z**5 + 5/24*z**4 + 0*z. Solve h(o) = 0 for o.
-1, 2/7
Let d(f) be the second derivative of -f**4/12 - 7*f**3/30 - f**2/5 + 13*f. Let d(w) = 0. Calculate w.
-1, -2/5
Let g(a) be the third derivative of 1/105*a**6 + 2/735*a**7 - 10*a**2 + 0*a + 0 - 1/21*a**4 + 0*a**3 - 1/105*a**5. Solve g(p) = 0 for p.
-2, -1, 0, 1
Let l = 9 - 4. Let i be (-2 + l)/(27/2). Factor 2/9*j**2 + 4/9*j + i.
2*(j + 1)**2/9
Let t(k) = 14*k**4 - 6*k**3 + 14*k**2 + 11*k + 11. Let v(j) = -5*j**4 + 2*j**3 - 5*j**2 - 4*j - 4. Let r(z) = 4*t(z) + 11*v(z). Suppose r(w) = 0. What is w?
0, 1
Suppose -2*l - 2*t = -6*t - 2, 2*t = -2*l + 2. Let c = l - -1. Find d, given that -2*d - 1 + d**2 + 0*d - 2*d**c = 0.
-1
Let n = 101 - 3029/30. Let a(v) be the second derivative of 0*v**2 + 1/45*v**6 - 1/63*v**7 - 1/18*v**4 + n*v**5 + v + 0 + 0*v**3. Let a(r) = 0. Calculate r.
-1, 0, 1
Let a(j) be the third derivative of -j**6/840 - j**5/140 - j**4/56 - j**3/42 + 8*j**2. Solve a(c) = 0 for c.
-1
Let l(o) = o**3 - 2*o**2 + 2. Let f be l(2). Factor -f*u**3 + 4/7 - 24/7*u**2 - 6/7*u.
-2*(u + 1)**2*(7*u - 2)/7
Let p(i) be the second derivative of i**4/24 - i**3/2 + 2*i**2 - 4*i + 8. Let p(f) = 0. Calculate f.
2, 4
Suppose -49*r = -45*r - 12. Solve 0 + 1/3*y**r + 1/3*y**2 - 1/3*y - 1/3*y**4 = 0 for y.
-1, 0, 1
Let y(i) = -2*i**2 + 3*i - 3. Let o(l) = 10*l**2 - 14*l + 14. Let k(d) = 3*o(d) + 14*y(d). Let q be k(1). Factor 8 - 3*p + q*p**2 + 5*p + 6*p.
2*(p + 2)**2
Let k(x) = -2*x - 7. Let a be k(-5). Suppose l**2 - 1 - a*l**2 + 3*l**2 = 0. Calculate l.
-1, 1
Let j(c) be the third derivative of c**6/40 + c**5/4 + 3*c**4/8 - 9*c**3/2 + 36*c**2. Factor j(x).
3*(x - 1)*(x + 3)**2
Let o = 17 - 12. Let b = 5 + -1. Factor -3*y**b + 2*y**5 + 4*y**4 + 2*y**3 - o*y**4.
2*y**3*(y - 1)**2
What is h in 0*h - 1/3*h**5 + 0*h**2 + 0 - 1/3*h**3 - 2/3*h**4 = 0?
-1, 0
Let x(j) be the third derivative of -j**8/672 + j**7/60 - 3*j**6/40 + j**5/6 - j**4/6 - 2*j**2. Factor x(y).
-y*(y - 2)**3*(y - 1)/2
Let u(k) = -7*k**4 + 7*k**3 + 18*k**2 - 8*k - 24. Let w(i) = 8*i**4 - 8*i**3 - 18*i**2 + 7*i + 24. Let r(c) = -5*u(c) - 4*w(c). Find a such that r(a) = 0.
-2, -1, 2
Let b(a) be the second derivative of -a**6/90 + a**5/30 + a**4/12 - a - 50. Factor b(f).
-f**2*(f - 3)*(f + 1)/3
Let t = -890/7 + 128. Let 0 - t*a**3 + 4/7*a**2 + 2/7*a**4 + 0*a = 0. Calculate a.
0, 1, 2
Let o(l) be the second derivative of 1/40*l**5 + 0 - 1/6*l**4 + 4*l + 5/12*l**3 - 1/2*l**2. Suppose o(s) = 0. Calculate s.
1, 2
Let r(d) be the third derivative of d**9/8640 - d**8/2240 + d**7/2520 + d**5/20 + 2*d**2. Let j(p) be the third derivative of r(p). Solve j(b) = 0 for b.
0, 2/7, 1
Let x be (-2)/(-5) - 2*(-5)/100. Find s such that x*s**2 + 1/4*s**3 + 1/4*s + 0 = 0.
-1, 0
Let c(k) = -k**3 - 4*k**2 + 3. Let i be c(-4). Factor -46*u**5 + 21*u**5 + 24*u**5 + 1 + 3*u - i*u**4 - 2*u**3 + 2*u**2.
-(u - 1)*(u + 1)**4
Let n(x) = -x**3 - 9*x**2 - 8*x + 4. Let h be