*2. Factor o(r).
-r*(r - 2)/4
Let r(x) = -x + 1. Suppose -2*w + 5*w + 30 = 0. Let v(l) = l**3 - 3*l**2 + 7*l - 5. Let g(d) = w*r(d) - 2*v(d). Suppose g(f) = 0. What is f?
0, 1, 2
Let j(k) be the third derivative of 1/1050*k**7 + 1/300*k**5 + 0*k**3 + 0 + 1/300*k**6 + 0*k**4 - 5*k**2 + 0*k. Let j(r) = 0. Calculate r.
-1, 0
Let o be (-168)/(-49) - (-12)/21. Let -2/3*d**5 + 0*d + 0*d**o + 0*d**2 + 0*d**3 + 0 = 0. What is d?
0
Let d(v) be the first derivative of -v**4/4 - v**3/3 + v**2/2 + v - 2. Let d(t) = 0. Calculate t.
-1, 1
Let t = 217/4 - 54. Factor 1/2*s - 1/4*s**2 - t.
-(s - 1)**2/4
Let v(c) be the first derivative of -2*c**5/15 + 2*c**3/3 + 2*c**2/3 + 11. Solve v(t) = 0.
-1, 0, 2
Let o be (-5)/(-2)*(-54)/(-27). Let 2/3*i**2 + 1/3*i**o + 0*i**3 - 1/3*i + 0 - 2/3*i**4 = 0. Calculate i.
-1, 0, 1
Let t(s) be the second derivative of -s**6/80 - s**5/40 + s**2 - 3*s. Let q(o) be the first derivative of t(o). Factor q(u).
-3*u**2*(u + 1)/2
Factor 1/2*s**3 - 3/2 + 7/2*s - 5/2*s**2.
(s - 3)*(s - 1)**2/2
Let y = -1 - -1. Suppose y*b - 55 = -5*b. Factor -5*r**4 + r**4 + 5*r**2 - 1 + 3 + 7*r**2 - r**3 + b*r.
-(r - 2)*(r + 1)**2*(4*r + 1)
Solve -5*w**5 - 5*w**3 + 11 - 15*w**2 + 15*w**4 - 11 + 10*w = 0 for w.
-1, 0, 1, 2
Let x(l) be the third derivative of 2/27*l**3 + 2*l**2 + 0*l + 5/108*l**4 + 2/135*l**5 + 0 + 1/540*l**6. Factor x(c).
2*(c + 1)**2*(c + 2)/9
Let y be -1 - (-1 + (-18)/15). Let s = -4/5 + y. Factor s*q + 2/5*q**2 + 0.
2*q*(q + 1)/5
Let j(i) be the third derivative of 0 + 0*i + 1/450*i**5 - i**2 + 0*i**3 + 1/180*i**4. What is t in j(t) = 0?
-1, 0
Let s be 4 + -5 - 44/(-3). Let f = -13 + s. Suppose 1/3 - 1/3*w**5 - w**4 + 2/3*w**2 - f*w**3 + w = 0. What is w?
-1, 1
Let d(n) = n**3 + 38*n**2 - 45*n - 232. Let w be d(-39). Determine b so that 0 - 2/11*b**3 + 0*b**w + 2/11*b**4 + 0*b = 0.
0, 1
Factor 10*h**3 - 18 - 15*h**3 + 4*h**4 + 21*h**3 + 12*h**2 - 16*h + 2.
4*(h - 1)*(h + 1)*(h + 2)**2
Suppose 4*t + 12 = 0, 5*f + t - 1 = -4. Let 0*m - 3/2 + f*m**3 + 3*m**2 - 3/2*m**4 = 0. Calculate m.
-1, 1
Let n(h) be the second derivative of 0*h**3 - 1/4*h**2 + 1/24*h**4 + 3*h + 0. Factor n(o).
(o - 1)*(o + 1)/2
Let i = 1053/4 - 262. Factor 1/2*k + 0 - i*k**3 - 1/4*k**2 - 1/2*k**4.
-k*(k + 1)*(k + 2)*(2*k - 1)/4
Suppose 25 = 9*x - 20. Let l(g) be the third derivative of 0 + g**2 + 0*g**4 + 1/30*g**x + 0*g - 1/3*g**3. Factor l(r).
2*(r - 1)*(r + 1)
Let y(o) be the first derivative of 4*o**3/3 - 16*o - 3. Find b such that y(b) = 0.
-2, 2
Let g(x) = x**3 - x + 1. Let c(j) = -2*j**4 + j**3 - 3*j + 3. Suppose 5*a = 4*u - 15, 4*a + 5*u = -a - 15. Let r(m) = a*g(m) + c(m). Solve r(s) = 0.
-1, 0
Let z(b) = -b**3 - 4*b**2 + b + 4. Let h be z(-4). Find f such that -5*f + f**3 + 3*f + f**3 + h*f = 0.
-1, 0, 1
Let c = 9 + -7. Suppose 3*g - 15 = -c*g. Find b such that -b**3 - b**3 + b**3 - g*b**2 - b + b**2 = 0.
-1, 0
Let o = 122 + -1094/9. Suppose 2/9*i**4 + 2/9 + 2/9*i - 4/9*i**2 - o*i**3 + 2/9*i**5 = 0. Calculate i.
-1, 1
Let h(l) be the second derivative of -l**7/126 + l**6/90 + l**5/12 - 5*l**4/36 - 2*l**3/9 + 2*l**2/3 + 7*l. Let h(w) = 0. What is w?
-2, -1, 1, 2
Let t(n) be the first derivative of n**4/12 - 2*n**3/9 - 4. Determine g so that t(g) = 0.
0, 2
Suppose 5*n - 15 = 5*f, -4*f + 0*n + 9 = 3*n. Factor 2/3*p**3 + 0*p**2 + 2*p**4 + f + 0*p.
2*p**3*(3*p + 1)/3
Let k(i) = i**3 - 3*i**2 + 3*i - 5. Let s(a) = -a**3 + 2*a**2 - 2*a + 4. Suppose -4*q = -2 - 14. Let t(h) = q*s(h) + 3*k(h). Factor t(j).
-(j - 1)*(j + 1)**2
Let o(q) = -q**2 - 5*q - 2. Let s be o(-4). Let n be s + 1/1 + 2. Solve -v**4 - 3 + 4*v**5 - n*v**5 + 3 = 0.
-1, 0
Let u(r) be the first derivative of -2/27*r**3 + 0*r - 1/9*r**2 + 1. Determine o, given that u(o) = 0.
-1, 0
Let y be 5/(-28) + 6/14. Factor -y*r**2 + 1/4*r + 0 + 1/4*r**4 - 1/4*r**3.
r*(r - 1)**2*(r + 1)/4
Let h(l) be the second derivative of -l**6/80 + l**5/40 - l**2 + 5*l. Let a(r) be the first derivative of h(r). Factor a(k).
-3*k**2*(k - 1)/2
Let j(f) be the second derivative of -f**7/35 - f**6/6 - 3*f**5/10 - f**4/6 + f**2 - 4*f. Let z(h) be the first derivative of j(h). Suppose z(b) = 0. What is b?
-2, -1, -1/3, 0
Let j(m) be the second derivative of m**6/540 + m**5/180 - m**4/18 + 4*m**3/3 + 5*m. Let k(n) be the second derivative of j(n). Factor k(y).
2*(y - 1)*(y + 2)/3
Let z(y) be the second derivative of 0 - 3*y - 3/80*y**5 + 0*y**3 + 1/56*y**7 - 1/16*y**4 + 1/40*y**6 + 0*y**2. Factor z(q).
3*q**2*(q - 1)*(q + 1)**2/4
Let g(x) = 4*x**2 + 3*x - 1. Let o(a) = -a**2 + 1. Let s be 0/2 + 3 + 2. Let f(r) = s*o(r) - g(r). Determine i so that f(i) = 0.
-1, 2/3
Let v be (-3)/(-99)*41 - (-73)/803. Find u, given that -2/3*u**2 - v*u + 0 = 0.
-2, 0
Let b(s) = 5*s**3 - 30*s**2 + 60*s - 35. Let z(o) = 5*o**3 - 30*o**2 + 60*o - 36. Let n(w) = -4*b(w) + 5*z(w). Let n(y) = 0. Calculate y.
2
Let c(h) be the second derivative of h**4/12 + 4*h**3/3 + 8*h**2 + 13*h. Factor c(m).
(m + 4)**2
Let w(d) be the first derivative of 3*d**6 + 66*d**5/5 + 37*d**4/2 + 10*d**3 + 2*d**2 - 5. Suppose w(t) = 0. What is t?
-2, -1, -1/3, 0
Let c(p) be the third derivative of 1/21*p**7 - 1/6*p**6 + 0 + 0*p - 6*p**2 + 1/3*p**3 - 5/12*p**4 - 1/168*p**8 + 1/3*p**5. Factor c(m).
-2*(m - 1)**5
Let y(z) = -z**5 + z**4 - z**3 + z**2 + z. Let h(u) = -11*u**5 + 31*u**4 - 36*u**3 - 4*u**2 + 41*u - 15. Let k(r) = -h(r) + 6*y(r). Factor k(v).
5*(v - 3)*(v - 1)**3*(v + 1)
Let d(y) be the third derivative of -1/672*y**8 + 0*y**4 + 0*y + 0*y**7 + 0 + 0*y**3 + 0*y**5 + 4*y**2 + 0*y**6. Factor d(t).
-t**5/2
Suppose y**3 - y**4 - 3*y - 2*y + 5*y**4 - 2 - 3*y**4 - 3*y**2 = 0. What is y?
-1, 2
Let b(i) be the third derivative of -i**8/112 - i**7/14 - 7*i**6/40 - 3*i**5/20 - 22*i**2. Suppose b(m) = 0. What is m?
-3, -1, 0
Let s(v) be the first derivative of 2*v**3/27 - v**2/3 + 4*v/9 - 6. Determine b, given that s(b) = 0.
1, 2
Let x(l) = -3*l**2 - 3*l + 6. Let r = 5 - 1. Let q(c) = 3*c**2 + 3*c - 6. Let j(o) = r*q(o) + 5*x(o). Factor j(k).
-3*(k - 1)*(k + 2)
Let c = 2 + 1. Let o be (c/(-2))/((-4)/8). Determine w, given that -2/9*w**2 + 2/9*w - 2/9*w**o + 2/9 = 0.
-1, 1
Factor -1/3*v**5 + v**4 - 1/3 - 2/3*v**3 - 2/3*v**2 + v.
-(v - 1)**4*(v + 1)/3
Let j(h) be the second derivative of h**6/60 + h**5/30 - 3*h**2/2 + h. Let n(o) be the first derivative of j(o). Determine y so that n(y) = 0.
-1, 0
Factor 3/7*p**2 - 3 + 18/7*p.
3*(p - 1)*(p + 7)/7
Let j = 17 + -13. Suppose 3*h**3 - 2*h**5 + 9*h**4 - 4*h**2 - h**3 - 10*h**j + 5*h**4 = 0. Calculate h.
-1, 0, 1, 2
Suppose -26*w + 27*w = 0. Let v(a) be the second derivative of 0*a**4 + 0*a**3 + 2*a + 1/80*a**5 - 1/168*a**7 + 0*a**2 + w*a**6 + 0. Find u such that v(u) = 0.
-1, 0, 1
Let j(i) be the third derivative of -i**6/180 + i**4/12 - i**3/2 + 2*i**2. Let s(v) be the first derivative of j(v). Factor s(c).
-2*(c - 1)*(c + 1)
Find o, given that -o**2 + 0 - 1/3*o**3 - 2/3*o = 0.
-2, -1, 0
Let r = 542 - 1083/2. What is b in 0 + r*b - 1/4*b**2 = 0?
0, 2
Let h be 30/(-8) + (-12)/(-3). Factor -h*b**2 + 1/4*b + 0.
-b*(b - 1)/4
Let v be (0 + 14/(-315))*-10. Let 2/3*f**3 - v*f**2 + 4/9 - 2/3*f = 0. What is f?
-1, 2/3, 1
Let q(a) be the third derivative of -a**5/160 - a**4/16 - a**3/4 - 17*a**2. Factor q(u).
-3*(u + 2)**2/8
Suppose -17 = 2*s - 25. Let t(a) be the second derivative of -3*a - 1/6*a**3 + 0*a**2 + 1/20*a**5 + 0 + 1/30*a**6 - 1/12*a**s. Factor t(i).
i*(i - 1)*(i + 1)**2
Find i, given that -1/8 + 3/8*i**2 + 1/4*i = 0.
-1, 1/3
Let b = 7 - 27/4. Let l be -2 + 16/(4 + 0). Factor 0 - b*x - 1/4*x**l.
-x*(x + 1)/4
Let a(w) be the third derivative of 1/540*w**6 - 1/30*w**5 - w**2 - w**3 + 0*w + 1/4*w**4 + 0. Factor a(t).
2*(t - 3)**3/9
Factor o**3 + o**4 - 10*o**5 - o**2 + 2*o**3 - 2*o + 9*o**5.
-o*(o - 2)*(o - 1)*(o + 1)**2
Let y be (-3)/(15/(-17)) - 2/5. Let d(r) be the third derivative of 0*r**7 + 1/504*r**8 + 0 + 0*r**y + 0*r**6 + 3*r**2 + 0*r**5 + 0*r + 0*r**4. Factor d(g).
2*g**5/3
Let i(d) = -d**4 + d**3 + d. Let v(c) = c**5 + 9*c**4 + 10*c**3 + 12*c**2 + c. Let s(q) = 3*i(q) + v(q). Factor s(f).
f*(f + 1)**2*(f + 2)**2
Suppose 2*v = -3*v + 10. Determine g so that -g**2 - 9*g - g**2 - g**v = 0.
-3, 0
Let q = 1 - -2. Factor -6*i + 21*i**2 - 12*i**q + 0*i**3 + 3*i**3 + 0*i**2.
-3*i*(i - 2)*(3*i - 1)
Let k(z) be the third derivative 