)**2
Suppose 105 = 9*i + 87. Factor 1/2*y + 1/2*y**i + 0.
y*(y + 1)/2
Let v(d) be the first derivative of -d**6/6 - 16*d**5/45 - 5*d**4/36 + 2*d**3/27 + 11. Factor v(p).
-p**2*(p + 1)**2*(9*p - 2)/9
Suppose -c + 4*k - 10 = -0*c, 2*c - 4*k + 8 = 0. Factor -r + 2*r**2 - 4*r - 2*r**4 + 3*r**5 + 4*r - c*r**5.
r*(r - 1)**3*(r + 1)
Factor 1/8*h - 3/8*h**2 - 1/8*h**3 + 3/8.
-(h - 1)*(h + 1)*(h + 3)/8
Let i(o) = 105*o**4 + 42*o**3 - 105*o**2 - 60*o. Let a(b) = 30*b**4 + 12*b**3 - 30*b**2 - 17*b. Let r(c) = 18*a(c) - 5*i(c). Factor r(n).
3*n*(n - 1)*(n + 1)*(5*n + 2)
Let h(o) be the second derivative of -1/50*o**5 + 0 + 0*o**2 - 1/75*o**6 + 1/30*o**4 - 3*o + 1/15*o**3. Factor h(z).
-2*z*(z - 1)*(z + 1)**2/5
Let u(r) = -5*r**3 - 42*r**2 - 78*r. Let s(c) = 110*c**3 + 925*c**2 + 1715*c. Let q(m) = -2*s(m) - 45*u(m). Find l, given that q(l) = 0.
-4, 0
Let x(k) be the first derivative of -3/2*k**2 - 3*k - 1 + 3/4*k**4 + k**3. Factor x(l).
3*(l - 1)*(l + 1)**2
Suppose -3/2*t**3 - 3*t + 9/2*t**2 + 0 = 0. Calculate t.
0, 1, 2
Let y(f) be the second derivative of f**9/60480 - f**8/8960 + f**6/720 + f**4/12 + 3*f. Let b(d) be the third derivative of y(d). Find a such that b(a) = 0.
-1, 0, 2
Let s = 8/15 + 4/15. Factor 2/5*m**2 + s + 6/5*m.
2*(m + 1)*(m + 2)/5
Let h(i) = -i**4 + 6*i**3 + 3*i**2 - i. Let k(d) = 0*d + 0*d - 4*d**2 - 6*d**3. Let r(s) = 2*h(s) + 3*k(s). Find q, given that r(q) = 0.
-1, 0
Suppose -4*x - 3*s - s + 16 = 0, 0 = -2*x - 4*s + 12. Suppose 3*l + 2*a = 22, 3*l - 10 = 3*a + x. Let -l*m - 2*m**3 + 6*m = 0. Calculate m.
0
Let i(x) = -x**2 - 3*x - 2. Let r(z) = 5*z**2 + 13*z + 9. Let q = 12 - 30. Let l(f) = q*i(f) - 4*r(f). Let l(g) = 0. Calculate g.
0, 1
Factor -1 - 2*w + 0 - w**2 + 5 - 1.
-(w - 1)*(w + 3)
Let j(a) be the third derivative of 2*a**7/945 + a**6/60 + 2*a**5/45 + a**4/27 + 12*a**2. Determine g, given that j(g) = 0.
-2, -1/2, 0
Let b be 4/((-16)/2)*0. Solve 2/5 + b*k - 2/5*k**2 = 0.
-1, 1
Let -53*x**5 - 52*x**5 + 104*x**5 - x**4 = 0. What is x?
-1, 0
Let t be 810/2280 - 2/19. Let o(a) be the first derivative of 3/8*a**2 - 3 - 3/4*a - 3/16*a**4 + t*a**3. Factor o(w).
-3*(w - 1)**2*(w + 1)/4
Suppose 2/17*z**2 - 6/17*z + 4/17 = 0. What is z?
1, 2
Let b = 8 + -3. Suppose 19/4*v**4 + 0 - 15/4*v**3 - 7/4*v**b + 1/4*v**2 + 1/2*v = 0. Calculate v.
-2/7, 0, 1
Let s(t) be the first derivative of t**3/12 + t**2 + 4*t - 14. What is j in s(j) = 0?
-4
Let q(g) be the first derivative of 1/4*g**2 + 0*g + 0*g**3 - 1/8*g**4 + 2. Factor q(a).
-a*(a - 1)*(a + 1)/2
Let a(n) be the third derivative of -n**8/112 + n**7/105 - n**6/360 - 3*n**2. Solve a(t) = 0.
0, 1/3
Let k = -5 - -25. Suppose -4*f = -k + 4. Find n such that -3*n**2 + f - 4 + 3*n - 6*n = 0.
-1, 0
Let m(h) be the third derivative of -h**5/180 + h**4/36 - h**3/18 - 7*h**2. Determine b, given that m(b) = 0.
1
Let y(j) = -3*j - 1. Suppose 3*l + 1 = 2*l. Let g be y(l). Factor -i + i**2 + 0*i - g*i + 4*i.
i*(i + 1)
Let l(u) be the first derivative of -u**8/336 + 13*u**7/840 - u**6/90 - u**5/30 + u**3/3 - 2. Let s(n) be the third derivative of l(n). Factor s(r).
-r*(r - 2)*(r - 1)*(5*r + 2)
Let i(u) be the third derivative of 0*u**3 + 0*u**5 + 0*u + 0*u**6 - 4*u**2 + 0 + 1/945*u**7 + 0*u**4 + 1/1512*u**8. Factor i(l).
2*l**4*(l + 1)/9
Let n(j) be the first derivative of 0*j**2 + 0*j + 2 - 1/9*j**3. Find p such that n(p) = 0.
0
Let u(b) be the first derivative of 4/5*b + 3/5*b**2 - 6 + 0*b**3 - 1/10*b**4. Solve u(p) = 0.
-1, 2
Let t = -6 + 13. Let b(k) = -t*k**3 - 9*k**2 - 1 + 2*k**4 - 2*k**4 - k + 2*k**4. Let z(r) = -r**4 + r**3 + r**2 - r. Let a(c) = -b(c) - 3*z(c). Solve a(i) = 0.
-1
Let i(s) = -s**2 + 9*s - 6. Let t be i(8). Let o(z) be the first derivative of -t*z**2 - 2 - 14/5*z**5 + 2*z**3 + 0*z + 3/2*z**4 + z**6. Factor o(d).
2*d*(d - 1)**3*(3*d + 2)
Let 0 - 4/9*s**2 - 8/9*s = 0. Calculate s.
-2, 0
Let a be (-57)/(-5) - (-2)/(-5). Let g = -7 + a. Factor g*p**2 - 2*p**3 + 2*p**2 - 4*p**2.
-2*p**2*(p - 1)
Let p be 105/70 - (0 - -1). Suppose -1/2*i**2 - 1/2*i + 1/2*i**3 + 0 + p*i**4 = 0. What is i?
-1, 0, 1
Let y be -6 + 5 + (-12)/(-3). Suppose 5 = -y*u + 2*u, -2*d - 5 = u. Factor 9/7*g**4 - 3/7*g**5 + 0 - 9/7*g**3 + d*g + 3/7*g**2.
-3*g**2*(g - 1)**3/7
Let t(c) be the second derivative of 0 + 3*c + 1/4*c**4 - 1/2*c**3 + 0*c**2. Factor t(p).
3*p*(p - 1)
Suppose p + 2*p = 0. Suppose 5*u + 15 = 2*v + 3*v, -4*u - 4 = p. Factor -2*d**3 - 3*d**v + 2*d**2 - 2*d + 5*d**2.
-2*d*(d - 1)**2
Let r(d) = d**2 + 4*d - 10. Let v be r(-6). What is q in 8/7*q**4 + 4/7*q**2 + 2/7*q + 0 - v*q**3 = 0?
-1/4, 0, 1
Find i, given that 5/8*i + 1/2*i**2 + 1/8*i**3 + 1/4 = 0.
-2, -1
Suppose 8*i**5 - 22*i**5 - 20*i**3 - 21*i**5 + 80*i**4 = 0. What is i?
0, 2/7, 2
Let h(f) = 2*f**3 + 16*f**2 - 5*f**2 - f**3 - 12*f. Let n be h(-12). Solve -1 + 3/4*m**2 - 1/4*m**3 + n*m = 0.
-1, 2
Let w = 234 + -1161/5. Suppose w*s + 6/5 + 3/5*s**2 = 0. What is s?
-2, -1
Find l, given that 5*l**3 + l**2 - 5 + 5 + 5*l - 11*l**2 = 0.
0, 1
Let w(h) = h**3 + h**2 + h - 1. Let s(i) = -i**3 - 2*i**2 - 2*i + 2. Let c be (3/6)/((-2)/(-16)). Let q = 6 - c. Let x(k) = q*w(k) + s(k). Factor x(n).
n**3
Let s(z) be the first derivative of z**6/15 + 2*z**5/25 - z**4/10 - 2*z**3/15 + 9. Factor s(x).
2*x**2*(x - 1)*(x + 1)**2/5
Let y be (12 + 0)*5/15. Let q(k) be the third derivative of 0*k - k**2 + 0 + 0*k**5 + 1/60*k**y + 0*k**3 - 1/300*k**6. Suppose q(z) = 0. What is z?
-1, 0, 1
Let u(r) = r**4 - r**3 + r - 1. Let k(x) = 15*x**4 + 5*x**3 - 36*x**2 - 45*x - 19. Let h(w) = k(w) - 3*u(w). Factor h(b).
4*(b - 2)*(b + 1)**2*(3*b + 2)
Let s(y) = y**2 + y - 2. Let t be s(5). Let g be (-46)/(-14) - 8/t. Factor -2*f**2 - 2*f**g + 3*f**3 - 4*f**3.
-f**2*(3*f + 2)
Let r(k) be the first derivative of -k**4/6 + k**3/9 + k**2/6 - 7. Factor r(t).
-t*(t - 1)*(2*t + 1)/3
Let h(w) be the second derivative of w**4/6 + w**3 - 4*w**2 + 3*w - 6. Suppose h(i) = 0. What is i?
-4, 1
Let s(g) = g**3 + 8*g**2 - 9*g + 3. Let z(d) = d**3 + 6*d**2 + d - 3. Let u be z(-6). Let b be s(u). Let 4*l**2 - l - 3*l - l - 2*l**b + 3*l = 0. What is l?
0, 1
Factor r + 0*r**4 - 2*r**5 - r + 8*r**2 - 6*r**4.
-2*r**2*(r - 1)*(r + 2)**2
Let i = -467/91 + 37/7. Factor 2/13*z**4 + 6/13*z**2 + 6/13*z**3 + 0 + i*z.
2*z*(z + 1)**3/13
Let 0 - 3*v + 3/2*v**3 + 3/2*v**2 = 0. Calculate v.
-2, 0, 1
Let u(t) be the second derivative of -t**6/1080 - t**5/60 - t**4/8 + t**3 + 3*t. Let b(q) be the second derivative of u(q). Suppose b(d) = 0. Calculate d.
-3
Let o(h) be the second derivative of -h**4/12 - h**2/2 - 6*h. Let c(q) = 4*q**3 + 16*q**2 + 14*q + 6. Let l(g) = c(g) + 2*o(g). Determine k so that l(k) = 0.
-2, -1, -1/2
Let h(a) be the third derivative of -a**8/560 + a**7/175 - a**5/50 + a**4/40 + 8*a**2. Factor h(o).
-3*o*(o - 1)**3*(o + 1)/5
Let m(k) = -k + 1 + 0*k - 5 + 0*k. Let j be m(-7). Factor 6*h**3 - 4*h**3 - h**j + 2*h**3 + h**2.
h**2*(3*h + 1)
Let z(s) = s**2 - 1. Let g(n) = -14*n**3 - 19*n**2 - 4*n - 1. Let u(w) = -g(w) - 6*z(w). Let t(i) be the first derivative of u(i). Solve t(o) = 0 for o.
-1/3, -2/7
Let c(s) = 6*s + 6. Let l(o) = -o - 8. Let q be l(-5). Let k(f) = -f**2 + 6*f + 7. Let r(u) = q*k(u) + 2*c(u). Factor r(y).
3*(y - 3)*(y + 1)
Suppose -3*b + 5*b = 0, -810 = 3*j - b. Let c be (-354)/j + (-2)/10. Factor 2*n**2 + c*n**4 + 0 - 4/9*n - 8/3*n**3.
2*n*(n - 1)**2*(5*n - 2)/9
Let p(h) = 4*h**5 + 4*h**4 - 4*h**3. Let r(o) = o**5 + o**4 - o**3 + o**2. Let m(u) = p(u) - 2*r(u). Factor m(s).
2*s**2*(s - 1)*(s + 1)**2
Let f be (-3 - -4)*(-3)/(-18). Let s(d) be the first derivative of f*d**3 - 1/2*d - 4 + 1/4*d**2 - 1/8*d**4. Suppose s(q) = 0. What is q?
-1, 1
Let d(k) be the second derivative of 4*k**3 + 3/20*k**5 + 7*k + 24*k**2 + 0 - 7/4*k**4. Factor d(i).
3*(i - 4)**2*(i + 1)
Let l(n) be the first derivative of -3*n**5/5 - 7*n**4/4 + 4*n**3/3 - 7. Let a(r) = -21*r**4 - 48*r**3 + 27*r**2. Let j(h) = 4*a(h) - 27*l(h). Factor j(b).
-3*b**3*(b + 1)
Suppose 0 = -z - z + 42. Let y = 43/2 - z. Factor -1/2*x + y*x**2 - 1/2*x**4 + 0 + 1/2*x**3.
-x*(x - 1)**2*(x + 1)/2
Suppose 2*t + 0 - 6 = 0. Find d, given that -12*d**2 - 9*d**t - 3*d - 5*d - 2*d**4 - 2 + d**3 = 0.
-1
Let a be 1 + (3 - (1 + 1)). Factor u**a + u**2 + u - u**2.
u*(u + 1)
Suppose 4*d + 5 = -3*c, 3 = 2*c + c. Let b = 3 - d. Factor