 Suppose z(r) = 0. What is r?
1
Factor -5*b**2 + 3*b**3 - 3*b**3 + 6*b**4 - b**4.
5*b**2*(b - 1)*(b + 1)
Let h(b) = -4*b**2 - 6*b + b**2 - 7 + 7. Let j(n) = -2*n**2 - 3*n. Let l(z) = -3*h(z) + 5*j(z). Factor l(a).
-a*(a - 3)
Let l(q) be the second derivative of -q**6/240 + q**5/60 - q**4/48 + q**2 - 6*q. Let z(w) be the first derivative of l(w). Let z(o) = 0. Calculate o.
0, 1
Let g = -3 - -5. Let p(a) be the second derivative of 0 + 0*a**g - 1/3*a**3 + 1/3*a**4 - 1/10*a**5 + 3*a. Suppose p(l) = 0. What is l?
0, 1
Let l(v) be the third derivative of v**2 + 0 - 1/12*v**4 + 1/6*v**3 + 0*v + 1/60*v**5. Factor l(n).
(n - 1)**2
Suppose -5*m - 5*t = -25, m - 20 = -5*t + t. Let o be ((-4)/15)/((-4)/10). Factor -4/3*p + 4/3*p**3 + 2/3*p**4 + m*p**2 - o.
2*(p - 1)*(p + 1)**3/3
Let k(c) be the second derivative of c**5/70 + 2*c**4/21 + 5*c**3/21 + 2*c**2/7 - 11*c + 2. Find s such that k(s) = 0.
-2, -1
Factor 0*c**4 - 27*c - c**4 + 3*c**4 + c**4 - 21*c**3 + 45*c**2.
3*c*(c - 3)**2*(c - 1)
Let z be (4 - 1)*(1 - 20/25). Solve -6/5*g + 3/5*g**2 + z = 0.
1
Let c(a) be the first derivative of -a**5/300 + a**4/60 - 3*a**2/2 - 2. Let m(o) be the second derivative of c(o). Factor m(s).
-s*(s - 2)/5
Let a be -2*(4 - (-26)/(-4)). Let b(q) be the second derivative of -1/3*q**4 + 0 + 1/3*q**3 + q**2 + 1/15*q**6 + 1/21*q**7 + q - 1/5*q**a. Factor b(c).
2*(c - 1)**2*(c + 1)**3
Let k be 0 - 1/1 - 5. Let b be 8/(-2) + (-27)/k. Factor -3/2*z**3 + 0 - 3/2*z**4 - b*z**2 - 1/2*z**5 + 0*z.
-z**2*(z + 1)**3/2
Let v = -119 - -123. Let i(a) be the third derivative of 2*a**2 - 1/3*a**3 + 1/8*a**v + 0 - 1/60*a**5 + 0*a. Factor i(j).
-(j - 2)*(j - 1)
Let h be (-63)/(-3) - 2*1. Suppose -2*n + 23 = h. What is s in 0 - 1/4*s**3 + 0*s + 1/4*s**4 - 1/4*s**n + 1/4*s**5 = 0?
-1, 0, 1
Let s = 9 + -6. Let n(u) be the second derivative of 1/3*u**2 + 0 + 2*u - 1/6*u**s + 7/20*u**5 - 5/9*u**4. Factor n(q).
(q - 1)*(3*q + 1)*(7*q - 2)/3
Let y = -1 - -7. Factor 2*q**5 + y*q**4 + 2*q**3 - 4*q**5 + q**3 + 5*q**5.
3*q**3*(q + 1)**2
Let k(d) = -5*d**3 - 3*d**2 - 3*d + 3. Let m(j) = j**3 + j**2 + j - 1. Let g(z) = k(z) + 4*m(z). Suppose g(l) = 0. Calculate l.
-1, 1
Let b(h) be the second derivative of h**6/40 - h**4/8 + 3*h**2/2 + h. Let c(r) be the first derivative of b(r). Factor c(m).
3*m*(m - 1)*(m + 1)
Let r(o) be the third derivative of -o**7/945 + o**5/135 - o**3/27 + 4*o**2. Determine h, given that r(h) = 0.
-1, 1
Factor 6/19*m**2 + 20/19*m + 6/19.
2*(m + 3)*(3*m + 1)/19
Let u be (-9 - 0) + (-1)/(-1). Let x be (-20)/u - 2/4. Factor -2*d**2 + 4*d**3 + 2*d**2 - 2*d - x*d**5.
-2*d*(d - 1)**2*(d + 1)**2
Let a(n) be the first derivative of -n**3 - 3*n - 3. Let d(i) = -i**3 + 2*i**2 - i + 4. Let c(m) = -4*a(m) - 3*d(m). Factor c(z).
3*z*(z + 1)**2
Let o(g) be the first derivative of -3*g**4/2 + 2*g**3/3 + 3*g - 2. Let h(l) be the first derivative of o(l). Suppose h(x) = 0. What is x?
0, 2/9
Let p(y) be the third derivative of y**6/280 - y**5/70 - y**4/56 + y**3/7 - 13*y**2. Suppose p(v) = 0. What is v?
-1, 1, 2
Let t(n) = n**5 - n**4 - 2*n**2 - 2*n. Let k(f) = -2*f**5 + 3*f**4 + 5*f**2 + 5*f. Let i(g) = -2*k(g) - 5*t(g). Factor i(o).
-o**4*(o + 1)
Let j = -5 + 7. Suppose 3*i = -5*d + 23, 6 = j*d + i - 3*i. Factor 1 - r**2 - 4 + d*r - 1.
-(r - 2)**2
Let k = 66 - 47. Let d = 39/2 - k. Factor 0 - 1/2*w + 1/2*w**3 - d*w**2 + 1/2*w**4.
w*(w - 1)*(w + 1)**2/2
Let x(u) be the second derivative of 0 + 4/15*u**3 + 1/150*u**5 - 1/2*u**2 + 1/15*u**4 + 2*u. Let j(y) be the first derivative of x(y). Factor j(c).
2*(c + 2)**2/5
Let j(s) be the first derivative of -256*s**5/5 + 432*s**4 - 400*s**3 + 146*s**2 - 24*s + 4. Let j(p) = 0. Calculate p.
1/4, 6
Let b(n) be the second derivative of 1/24*n**6 - 1/168*n**7 - 1/8*n**5 + 5/24*n**4 + 1/8*n**2 - n - 5/24*n**3 + 0. Find g such that b(g) = 0.
1
Suppose v - 52 = 4*p, 3*v = 4*v - 2*p - 46. Factor 43*o + 4 - 3*o**2 + 2 - v*o.
-3*(o - 2)*(o + 1)
Let b(j) be the first derivative of -j**6/18 + j**5/5 - 4*j**3/9 + 16. Factor b(u).
-u**2*(u - 2)**2*(u + 1)/3
Let z(a) be the first derivative of a**4/16 + 13*a**3/4 + 507*a**2/8 + 2197*a/4 + 54. Factor z(l).
(l + 13)**3/4
Let r(b) = -b**3 - b + 50. Let u be r(0). Let w be 1/(-1) - u/(-20). What is k in -1/4*k**2 - w*k - 9/4 = 0?
-3
Let u(g) be the first derivative of -1/5*g**2 + 1/15*g**3 + 5 + 0*g. Suppose u(a) = 0. What is a?
0, 2
Let h(b) = 6*b**3 - b**2 + 2*b - 1. Let n be h(1). Let -4*i**3 + 9*i**3 + i**2 - n*i**3 - i**4 + i = 0. Calculate i.
-1, 0, 1
Let a(r) be the second derivative of -r**4/18 + 4*r**3/9 - r**2 + 3*r. Let a(n) = 0. What is n?
1, 3
Determine p so that -2/9 + 2/9*p**2 + 0*p = 0.
-1, 1
Let h(j) be the third derivative of -j**5/120 + j**4/24 - j**3/12 + j**2. Factor h(p).
-(p - 1)**2/2
Let y(g) be the first derivative of 5*g**6/6 - 2*g**5 - 15*g**4/4 + 40*g**3/3 - 10*g**2 + 42. What is j in y(j) = 0?
-2, 0, 1, 2
Let w = 8 - 8. Suppose w = -4*b + 3*a + a + 24, -4*b - 5*a = 12. Factor 6*k**3 + 2*k - 2*k**4 + 22*k**2 + 0*k**4 - 28*k**b.
-2*k*(k - 1)**3
Suppose -h + 8 - 5 = 0. Suppose 0 = 2*l - 11 + 3. Determine t so that 1/4*t**h - 1/4*t**l + 0 + 1/4*t**2 - 1/4*t**5 + 0*t = 0.
-1, 0, 1
Let r(y) be the second derivative of -4*y + 1/54*y**4 - 1/135*y**6 - 1/27*y**3 + 1/90*y**5 + 0 + 0*y**2. Factor r(t).
-2*t*(t - 1)**2*(t + 1)/9
Solve -x - 6*x + 6*x - x**2 = 0 for x.
-1, 0
Let w = 87581/22 - 3980. Let d = w + -5/11. Factor 1/2*c**2 + d*c**3 - 1/2*c - 1/2.
(c - 1)*(c + 1)**2/2
Let g(r) be the first derivative of -512*r**5/15 - 176*r**4/3 - 24*r**3 - 25*r**2/6 - r/3 + 1. Factor g(u).
-(u + 1)*(8*u + 1)**3/3
Solve -2/3*y**2 + 4/9 - 10/9*y = 0 for y.
-2, 1/3
Let a(u) = -16*u**5 + 8*u**4 + 3*u**3 + 3. Let p(c) = -16*c**5 + 8*c**4 + 3*c**3 + 4. Let k(l) = -4*a(l) + 3*p(l). Factor k(f).
f**3*(4*f - 3)*(4*f + 1)
Let z = 10337885/8434356 - 4/51429. Let n = z + 1/41. Factor d**2 - 1/4*d + 0 - n*d**3 + 1/2*d**4.
d*(d - 1)**2*(2*d - 1)/4
Let g(i) = 9*i - 1 + i**2 - 5 + 3 - 5. Let d be g(-10). Find o such that 0 + 2/5*o**4 - 2/5*o**5 - 2/5*o**d + 2/5*o**3 + 0*o = 0.
-1, 0, 1
Let q be -9 + 6 + (-2)/(-2). Let s(i) = -i**3 - 2*i**2 + 2. Let h be s(q). Factor -2*n**3 - h*n**4 + 2*n**2 + 2*n**3.
-2*n**2*(n - 1)*(n + 1)
Let g be (4/30)/(16/20). Let v(m) be the second derivative of g*m**4 + 0 + 0*m**2 + m + 2/3*m**3. Factor v(r).
2*r*(r + 2)
Let g be 6/2*(-4)/6. Let k be ((-4)/(-27))/(g/(-3)). Factor 0 - k*c - 2/9*c**2.
-2*c*(c + 1)/9
Let s(q) = -q**2 - q + 1. Suppose 0 = -5*v + v + 4. Let u(d) = -7*d**2 - 7*d + 5. Let n(m) = v*u(m) - 5*s(m). Factor n(r).
-2*r*(r + 1)
Suppose 14*p - 12*p = 0. Suppose 6*w - 4 = 3*w + q, -3*q - 12 = p. Factor w - 2/5*f**2 + 2/5*f**4 + 0*f + 0*f**3.
2*f**2*(f - 1)*(f + 1)/5
Factor -4/3 - 10/3*c - 8/3*c**2 - 2/3*c**3.
-2*(c + 1)**2*(c + 2)/3
Let h = -94 + 862/9. Factor 0 - 140/9*b**3 + 98/9*b**4 - 104/9*b**2 - h*b.
2*b*(b - 2)*(7*b + 2)**2/9
Suppose 2*z = -3*z. Suppose -2*p + 5*p - 9 = z. Determine b, given that -1/2*b**2 - 2*b**p + 2*b + 1/2 = 0.
-1, -1/4, 1
Let y = -13 + 15. Let k(b) = -82*b**2 + 37*b - 5. Let i(o) = -o**2 + o - 1. Let m(x) = y*k(x) - 2*i(x). Solve m(w) = 0 for w.
2/9
Let z(u) = 7*u**3 - 11*u**2 - 25*u - 17. Let a(n) = -3*n**3 + 6*n**2 + 12*n + 9. Let b(t) = 5*a(t) + 3*z(t). Let b(c) = 0. Calculate c.
-1, -1/2, 2
Let h(j) = -j**4 - j. Let a(n) = -n**4 - n**3 - n**2 + 2*n. Let o(r) = -3*r. Let s(q) = -3*a(q) - 3*o(q). Let i(g) = 2*h(g) + s(g). Solve i(m) = 0.
-1, 0
Let s(q) = 2*q**3 + 6*q**2 + q. Let l(g) be the first derivative of g**3/3 - 4. Let d(p) = 3*l(p) - s(p). Factor d(v).
-v*(v + 1)*(2*v + 1)
Let u(m) be the first derivative of m**6/14 - 3*m**4/14 + 3*m**2/14 + 17. Solve u(r) = 0.
-1, 0, 1
Determine i so that -15 - 5*i**2 - 3*i**3 - 7*i**3 + 5*i**3 + 25*i = 0.
-3, 1
Let g(b) be the third derivative of b**9/15120 + b**8/8400 - b**7/4200 - b**6/1800 - b**3/3 - 3*b**2. Let p(d) be the first derivative of g(d). Factor p(l).
l**2*(l - 1)*(l + 1)**2/5
Let j(d) be the first derivative of d**5/5 + d**4/3 - 4*d - 9. Let n(h) be the first derivative of j(h). Factor n(x).
4*x**2*(x + 1)
Let z(r) be the third derivative of -r**6/2340 + r**5/195 - r**4/39 + r**3/2 + r**2. Let c(x) be the first derivative of z(x). Factor c(o).
-2*(o - 2)**2/13
Let f(b) be the third derivative of