*2 + n*r**3 + 0 - 2/45*r**6 + 1/30*r**5 + 1/63*r**7. Suppose j(i) = 0. Calculate i.
0, 1
Let v(n) be the first derivative of -3*n**5/4 + 33*n**4/16 - n**3/2 - 20. Determine r so that v(r) = 0.
0, 1/5, 2
Let g = 138512/7 + -19706. Let z = 82 - g. Factor -2/7*h**3 - z*h**2 + 2/7*h + 4/7.
-2*(h - 1)*(h + 1)*(h + 2)/7
Let x(f) be the third derivative of -f**5/120 - f**4/8 - 3*f**3/4 - 25*f**2. Determine o, given that x(o) = 0.
-3
Let a be (8/28)/(0 - 18/(-14)). Determine y so that 0 + 2/9*y + 0*y**2 - a*y**3 = 0.
-1, 0, 1
Factor 0*b**2 + 0 + 3/2*b - 3/2*b**3.
-3*b*(b - 1)*(b + 1)/2
Let x(y) be the first derivative of -y**3/4 + 5*y**2/8 - y/2 + 1. Determine m so that x(m) = 0.
2/3, 1
Let d = 37 - 37. Let g(j) be the third derivative of 49/180*j**6 + 8/9*j**4 + d*j - 77/90*j**5 - 2*j**2 - 4/9*j**3 + 0. Factor g(n).
2*(n - 1)*(7*n - 2)**2/3
Factor -w**3 - 1/2*w**5 + w**2 - 3/2*w**4 + 1/2 + 3/2*w.
-(w - 1)*(w + 1)**4/2
Let k(t) be the first derivative of t**7/1680 - t**3/3 - 1. Let j(v) be the third derivative of k(v). Factor j(c).
c**3/2
Factor 2*w + 51*w**2 - 48*w**2 + w.
3*w*(w + 1)
Suppose -5*d = 4*b - 10, -d + 5*d - 3*b = 39. Factor d*g**2 + 6*g**3 - 3*g - 6 + 4*g**3 - 7*g**3.
3*(g - 1)*(g + 1)*(g + 2)
Let a(n) be the first derivative of -n**4/42 + n**3/21 + 2*n**2/7 + 2*n + 1. Let y(o) be the first derivative of a(o). Factor y(x).
-2*(x - 2)*(x + 1)/7
Let f(b) be the second derivative of -1/15*b**6 + 0*b**4 + 2*b + b**2 + 0 + 1/5*b**5 - 2/3*b**3. Suppose f(x) = 0. Calculate x.
-1, 1
Factor 0 - 12*q - 49/3*q**5 + 322/3*q**4 + 92*q**2 - 613/3*q**3.
-q*(q - 3)**2*(7*q - 2)**2/3
Let k(q) be the third derivative of q**8/672 - q**7/210 + q**5/60 - q**4/48 + 5*q**2. Factor k(l).
l*(l - 1)**3*(l + 1)/2
Let i(x) be the second derivative of -3*x**6/10 + 33*x**5/20 - 15*x**4/4 + 9*x**3/2 - 3*x**2 + 5*x. Suppose i(a) = 0. What is a?
2/3, 1
Let d(g) = g**4 + 10*g**3 + 4*g**2 - 14*g - 7. Let l(c) = -3*c**4 - 39*c**3 - 15*c**2 + 57*c + 27. Let s(k) = 9*d(k) + 2*l(k). Solve s(r) = 0 for r.
-3, -1, 1
Let v(q) be the third derivative of -q**6/300 + 7*q**5/100 - q**4/2 + 5*q**3/6 - 19*q**2. Factor v(w).
-(w - 5)**2*(2*w - 1)/5
Let q(n) be the second derivative of -n**6/60 - 3*n**5/40 - n**4/8 - n**3/12 - 3*n. Suppose q(v) = 0. Calculate v.
-1, 0
Let a be 5/10 - 10/(-4). Suppose -15 = -4*d - a. Factor 0 + 6*f - 6*f**d + 2 - 3*f**4 - 2 + 3.
-3*(f - 1)*(f + 1)**3
Let y(l) be the second derivative of 1/2*l**4 + 0*l**2 - 2/3*l**3 + 4*l - 1/10*l**5 + 0. Factor y(r).
-2*r*(r - 2)*(r - 1)
Suppose 6/5*c**2 + 9/5*c + 0 + 1/5*c**3 = 0. What is c?
-3, 0
Suppose 0 + 0*m + 0*m**2 - 2/17*m**5 + 4/17*m**4 + 6/17*m**3 = 0. What is m?
-1, 0, 3
Let h(v) be the second derivative of -2/15*v**3 - 1/5*v**2 - 1/30*v**4 + 2*v + 0. Find p such that h(p) = 0.
-1
Let d be ((-106)/1855)/((-1)/5). Determine v, given that -10/7*v - d*v**3 - 8/7*v**2 - 4/7 = 0.
-2, -1
Let u(p) = -p**3 - 7*p**2 - 4. Let t be u(-7). Let l = 4 + t. Factor l*z + 2/7*z**2 + 0 + 2/7*z**4 - 4/7*z**3.
2*z**2*(z - 1)**2/7
Let b(q) be the first derivative of q**6/30 + 2*q**5/25 - 2*q**3/15 - q**2/10 - 11. Factor b(u).
u*(u - 1)*(u + 1)**3/5
Let y be (-4)/18 - 20/(-9). Let j(q) = q**3 - 5*q**2 - 7*q + 7. Let f be j(6). Factor -f + 0*w**2 + w**y + 1.
w**2
Factor -2 - 2*f + 5*f**2 - 8 - 4*f + f.
5*(f - 2)*(f + 1)
Let t(o) be the third derivative of o**7/420 - o**5/60 + o**3/2 - 3*o**2. Let v(y) be the first derivative of t(y). Solve v(g) = 0 for g.
-1, 0, 1
Let i be 1/4 - 5/36. Let v(a) be the second derivative of -i*a**3 + 0*a**2 + 0 + 1/30*a**5 - a + 0*a**4. Factor v(o).
2*o*(o - 1)*(o + 1)/3
Let j = -2523/7 + 361. Solve 4/7*y**3 - 2/7 + 2/7*y**4 + 0*y**2 - j*y = 0.
-1, 1
Let w(i) = 4*i**2 - 6*i + 2. Let a(g) = -5*g**2 + 6*g - 1. Let d(v) = 2*a(v) + 3*w(v). Factor d(h).
2*(h - 2)*(h - 1)
Let g be (-24)/30*30/4. Let q be 2/g - (-50)/15. Factor -6*u**4 - 2*u**5 + 2*u**q + 6*u**4.
-2*u**3*(u - 1)*(u + 1)
Let o(f) be the second derivative of f**4/42 - f**2/7 - f. Factor o(c).
2*(c - 1)*(c + 1)/7
Let x(a) be the third derivative of 1/15*a**6 + 0 + 2/3*a**3 + 8/105*a**7 - 1/3*a**5 + 0*a + 1/12*a**4 - 7*a**2 - 5/168*a**8. Suppose x(g) = 0. Calculate g.
-1, -2/5, 1
Let c be 3/(-9) - 52/(-3). Suppose 5*b - 37 = -c. Factor 5/4*v**2 + v**3 + 0 + 1/4*v**b + 1/2*v.
v*(v + 1)**2*(v + 2)/4
Factor 92/3*v**2 - 80/3*v - 28/3*v**3 + 16/3.
-4*(v - 2)*(v - 1)*(7*v - 2)/3
Let t(n) = 5*n - 1. Let h be t(5). Let d(u) = 63*u**2 + h - 24 + 39 - 84*u. Let f(b) = 18*b**2 - 24*b + 11. Let v(j) = -5*d(j) + 18*f(j). Factor v(z).
3*(z - 1)*(3*z - 1)
Let v(t) = t**3 - 15*t**2 - 17*t + 18. Let z be v(16). Let x(r) be the first derivative of 0*r + 2/21*r**3 - 2/35*r**5 + 0*r**z + 0*r**4 - 2. Factor x(s).
-2*s**2*(s - 1)*(s + 1)/7
Let a(c) be the second derivative of -c**6/120 + c**5/80 + c**4/24 + 3*c. Solve a(p) = 0 for p.
-1, 0, 2
Let b(m) be the second derivative of m**6/45 - m**4/6 - 2*m**3/9 + 6*m. Factor b(j).
2*j*(j - 2)*(j + 1)**2/3
Factor -4/3*f**3 - 1/3*f + 10/3*f**2 - 8/3*f**4 + 5/3*f**5 - 2/3.
(f - 1)**3*(f + 1)*(5*f + 2)/3
Let s(l) be the second derivative of -l**7/357 - l**6/255 + l**5/85 + l**4/51 - l**3/51 - l**2/17 + 10*l. Let s(r) = 0. Calculate r.
-1, 1
Let q = -138686/91 + 1524. Let t = q + 99/364. Solve t*b**4 + 0*b + 0*b**2 + 0*b**3 + 0 - 1/4*b**5 = 0.
0, 1
Suppose 7*u = -3*u + u. Factor -3/2*c**3 + u + 0*c**2 + 0*c.
-3*c**3/2
Let r be (-8)/24 + (4/(-6))/(-2). Suppose r*w**2 + 1/4*w**4 + 0 + 0*w - 1/4*w**3 = 0. What is w?
0, 1
Factor -44*k - 20 + 2*k**3 + 6*k**3 - 28*k**2 - 12*k**3.
-4*(k + 1)**2*(k + 5)
Suppose -4*r + 22 = 2*i, -4*r + 2 = -3*i + 5. What is b in -b**3 + 3*b**3 - r*b**2 + b**2 + 0*b**3 = 0?
0, 1
Let l = -6 + 12. Let a(w) be the first derivative of 1 + 0*w + 1/6*w**3 + 1/8*w**4 - 1/10*w**5 - 1/12*w**l + 0*w**2. Suppose a(f) = 0. What is f?
-1, 0, 1
Let f(h) be the first derivative of 1/30*h**4 - 4 - 1/45*h**6 + 0*h + 0*h**5 + 0*h**3 + 0*h**2. Let f(z) = 0. Calculate z.
-1, 0, 1
Factor 8/3 + 2/3*k**2 - 8/3*k.
2*(k - 2)**2/3
Let s(i) = 3*i**2 - 7*i + 2. Suppose f + 22 + 5 = 0. Let z(g) = -39*g**2 + 90*g - 27. Let r(p) = f*s(p) - 2*z(p). Factor r(m).
-3*m*(m - 3)
Let y(r) be the third derivative of -r**7/840 + r**6/240 - 2*r**2. Solve y(z) = 0.
0, 2
Let c be ((-27)/6 + 2)*-2. Suppose 5*p = 2*n + 12, -c*n = -3*p + 12 - 1. Factor 6*t**2 + 8*t**3 - 3*t + 2*t**4 + 5*t - p*t**3.
2*t*(t + 1)**3
Let j be (-41)/2 + (-1)/(-2). Let g be (-32)/j - (-2)/5. Factor 2*x + 4 - 2 + 0*x**3 - 2*x**3 - g*x**2.
-2*(x - 1)*(x + 1)**2
Let l(q) = 4*q**5 + 2*q**5 - 4 + 1 + 3*q**3 - 3*q**4. Let p(d) = -7*d**5 + 3*d**4 - 4*d**3 + 4. Let x(z) = -4*l(z) - 3*p(z). Factor x(o).
-3*o**4*(o - 1)
Suppose 2*x = 5*y - 20, 3*x + 2*x - 12 = -3*y. Let l(s) be the second derivative of s**2 + 2/3*s**3 + 1/6*s**4 + 3*s + x. Find q, given that l(q) = 0.
-1
Let n(r) be the third derivative of 1/50*r**5 - 1/60*r**4 + 0*r + 1/525*r**7 + 0*r**3 + 0 + 3*r**2 - 1/100*r**6. Factor n(t).
2*t*(t - 1)**3/5
Let m = 67/165 - 4/55. Factor -2/3*y + m*y**2 + 0.
y*(y - 2)/3
Let s(z) be the second derivative of -z**7/42 + z**6/10 - z**5/15 - 3*z**2/2 + 2*z. Let h(c) be the first derivative of s(c). Factor h(w).
-w**2*(w - 2)*(5*w - 2)
Let d(x) = x**3 + 5*x**2 - 3*x + 7. Let p be d(-6). Let i = 13 + p. Suppose 0*t + 1/2*t**3 - 1/4*t**i - 1/4*t**4 + 0 = 0. What is t?
0, 1
Suppose -3*n - 3*c = c + 46, -2*n - 4*c - 28 = 0. Let g = 37 - n. Find b, given that -6 + g*b**2 - 8*b + 59*b**3 + 1 + 1 - 210*b**4 = 0.
-1/3, -2/7, 2/5, 1/2
Suppose -3*l - 3*s = l - 17, 8 = -2*l + 4*s. Let m be l/1 - (-1 - -1). Factor 1 - r**2 - 2 + m*r**2.
(r - 1)*(r + 1)
Let g(r) = 2*r**3 + 4*r**2 - 5*r + 5. Let d(v) = 5*v**3 + 8*v**2 - 10*v + 11. Let b(a) = -3*d(a) + 7*g(a). Factor b(h).
-(h - 2)*(h - 1)**2
Let n(v) = -4*v - 6*v**4 - 6*v**3 - 7 + 8*v**2 - 3*v**3 + 4*v**3 - v**3. Let t(o) = -o**4 - o**3 + o**2 - o - 1. Let d(s) = -n(s) + 5*t(s). Factor d(w).
(w - 1)**2*(w + 1)*(w + 2)
Factor 6/7*h + 2/7*h**2 + 4/7.
2*(h + 1)*(h + 2)/7
Determine p so that -14*p**3 - 3*p**5 - 6*p**5 + 16*p**4 - 5*p**5 + 4*p**2 + 8*p**5 = 0.
0, 2/3, 1
Let s(i) be the second derivative of -1/3*i**3 + 0*i**4 - i + 0 + 1/180*i**6 + 0*i**2 + 1/60*i**5. Let d(l) be the second derivative of s(l). Factor d(g).
2*g*(g + 1)
Suppose 4 = -