*7/2520 + g**6/720 + g**5/20 - g**2. Let f(x) be the third derivative of o(x). Factor f(y).
-(y - 1)*(y + 1)**3
Let k(t) = t**3 + 12*t**2 + 10*t - 5. Let d be k(-11). Suppose 0 = d*b - b - 10. Suppose 2/9*r**3 + 2/3*r - 2/3*r**b - 2/9 = 0. Calculate r.
1
Let h(t) = -t. Let w(s) = -s**2 - 7*s. Let j(n) = 3*h(n) - w(n). Factor j(c).
c*(c + 4)
Suppose 0 = 2*o + 3*o - 15. Suppose 2*y - 2*c - 7 = -3*y, -2*c = o*y - 17. Factor -3*m**2 - m**2 - m**y + 5*m**2.
-m**2*(m - 1)
Let q(z) be the third derivative of 0*z**3 - 1/168*z**8 + 0*z**5 + 0*z + 0*z**6 - z**2 + 0 - 1/105*z**7 + 0*z**4. Determine u so that q(u) = 0.
-1, 0
Let a = -10 - -7. Let v(s) = -2*s**5 - 2*s**4 - s**3 - 4*s**2. Let b(z) = z**5 + z**4 + z**2. Let y(w) = a*b(w) - v(w). Determine g so that y(g) = 0.
-1, 0, 1
Let o(x) = -x**3 + x**2 + 1. Let j(l) = 15*l**3 - 30*l**2 + 20*l - 10. Let a(c) = -j(c) - 10*o(c). Find g, given that a(g) = 0.
0, 2
Let b be (-4)/2 - (-5 + 1). Factor 4*i - 2*i + i**2 - 2*i**3 + i**b - 2.
-2*(i - 1)**2*(i + 1)
Factor -f + 0 + 12 + 9*f**2 - 25*f + 2*f.
3*(f - 2)*(3*f - 2)
Let i(r) = 1 - r**3 + 2 + 2*r**2 - 4*r + 2*r**2. Let f be i(3). Factor -4*s - 1 + f*s**2 + 2*s**2 + 3.
2*(s - 1)**2
Let a(i) be the first derivative of 4*i**5/5 + i**4 - 4*i**3 - 2*i**2 + 8*i + 3. Factor a(h).
4*(h - 1)**2*(h + 1)*(h + 2)
Factor d - 1/4*d**4 + 0*d**3 - 3 + 9/4*d**2.
-(d - 3)*(d - 1)*(d + 2)**2/4
Let r(c) be the third derivative of 4*c**7/105 + 13*c**6/30 + c**5 - c**4/6 - 10*c**3/3 - 11*c**2. Factor r(w).
4*(w + 1)**2*(w + 5)*(2*w - 1)
Let -1/5*t**2 + 0 - 2/5*t = 0. What is t?
-2, 0
Suppose 3/5*j**3 + 144/5*j - 36/5*j**2 - 192/5 = 0. Calculate j.
4
Let a be (20/100)/(4 + -1). Let d(w) be the second derivative of 0*w**2 - 1/30*w**4 - 2*w + 0 + a*w**3. Suppose d(h) = 0. What is h?
0, 1
Let h(m) be the second derivative of m**7/1260 - m**6/180 + m**4/2 + 5*m. Let q(k) be the third derivative of h(k). Factor q(w).
2*w*(w - 2)
Let p = -12 - -22. Suppose j + 3*n - p = 0, 0*j + 4*n = -2*j + 14. Find o such that -o**2 + 3 + 4*o - 2*o - 3*o - j = 0.
-2, 1
Find i such that 35*i - 23*i - 87*i + 5*i**2 + 60*i**2 + 10 = 0.
2/13, 1
Suppose -2*r - 2*r + 48 = 0. Solve -r*n**2 + 9*n**2 + 2*n**2 = 0.
0
Suppose -4*k = r - 19, 2*k - r = 2*r - 1. Find f, given that 3*f**5 + f**k - 2*f**3 - 8*f + 23*f**4 + 7*f**5 - 24*f**2 = 0.
-2, -1, -2/5, 0, 1
Suppose -3*z**3 - 7*z**2 + 0*z**3 + 6*z**2 - 3*z**4 - z**5 = 0. What is z?
-1, 0
Let k(p) = 6*p**2 - 2*p - 8. Let o(h) be the second derivative of h**4/6 - h**3/6 - 3*h**2/2 + 3*h. Let s(b) = 3*k(b) - 8*o(b). Factor s(l).
2*l*(l + 1)
Let b(o) = -100*o**2 - 100*o - 55. Let k(c) = 11*c**2 + 11*c + 6. Let t(u) = 6*b(u) + 55*k(u). Find i, given that t(i) = 0.
-1, 0
Let i(u) be the first derivative of u**7/231 - u**6/55 + 3*u**5/110 - u**4/66 - 6*u - 5. Let n(l) be the first derivative of i(l). Let n(w) = 0. Calculate w.
0, 1
Suppose -7*f + 6 = -4*f - 4*k, -5*f - 3*k + 10 = 0. Factor 4/3 + 2/3*v**f - 2*v.
2*(v - 2)*(v - 1)/3
Find o, given that -20*o + 24*o + 2*o**2 + 2*o**2 = 0.
-1, 0
Let j(q) = -6*q**4 - q**2 - 7. Let a(n) = 2*n**4 + 2. Suppose 3*h + 2*z + 14 = -2*h, z = 3*h + 4. Let t(u) = h*j(u) - 7*a(u). Factor t(s).
-2*s**2*(s - 1)*(s + 1)
Let p(u) = -3*u**2 + 2 + 2*u**2 - 4*u - 1. Let m be p(-3). Find h such that 0*h**2 - 3*h**m + h**4 + 2*h**2 = 0.
-1, 0, 1
Let j(k) = -k + 14. Let n be j(7). Determine u so that -5*u + 6*u - n*u**2 + 2*u**2 + 7*u**3 - 3*u**4 = 0.
0, 1/3, 1
Suppose -a = 4*s + 96, s + 8 = 4*a - 16. Let o = s + 73/3. Solve o*v**2 - 2/3*v + 0 = 0 for v.
0, 2
Let o(t) = -40*t**2 + 48*t - 8. Let k(n) = -39*n**2 + 47*n - 8. Let j(x) = -4*k(x) + 5*o(x). Let j(z) = 0. What is z?
2/11, 1
Let m(g) be the third derivative of -g**5/12 + 5*g**4/12 - 5*g**3/6 + 2*g**2. Determine z, given that m(z) = 0.
1
Suppose -z = 2*z - 12. Let w = -3 + 5. Determine q so that 2*q**5 + 7*q**z - 4*q**4 - 4*q**w - q**5 = 0.
-2, 0, 1
Determine f, given that -2/5*f**2 + 2/5*f + 4/5 = 0.
-1, 2
Let f = 14 - 8. Let w = f + -1. Determine l so that -6*l**2 - l + 2*l**3 + 6*l**4 - 3*l - 3*l**5 + w*l**5 = 0.
-2, -1, 0, 1
Let c(s) be the third derivative of s**5/150 + s**4/5 + 12*s**3/5 + 8*s**2. Suppose c(p) = 0. What is p?
-6
Factor 0 - 32/7*r**4 - 18/7*r**2 + 0*r - 6*r**3 - 8/7*r**5.
-2*r**2*(r + 1)*(2*r + 3)**2/7
Let g be ((-10)/(-8))/(3/2). Let q(h) be the first derivative of -8/15*h**5 + 0*h + 2 + g*h**4 + 0*h**2 - 2/9*h**3. Factor q(c).
-2*c**2*(c - 1)*(4*c - 1)/3
Suppose -i + 5*y = -2, 4*y + 57 = 5*i + 5. Find l, given that 6*l + 14*l**2 + 2*l - i*l**2 + 8 = 0.
-2
Let s(h) be the second derivative of -h**10/1890 - h**9/540 - h**8/840 + h**7/630 + 5*h**4/12 + 8*h. Let y(p) be the third derivative of s(p). Factor y(g).
-4*g**2*(g + 1)**2*(4*g - 1)
Let l(y) be the second derivative of -y**6 + 0*y**2 - 3*y + 2/7*y**7 + 1/8*y**3 + 0 + 99/80*y**5 - 5/8*y**4. Suppose l(v) = 0. Calculate v.
0, 1/4, 1
Suppose -43 = -4*s - m, m = 5*m - 12. Suppose 5*u - s + 0 = 0. Solve -13*t - 27/2*t**2 + 149/4*t**3 + 28*t**4 - u - 147/4*t**5 = 0 for t.
-2/3, -2/7, 1
Let i be (-42)/21 + (-5)/(-1). Factor m**2 - 3/2*m**4 - 1/2*m**i + 0 + 0*m.
-m**2*(m + 1)*(3*m - 2)/2
Let i(v) be the second derivative of 0*v**2 + 0 + 1/20*v**4 - 1/15*v**3 + 2*v. Let i(k) = 0. Calculate k.
0, 2/3
Let p(k) be the second derivative of k**6/200 - k**4/40 - k**2 - 4*k. Let t(d) be the first derivative of p(d). Factor t(o).
3*o*(o - 1)*(o + 1)/5
Let p(i) be the second derivative of 0*i**2 + 0*i**3 + 0 + 0*i**4 + 4*i + 1/110*i**5. Suppose p(h) = 0. What is h?
0
Let r(a) be the second derivative of a**6/420 - a**5/210 - a**4/84 + a**3/21 + 3*a**2/2 + 4*a. Let b(x) be the first derivative of r(x). Factor b(v).
2*(v - 1)**2*(v + 1)/7
Suppose -4*p + 13 = 1. Suppose -2*q = -2*d - 16, d + 1 = -p*q - d. Let -2/3*z + 0*z**2 + 2/3*z**q + 0 = 0. Calculate z.
-1, 0, 1
Let i(p) be the first derivative of -p**3/15 + 3*p**2/10 - 20. Factor i(u).
-u*(u - 3)/5
Suppose -4*f - 12 = 2*c, -c - 27 = -4*c + 3*f. Let z(r) be the second derivative of 0*r**3 + 0 - 1/35*r**5 + r + 1/14*r**c - 1/7*r**2. Solve z(l) = 0 for l.
-1/2, 1
Let t(s) be the first derivative of -9*s**4/8 - 11*s**3/4 - 3*s**2/2 + 4*s + 4. Let q(a) be the first derivative of t(a). Factor q(y).
-3*(y + 1)*(9*y + 2)/2
Let m be 5/2*-3*8/(-12). Let d(x) be the third derivative of 1/2*x**6 + 1/4*x**4 + 0*x - 2*x**2 + 0*x**3 - 13/20*x**m + 0. Suppose d(b) = 0. Calculate b.
0, 1/4, 2/5
Let x = 3 + -3. Suppose -5*f + 2*p + 14 = x, -2*f + 14 = f - 4*p. Factor 1/4*s**f + 1/4*s + 0.
s*(s + 1)/4
Let h = -371/6 + 62. Let k(t) be the first derivative of 0*t - h*t**2 + 1/9*t**3 - 1. Factor k(b).
b*(b - 1)/3
Suppose -5*x + 26 = -4. Factor 0*k**2 - 3*k**4 - k**2 + 6*k + 0*k**2 + 4*k**2 - x*k**3.
-3*k*(k - 1)*(k + 1)*(k + 2)
Suppose 5*p + 0*p = 35. Factor -p*c + 5*c**2 - 6 - 7*c**2 + 0*c - c.
-2*(c + 1)*(c + 3)
Let a(x) = -x**2 + 3*x + 1. Let u be a(5). Let f = u + 11. Factor 2/3 - 1/3*q**f + 1/3*q.
-(q - 2)*(q + 1)/3
Let n(y) be the third derivative of y**5/15 + y**4/6 - 7*y**2. Factor n(m).
4*m*(m + 1)
Let g(i) = -i**4 + i**2 + i + 1. Let y(o) = -o**4 + 14*o**3 + 27*o**2 + 20*o + 8. Let c = -15 + 11. Let b(x) = c*g(x) + y(x). Determine v so that b(v) = 0.
-2, -1, -2/3
Let n(d) = 3*d**3 + 6*d**2 - 9*d + 6. Let v(p) = -2*p**3 - 6*p**2 + 8*p - 5. Let z(x) = -5*n(x) - 6*v(x). Factor z(c).
-3*c*(c - 1)**2
Let z(a) be the second derivative of 8*a**6/15 - 19*a**5/5 + 19*a**4/3 + 4*a**3 + 20*a. Find b, given that z(b) = 0.
-1/4, 0, 2, 3
Let p(c) be the first derivative of 0*c + 9 - 5*c**3 - 7/4*c**4 - 9/2*c**2 - 1/5*c**5. Suppose p(g) = 0. What is g?
-3, -1, 0
Let v(o) be the second derivative of o**6/450 - o**5/100 - o**4/30 + o**3/2 - 3*o. Let m(n) be the second derivative of v(n). Factor m(d).
2*(d - 2)*(2*d + 1)/5
Let c(y) be the first derivative of y**5/20 - y**4/48 + 4*y + 3. Let x(a) be the first derivative of c(a). Factor x(q).
q**2*(4*q - 1)/4
Let q(b) be the first derivative of -4*b**3/21 + 34. Suppose q(f) = 0. What is f?
0
Suppose -f - 4 + 7 = 2*r, -4*f - 4*r = 4. Let u be (51/f)/(-3) - 3. Factor u*t**3 + 0 + 2/5*t**2 + 0*t.
2*t**2*(t + 1)/5
Let f(n) be the third derivative of -2*n**2 - 1/28*n**4 + 2/21*n**3 + 1/210*n**5 + 0 + 0*n. Factor f(q).
2*(q - 2)*(q - 1)/7
Suppose 17 - 1 = 4*w