 given that a(f) = 0.
1
Let d = 166/5 - 33. Let v(j) be the second derivative of 1/6*j**4 + 0*j**2 - 7/15*j**6 - d*j**5 + 0*j**3 - 4/21*j**7 - j + 0. Let v(m) = 0. What is m?
-1, 0, 1/4
Let j = 62 + -54. Find y, given that -1/2 - 4*y - j*y**2 = 0.
-1/4
Let i(u) be the first derivative of 2 + 8/11*u + 1/22*u**4 + 10/33*u**3 + 8/11*u**2. Factor i(z).
2*(z + 1)*(z + 2)**2/11
Let 2/3*f + 4/3 - 2/3*f**2 = 0. Calculate f.
-1, 2
Let v(c) = -c**3 - 5*c. Suppose 0 = -3*r - 5 - 4. Let q(a) = 2*a**3 + 3*a**3 + 6*a - 3*a**3. Let b(j) = r*q(j) - 4*v(j). Factor b(g).
-2*g*(g - 1)*(g + 1)
Let q be ((50/4)/(-5))/(60/(-48)). Factor -2/7*v + 0 - 2/7*v**q.
-2*v*(v + 1)/7
Let k be (72/6)/(6/4). Suppose 8 = -2*c + 3*r - 4, -k = -2*r. Let -1/3*n**3 + 0*n + 0*n**2 + c = 0. What is n?
0
Let z(c) be the second derivative of c**4/3 + 4*c**3 + 18*c**2 - c. Factor z(d).
4*(d + 3)**2
Let h be -6*(-1 + 4/12). Let a(i) be the first derivative of i**3 + i + 3 + 1/4*i**h + 3/2*i**2. Determine r so that a(r) = 0.
-1
Let p(l) = -l**5 + l**4 - l**3 + l**2 - 1. Let q(z) = -5*z**5 + 5*z**4 - 7*z**3 + 7*z**2 - 6. Let k(o) = 6*p(o) - q(o). Factor k(j).
-j**2*(j - 1)**2*(j + 1)
Let b = -209/3 - -71. Let n(o) be the third derivative of 2*o**2 - 7/3*o**4 + 0 + b*o**3 + 13/6*o**5 + 0*o - 5/6*o**6. Factor n(k).
-2*(2*k - 1)*(5*k - 2)**2
Let y(x) = 91*x**3 - 511*x**2 + 851*x - 180. Let m(s) = -18*s**3 + 102*s**2 - 170*s + 36. Let h(r) = 11*m(r) + 2*y(r). Factor h(v).
-4*(v - 3)**2*(4*v - 1)
Let h(j) be the third derivative of j**6/200 - j**5/50 + j**4/40 - 5*j**2. Factor h(d).
3*d*(d - 1)**2/5
Let h(n) be the third derivative of -n**2 - 1/180*n**5 - 1/24*n**4 + 1/9*n**3 + 0 - 1/630*n**7 + 1/120*n**6 + 0*n. Let h(a) = 0. Calculate a.
-1, 1, 2
Let o(r) = 10*r**2 + 23*r + 3. Let f(k) = -9*k**2 - 23*k - 4. Let x(m) = 6*f(m) + 4*o(m). Let x(h) = 0. What is h?
-3, -2/7
Factor 2*t**4 + 55*t**2 + 26*t**3 + 20*t - t**3 + 3*t**4 - 15*t**2.
5*t*(t + 1)*(t + 2)**2
Suppose -3*t = t - 4. Let g be t/((1/(-2))/(-1)). Suppose -1/2*h + 0 - 1/2*h**g = 0. What is h?
-1, 0
Factor 2/5*g + 0 + 4/5*g**2 + 2/5*g**3.
2*g*(g + 1)**2/5
Let s(q) be the first derivative of 2*q**5/45 + 2*q**4/3 + 44*q**3/27 - 28*q**2/3 + 98*q/9 + 24. Factor s(x).
2*(x - 1)**2*(x + 7)**2/9
Let n(q) be the third derivative of 2*q**7/35 - 2*q**6/15 - 2*q**5/15 + 2*q**4/3 - 2*q**3/3 + 43*q**2. Find a, given that n(a) = 0.
-1, 1/3, 1
Let p(k) be the second derivative of k**6/60 - k**5/80 - k**4/16 + k**3/24 + k**2/8 + 5*k. Factor p(a).
(a - 1)**2*(a + 1)*(2*a + 1)/4
Let b(a) = -a**5 - 5*a**3 - 12 + 6 + 5*a**2 + 7. Let l(v) = v**5 - v**4 + 6*v**3 - 6*v**2 + v - 1. Let j(u) = -4*b(u) - 5*l(u). Factor j(m).
-(m - 1)**5
Let h(c) = -29*c**2 - 65*c - 36. Let l(j) = 5*j**2 + 11*j + 6. Let m(y) = -6*h(y) - 34*l(y). Factor m(k).
4*(k + 1)*(k + 3)
Let p(k) be the third derivative of k**6/40 - 33*k**5/20 + 363*k**4/8 - 1331*k**3/2 - 50*k**2. Suppose p(w) = 0. Calculate w.
11
Let s(l) be the first derivative of l**6/30 - 2*l**5/25 - l**4/20 + 2*l**3/15 - 21. Suppose s(a) = 0. Calculate a.
-1, 0, 1, 2
Let i(q) be the third derivative of q**9/10584 - q**8/7840 - q**7/4410 + q**4/24 + q**2. Let m(n) be the second derivative of i(n). Solve m(p) = 0 for p.
-2/5, 0, 1
Let w(s) be the first derivative of 0*s + s**2 - 1/90*s**5 - 1/18*s**4 + 0*s**3 - 3. Let z(j) be the second derivative of w(j). Suppose z(h) = 0. What is h?
-2, 0
Factor 4/3*x**2 - 4/3*x + 0 - 1/3*x**3.
-x*(x - 2)**2/3
Let g(r) = r**3 - 4*r**2 - 33*r + 11. Let p be g(8). Factor 0*x**2 + 0 - 3/7*x**p + 0*x.
-3*x**3/7
Let z(f) be the third derivative of f**5/210 - f**4/42 - f**3/7 - 7*f**2. Factor z(p).
2*(p - 3)*(p + 1)/7
Let t(y) be the second derivative of -y**8/6720 + y**6/240 + y**5/60 - y**4/12 - 2*y. Let s(h) be the third derivative of t(h). Let s(v) = 0. Calculate v.
-1, 2
Let n be (-15)/2*2/(-3). Let x be (-76)/(-6) + (-7)/(-21). What is r in -r**2 - r**2 + n*r - 8 - x*r = 0?
-2
Let x(u) be the second derivative of -1/21*u**4 - 1/70*u**5 + 0 + 0*u**2 + 4*u - 1/21*u**3. Solve x(j) = 0 for j.
-1, 0
Suppose -6*m + m + 30 = 0. Suppose -2*k**4 - 4*k**2 + 7 + m*k**3 - 7 = 0. Calculate k.
0, 1, 2
Let u(l) = -l**3 - 10*l**2 - l - 7. Let x(h) = -h**3 + 13*h**2 - h + 3. Let m be x(13). Let b be u(m). Factor 2/5*a**2 - 2/5 - 2/5*a + 2/5*a**b.
2*(a - 1)*(a + 1)**2/5
Let m(b) be the first derivative of 2/5*b**2 - 6/25*b**5 - 1/15*b**6 + 0*b - 1/10*b**4 + 8 + 2/5*b**3. Solve m(n) = 0 for n.
-2, -1, 0, 1
Let a(v) be the third derivative of v**7/140 - v**6/96 - v**5/240 - 38*v**2. Suppose a(u) = 0. What is u?
-1/6, 0, 1
Suppose 15 = 3*n, 7 = 4*m - m + 5*n. Let v = 6 + m. What is s in v + 2/3*s**2 - 5/3*s**3 + 0*s = 0?
0, 2/5
Suppose 3*d = -2*d. Suppose -5*l + 20 = -d*l - 5*h, -h = -3*l + 8. Determine c, given that -c - 1 - 3 - 2*c**l + 3*c + 4*c**2 = 0.
-2, 1
Let q(w) = -2*w**2 + 7*w - 2. Let f(c) = -c**2 + c - 1. Let o(j) = -5*j**2 + 11*j - 6. Let m(a) = -4*f(a) + o(a). Let i(d) = 6*m(d) - 5*q(d). Factor i(p).
(p + 2)*(4*p - 1)
What is i in -4/9*i - 2/9 - 2/9*i**2 = 0?
-1
Let o be (-6)/12 + (-13)/(-2). Let y(v) be the third derivative of 0*v**3 + 0 + 0*v + 2*v**2 - 1/120*v**o + 0*v**4 + 1/30*v**5. Factor y(d).
-d**2*(d - 2)
Let i(j) = 8*j**3 - 16*j**2 + 2*j + 2. Let h(f) = -f**2 + f - 1. Let u(d) = 2*h(d) + i(d). Factor u(z).
2*z*(z - 2)*(4*z - 1)
Find k such that -5/4*k**3 - 15/2 + 5/4*k + 15/2*k**2 = 0.
-1, 1, 6
Factor -15/4*a - 3/8*a**2 - 75/8.
-3*(a + 5)**2/8
Let a = -1 + 3. Let t(b) be the second derivative of 0*b**3 - 1/15*b**5 - b + 0*b**4 + 0*b**a + 0 - 2/15*b**6 - 1/14*b**7. Factor t(f).
-f**3*(3*f + 2)**2/3
Let d be (0/3)/(-5) - (-3 - 0). Factor 1/3*y**2 - 2*y + d.
(y - 3)**2/3
Suppose 0 = -a + 6*a + 25. Let d be a*1*(2 - 3). Factor 9*c**2 + 4 - 2 + d*c**3 + 2*c**4 - c**4 + 7*c.
(c + 1)**3*(c + 2)
Let n(t) = -t. Let u be n(-4). Find p such that -7*p**4 - p**2 + 6*p**4 + u - 4 - 2*p**3 = 0.
-1, 0
Let s(b) = b**3 - b - 1. Let d(y) = -y**4 + 4*y**3 + 3*y**2 - 4*y - 7. Let u(n) = 2*d(n) - 10*s(n). Factor u(h).
-2*(h - 1)**2*(h + 1)*(h + 2)
Let i(f) be the first derivative of 7 - 20/3*f**3 - 4*f**4 - 4*f**2 - 4/5*f**5 + 0*f. What is b in i(b) = 0?
-2, -1, 0
Let c = -26 - -30. Let f(k) be the third derivative of 0 - 3/4*k**c - 4*k**2 + 0*k + 9/2*k**3 + 1/20*k**5. Factor f(x).
3*(x - 3)**2
Let k be (3 - 3) + (5 - 2). Let r(d) be the second derivative of 2/15*d**3 + 0 - k*d - 1/50*d**5 + 0*d**2 + 1/30*d**4. Determine h, given that r(h) = 0.
-1, 0, 2
Let v(m) be the first derivative of -1/5*m**2 + 1/10*m**4 + 2/5*m - 2/15*m**3 + 3. Determine q, given that v(q) = 0.
-1, 1
Let s be 2*3*(-3)/(-6). Factor -24*t + 49*t**s + 8 + 3 - 7 + 21*t**2.
(t + 1)*(7*t - 2)**2
Let w(k) be the second derivative of -k**4/6 + k**3/3 + 7*k**2/2 - 2*k. Let r(o) = 1. Let n(h) = 3*r(h) - w(h). Let n(a) = 0. What is a?
-1, 2
Let k(l) = -l**2. Let r be 2/(-7) - 18/(-14). Let f(u) = u**2 - 3. Suppose -7 = -6*t - 19. Let d(h) = r*f(h) + t*k(h). Determine g, given that d(g) = 0.
-1, 1
What is d in 8/9 + 8/9*d + 2/9*d**2 = 0?
-2
Let d(h) be the third derivative of -h**8/1680 - h**7/180 - h**6/45 - h**5/20 - h**4/12 - 4*h**2. Let k(g) be the second derivative of d(g). Factor k(a).
-2*(a + 1)**2*(2*a + 3)
Let t = 13 - 9. Let q(r) be the second derivative of 1/15*r**t + 0*r**2 + r - 1/15*r**3 + 0. Suppose q(x) = 0. What is x?
0, 1/2
Let w(f) = -3*f**3 - f**2 + f + 1. Let u be w(-1). Let p(k) = k**3 + 8*k**2 + 6*k - 5. Let i be p(-7). Factor g**2 - 2*g + 0*g**i - 3*g**u.
-2*g*(g + 1)
Let g = -428/3 - -143. Find r such that 0*r + 0 + g*r**3 + 2/3*r**2 = 0.
-2, 0
Let 0*r**4 + 3/2*r + r**2 + 1/2*r**5 - 1 - 2*r**3 = 0. What is r?
-2, -1, 1
Let c be (3/(-6))/(15/(-42)). Solve c*y**3 + 0 - 3/5*y**4 + 0*y**2 - 4/5*y = 0 for y.
-2/3, 0, 1, 2
Let o = 133/4 - 33. Factor 0 + o*g**2 + 1/4*g.
g*(g + 1)/4
Let a(x) be the third derivative of x**2 + 1/8*x**4 + 1/32*x**6 + 0*x**3 + 1/10*x**5 + 1/280*x**7 + 0 + 0*x. Solve a(v) = 0 for v.
-2, -1, 0
Let a(h) be the second derivative of -3*h**7/2 - 13*h**6/10 + 5*h**5/2 + 11*h**4/3 + 4*h**3/3 + 2*h. Suppose a(m) = 0. What is m?
-2/3, -2/7, 0, 1
Let g(l) be the first derivative of l**6/24 - l**5/5 + 3*l**4/16 + l**3/3 - l**2/2 - 4. Factor g(v).
v*(v - 2)**2*(v - 1)*(v + 1)/4
Let c(n) be the first deri