. Suppose x(g) = 0. What is g?
-1, 0, 1
Let f(c) be the third derivative of c**8/10080 + c**7/2520 - c**5/15 + c**2. Let k(m) be the third derivative of f(m). Solve k(g) = 0 for g.
-1, 0
Let l be (7/(-2) + 5)*(-8)/(-6). Suppose -2/5*r + 2/5*r**3 + 2/5*r**l - 2/5 = 0. What is r?
-1, 1
Let o(z) = 8*z**3 - 23*z**2 - 4*z + 5. Let s(j) = 3*j**3 - 8*j**2 - j + 2. Let y(h) = 4*o(h) - 11*s(h). Factor y(i).
-(i + 1)**2*(i + 2)
Let g = 7 - 5. Solve -g*x**3 - 2*x**2 + 2*x**4 - 3*x + x + 6*x - 2*x = 0 for x.
-1, 0, 1
Suppose 0 = -n + 2, -3*n + 4*n = -3*j - 10. Let r be j + 38/4 + -4. Let -r*g + 21/4*g**2 - 3/4 - 3*g**3 = 0. What is g?
-1/4, 1
Determine o, given that -2/7*o + 0 + o**2 - 3/7*o**3 = 0.
0, 1/3, 2
Let a(c) be the third derivative of -c**6/20 - 13*c**5/20 - 3*c**4 - 9*c**3/2 + 45*c**2. Factor a(y).
-3*(y + 3)**2*(2*y + 1)
Suppose -4*x + 4*z = 20, 3 = 2*x + 3*z - 12. Solve x*v**3 + 2/5*v**4 + 0 + 0*v + 0*v**2 = 0 for v.
0
Let a(f) be the second derivative of 5*f**7/168 - f**6/8 + f**5/8 + 5*f**4/24 - 5*f**3/8 + 5*f**2/8 - 6*f. Factor a(l).
5*(l - 1)**4*(l + 1)/4
Let h(d) = -d**3 - 6*d**2 - 7*d - 7. Let j be h(-5). Factor -5 + 5 - 5*w**2 + w - 3*w**4 - w**3 + 8*w**j.
-w*(w - 1)**2*(3*w - 1)
Factor -8*a**2 + 2*a**3 + 31*a - 13*a - 4 - 8*a.
2*(a - 2)*(a - 1)**2
Factor -8/7 + 5/7*s**2 - 1/7*s**3 - 2/7*s.
-(s - 4)*(s - 2)*(s + 1)/7
Let z be (-8)/2 - 368/(-88). Solve -z - 2/11*i**2 - 4/11*i = 0 for i.
-1
Let v(d) be the second derivative of 0 + 0*d**3 + 0*d**4 + 0*d**2 - 6*d - 1/10*d**5 - 1/15*d**6. Factor v(t).
-2*t**3*(t + 1)
Let 8/7*q**3 + 4/7*q**5 + 0*q + 2/7*q**2 + 0 + 10/7*q**4 = 0. What is q?
-1, -1/2, 0
Let d(l) = -l**2 + 10*l + 4. Let p be d(10). Let b(s) be the second derivative of 0*s**3 + 0*s**2 + 1/42*s**p + 2*s + 0. Find m, given that b(m) = 0.
0
Let o = 1 - 4. Let h be (o/(-2))/(8/16). Factor 0 + 0*d - 2/5*d**4 + 2/5*d**5 - 2/5*d**h + 2/5*d**2.
2*d**2*(d - 1)**2*(d + 1)/5
Determine q, given that -4*q**3 - 12*q**2 + 8*q**2 + 2*q + 6*q**3 = 0.
0, 1
Let 4/3 + 2/9*f**2 + 10/9*f = 0. Calculate f.
-3, -2
Let c be 0/(-1) - (-1)/1. Suppose 3*q - c = 5*m, 4*q - 6 = -m + 3*m. Factor 1 + 3*d**4 - m - 5*d**4.
-2*d**4
Let z be (-1)/3*(0 + 0). Factor z - 1/4*m**2 + 0*m.
-m**2/4
Let x(d) = d**2 + 17*d + 4. Let y be x(-17). Find v, given that -10/11*v**2 + 4/11 + 6/11*v**y - 2/11*v + 2/11*v**3 = 0.
-1, 2/3, 1
Let i(b) be the first derivative of -b**2 - 2/3*b**3 + 2*b + 2 + 1/2*b**4. Let i(x) = 0. Calculate x.
-1, 1
Factor -50*n + 9*n**2 - 125*n**2 - 4 - 80*n**3 + 10*n.
-4*(n + 1)*(4*n + 1)*(5*n + 1)
Let n(k) = 18*k - 144. Let f be n(8). Factor f - 1/2*v + 3/4*v**2.
v*(3*v - 2)/4
Let g(j) be the second derivative of j**2 - j**3 + 1/2*j**4 - 1/10*j**5 + 0 - 3*j. What is x in g(x) = 0?
1
Suppose 3*q + 2*b = 7, 4*b - 3*b = 5*q + 10. Let l(m) = -m - 1. Let x(y) = 4*y**2 + 28*y + 24. Let c(a) = q*x(a) - 20*l(a). Factor c(n).
-4*(n + 1)**2
Factor -28/5*v**4 + 0*v + 49/5*v**5 + 0 + 0*v**2 + 4/5*v**3.
v**3*(7*v - 2)**2/5
Factor -2*t**4 + 3*t**2 - 1 - t**2 + t**4.
-(t - 1)**2*(t + 1)**2
Let y(c) be the third derivative of -c**6/40 - c**5/4 - 7*c**4/8 - 3*c**3/2 + 62*c**2. Find q, given that y(q) = 0.
-3, -1
Suppose -3*g = -3 - 6. Let 3/5*p**g - 6/5 - 9/5*p + 0*p**2 = 0. What is p?
-1, 2
Factor -9/2 + 6*t - 3/2*t**2.
-3*(t - 3)*(t - 1)/2
Suppose 2*p**3 + p - 7/2*p**2 + 1/2 = 0. What is p?
-1/4, 1
Let x(t) be the second derivative of -t**9/6048 + t**8/1680 - t**6/360 + t**5/240 - t**3/2 + t. Let w(s) be the second derivative of x(s). Factor w(k).
-k*(k - 1)**3*(k + 1)/2
Determine x so that -5*x**5 - 22*x**2 + 20 - 55*x - 3*x**2 + 25*x**3 + 5*x**4 + 35*x = 0.
-2, -1, 1, 2
Determine m, given that 3*m + 4*m**3 + m**3 - m + 8*m**2 - m**2 = 0.
-1, -2/5, 0
Let u(h) be the second derivative of -h**5/150 + h**4/60 + 2*h**3/15 + h**2/2 + h. Let d(s) be the first derivative of u(s). Factor d(x).
-2*(x - 2)*(x + 1)/5
Solve 5*h**5 + 37*h**3 - 40*h**2 - 30*h**4 - 66*h**3 + 89*h**3 = 0.
0, 2
Let d(q) = 2*q**2 + 6*q. Let j(x) = -x**2 - 5*x. Let s(b) = 3*d(b) + 2*j(b). Suppose s(p) = 0. Calculate p.
-2, 0
Let s = -19 + 22. Factor -8*i**2 + 11 - 3 - 2*i**3 - 2*i**s + 4*i.
-4*(i - 1)*(i + 1)*(i + 2)
Let c(l) be the third derivative of -l**8/20160 + l**5/12 + l**2. Let g(s) be the third derivative of c(s). Suppose g(t) = 0. Calculate t.
0
Let i = -50 + 28. Let r be 1/(42/i - -2). Factor 4*h**2 - 6*h**4 - 4*h + 1 - 1 + r*h**3 - 9*h**5.
-h*(h + 1)**2*(3*h - 2)**2
Let u(r) be the second derivative of -r**5/15 - 2*r**4/9 - 2*r**3/9 + 23*r. Determine g, given that u(g) = 0.
-1, 0
Let t be 10/60 + 1 - 1. Factor -1/6*m**2 - t - 1/3*m.
-(m + 1)**2/6
Determine k, given that 2*k**5 - 10/7*k**2 + 10/7*k**4 + 0 - 18/7*k**3 + 4/7*k = 0.
-1, 0, 2/7, 1
Let a(h) be the first derivative of -h**5/10 + h**4/4 + 2*h**3/3 - h**2/2 - 3*h/2 + 6. Factor a(k).
-(k - 3)*(k - 1)*(k + 1)**2/2
Let d be 4/6 - 24/36. Suppose d*w + 0 + 1/4*w**2 + 1/4*w**3 = 0. Calculate w.
-1, 0
Let r(w) be the second derivative of w**5/150 + w**4/45 + w**3/45 + 7*w. Factor r(d).
2*d*(d + 1)**2/15
Let q(m) be the second derivative of 0*m**3 + 0*m**2 + 1/10*m**6 + 0 + 1/10*m**5 + 1/42*m**7 + 0*m**4 + 2*m. Factor q(v).
v**3*(v + 1)*(v + 2)
Let o(y) be the second derivative of -y**4/28 + 2*y**3/7 - 9*y**2/14 - 6*y. Factor o(u).
-3*(u - 3)*(u - 1)/7
Suppose -2038*z**2 + 5*z**4 + 6*z**3 - 10*z + 2033*z**2 + 4*z**3 = 0. Calculate z.
-2, -1, 0, 1
Let v = 36 - 42. Let l be ((-1)/(-5))/(v/(-10)). Find h, given that -h**3 + l*h**2 + h**4 + 0*h - 1/3*h**5 + 0 = 0.
0, 1
Let r(k) be the second derivative of k**5/80 - k**4/48 - 3*k. Factor r(n).
n**2*(n - 1)/4
Let h = 5609/30 - 375/2. Let g = h + 6/5. Factor 4/3*o**2 + 0 + g*o**3 + 2/3*o.
2*o*(o + 1)**2/3
Let c(v) = -7*v + 105. Let g be c(15). Factor 4/3*m**2 + 22/3*m**3 + g + 0*m.
2*m**2*(11*m + 2)/3
Solve -2*b - 2*b - b**4 - 456*b**3 - 9*b**2 + 450*b**3 = 0 for b.
-4, -1, 0
Suppose -7 = 2*x - 3. Let t(l) = -l**2 - 3*l. Let c be t(x). Let 4*g**3 + c*g**4 + 2*g**2 + 2*g**2 - 2*g**2 = 0. Calculate g.
-1, 0
Suppose 0 = -k - k + 4. Factor 4*v + 2*v**2 + 8 + k - 8.
2*(v + 1)**2
Factor -24 - 3/2*j**3 - 27/2*j**2 - 36*j.
-3*(j + 1)*(j + 4)**2/2
Determine t so that -14*t**4 - 11*t**4 + 30*t**4 = 0.
0
Let d = -7 - -15/2. Determine i so that 1/4*i**4 + 0*i**2 - 1/4 - d*i**3 + 1/2*i = 0.
-1, 1
Let a(l) be the third derivative of 1/120*l**6 + 0*l**4 + 1/70*l**7 + 3*l**2 + 0*l - 1/336*l**8 - 7/60*l**5 + 2/3*l**3 + 0. Factor a(i).
-(i - 2)**2*(i - 1)*(i + 1)**2
Suppose 20 = 2*f - 3*p, f - 4*p - 8 = 12. Let z be (f/10)/(24/30). Suppose -z*g**2 + g - 1/2 = 0. Calculate g.
1
Let a(w) be the second derivative of -w**7/2520 + w**6/90 - 2*w**5/15 - w**4/12 + 8*w. Let v(l) be the third derivative of a(l). Solve v(q) = 0 for q.
4
Let w(d) be the second derivative of d**5/110 - 2*d**4/33 + 5*d**3/33 - 2*d**2/11 + 10*d. Solve w(x) = 0 for x.
1, 2
Let s(a) be the third derivative of 5*a**8/336 - 5*a**7/42 + a**6/3 - a**5/3 - 10*a**2. Determine l, given that s(l) = 0.
0, 1, 2
Suppose 3/2*r**3 + 2*r**4 + 1/3*r**2 + 0*r + 5/6*r**5 + 0 = 0. What is r?
-1, -2/5, 0
Determine m so that 41*m**4 + 22*m**2 - 28*m**2 - 39*m**2 + 75*m - 27*m**3 - 44*m**4 = 0.
-5, 0, 1
Let n(m) be the third derivative of -6*m**2 + 0*m**4 + 0*m**3 - 1/15*m**5 + 0*m + 2/15*m**6 + 0. Factor n(v).
4*v**2*(4*v - 1)
Find x such that -16/5 - 64/5*x**3 - 2*x**4 - 114/5*x**2 - 76/5*x = 0.
-4, -1, -2/5
Let c(l) be the second derivative of -1/2*l**5 + 0*l**2 + 0 - 5/3*l**6 - 2*l + 8/3*l**4 - 4/3*l**3. Find s, given that c(s) = 0.
-1, 0, 2/5
Let v = 149 - 445/3. Factor -1/3*u**4 + 0*u**2 + 0*u + 1/3*u**5 - v*u**3 + 0.
u**3*(u - 2)*(u + 1)/3
Let b(i) = 9 + 25 - 14*i**2 - 14 - 6*i. Let a(n) = -5*n**2 - 2*n + 7. Let j(v) = -8*a(v) + 3*b(v). Factor j(y).
-2*(y - 1)*(y + 2)
Let y(z) be the second derivative of 0*z**5 - 1/84*z**7 + 0*z**2 - 1/60*z**6 + 0*z**4 + 0*z**3 + 0 + 3*z. Determine w so that y(w) = 0.
-1, 0
Let z be ((-1)/2)/(1/8). Let g(a) = 6*a**2 - 5*a. Let n(x) be the first derivative of -5*x**3/3 + 2*x**2 - 6. Let m(k) = z*g(k) - 5*n(k). Factor m(y).
y**2
Determine s so that 442*s**4 - 600*s**3 + 10*s + 974*s**4 - 10*s**2 + 25*s**2 + 104*s**4 = 0.
-2/19, 0, 1/4
Factor -8/7*i**4 + 2*i**3 + 0 + 4/7*i**2 + 0*i.
-2*i**2*(i - 2)*(4*i + 1)/7
Let m(h) = 8