3 - t + 1. Let z(g) = 12*f(g) - h(g). Let z(p) = 0. What is p?
-2/5, 0, 1
Let u(v) be the second derivative of -v**4/96 + 7*v**3/24 - 49*v**2/16 + 11*v. Factor u(g).
-(g - 7)**2/8
Let v(a) = -4*a**2 + 3*a + 7. Let w(i) = 5*i**2 - 3*i - 8. Let m(f) = -4*v(f) - 3*w(f). Let h be m(4). Factor h*b**3 - 3*b**2 + b**3 + 2*b**3.
3*b**2*(b - 1)
Let g(w) be the second derivative of 0 + 2/9*w**3 + 1/15*w**6 + 4*w + 8/45*w**5 + 1/9*w**2 + 2/189*w**7 + 7/27*w**4. Factor g(m).
2*(m + 1)**4*(2*m + 1)/9
Suppose 3 = 2*y - 3. Suppose 0 = 4*n - y*n - 4. Factor -6*s**4 + 0*s**2 - 31*s**3 + 6*s**2 + 33*s**3 - n*s + 2*s**5.
2*s*(s - 2)*(s - 1)**2*(s + 1)
Let g(v) be the first derivative of v**6/120 + v**5/40 + v**4/48 + 3*v + 3. Let d(r) be the first derivative of g(r). Determine k so that d(k) = 0.
-1, 0
Let -102*r**3 + 51*r**3 + 54*r**3 + 48*r**2 + 192*r = 0. Calculate r.
-8, 0
Let f(c) be the second derivative of -c**5/110 + 2*c**4/33 - 5*c**3/33 + 2*c**2/11 - 6*c. Factor f(s).
-2*(s - 2)*(s - 1)**2/11
Let c(i) be the second derivative of -i**7/7 + i**6/10 + 3*i**5/10 - i**4/4 - 24*i. Suppose c(a) = 0. Calculate a.
-1, 0, 1/2, 1
Let l(c) be the first derivative of -3*c**4/4 + 4*c**3 - 15*c**2/2 + 6*c - 7. What is j in l(j) = 0?
1, 2
Let c(y) = y**4 + y**3 - y. Let z(f) = -10*f**4 - 15*f**3 - 6*f**2 + 5*f. Let s = -6 + 0. Let i(j) = s*c(j) - z(j). Solve i(t) = 0 for t.
-1, -1/4, 0
Suppose 0 = p - 3*w, -w = -2*w + 1. Let l(y) be the second derivative of y + 1/36*y**4 + 0*y**p - 1/6*y**2 + 0. Let l(t) = 0. What is t?
-1, 1
Let p be (21/(-70))/(3/(-4)). Let x = p - -1/10. Factor -1/2*n + x*n**2 + 0.
n*(n - 1)/2
Let h(p) be the third derivative of -17*p**6/960 + p**5/240 + 11*p**2. Find d such that h(d) = 0.
0, 2/17
Let l(n) = 17*n**2 - 5*n + 11. Let q(h) = 6*h**2 - 2*h + 4. Let a(c) = -4*l(c) + 11*q(c). Find i, given that a(i) = 0.
-1, 0
Let a(t) be the second derivative of -t**6/90 + t**5/15 - 5*t**4/36 + t**3/9 + t - 1. Factor a(w).
-w*(w - 2)*(w - 1)**2/3
Suppose -5*s + 29 = x, s = 4*x + 2 - 13. Factor 0 + 2/3*p - 4/3*p**3 + 0*p**x + 0*p**2 + 2/3*p**5.
2*p*(p - 1)**2*(p + 1)**2/3
Let j be ((-20)/(-2))/(-2 - -1). Let r = 14 + j. Solve i**r - 2*i - i**2 + 2*i = 0.
-1, 0, 1
Let w(g) be the second derivative of g**6/105 - 3*g**5/35 + 13*g**4/42 - 4*g**3/7 + 4*g**2/7 - 13*g. Solve w(u) = 0 for u.
1, 2
Let f(d) be the second derivative of -d**6/15 - 8*d**5/5 - 16*d**4 - 256*d**3/3 - 256*d**2 - 14*d. Suppose f(r) = 0. What is r?
-4
Factor 3/7 - 3/7*w**2 + 0*w.
-3*(w - 1)*(w + 1)/7
Let m = -38 + 38. Let b(s) be the second derivative of -1/14*s**7 + 0*s**3 + m*s**2 + 0 + 0*s**6 - 3*s + 3/20*s**5 + 0*s**4. Determine q, given that b(q) = 0.
-1, 0, 1
Let l(k) be the second derivative of k**5/60 - k**4/6 + 5*k**3/18 + 2*k - 22. Factor l(c).
c*(c - 5)*(c - 1)/3
Let i(w) be the third derivative of -w**5/240 - w**4/96 + w**3/12 + 2*w**2. Factor i(b).
-(b - 1)*(b + 2)/4
Factor 29*j**2 + 0*j - 1 - 32*j**2 + j**3 + 3*j.
(j - 1)**3
Let h(l) be the first derivative of -l**3/15 + l**2/5 - l/5 - 1. Suppose h(v) = 0. What is v?
1
Let f = 7 + -5. Factor b**f - 2*b**2 + 4*b**2 - b - 2*b.
3*b*(b - 1)
Suppose 0 = 2*f - x - 11, 5*f - 32 = -0*f + 4*x. Let -2*v**f + 0*v**3 - 2*v**4 - v**2 + 2*v**3 + 3*v**4 = 0. What is v?
0, 1
Suppose 114 = 3*o + 3*k, -3*k + k - 68 = -2*o. What is j in j**2 + j + o - 36 = 0?
-1, 0
Let r = -593/5 - -119. What is t in -r*t**3 + 1/5 - 2/5*t + 7/5*t**4 + 4/5*t**5 - 8/5*t**2 = 0?
-1, 1/4, 1
Let 9*i**2 - 6*i**2 + 6*i**2 + 4*i**3 - i**2 = 0. Calculate i.
-2, 0
Factor -2/7 - 6/7*p**2 - 2/7*p**3 - 6/7*p.
-2*(p + 1)**3/7
Let k(c) be the first derivative of -c**6/150 + c**5/25 - c**4/12 + c**3/15 - 6*c + 6. Let o(y) be the first derivative of k(y). Factor o(i).
-i*(i - 2)*(i - 1)**2/5
Let k(m) be the second derivative of -m**5/120 - m**4/8 - 3*m**3/4 - m**2/2 - 6*m. Let q(o) be the first derivative of k(o). Factor q(u).
-(u + 3)**2/2
Let f(v) be the third derivative of -v**5/30 + v**4/12 - 2*v**2. Factor f(x).
-2*x*(x - 1)
Let w(u) be the first derivative of u**3 - 6*u**2 + 12*u + 9. Determine l, given that w(l) = 0.
2
Let q(y) be the third derivative of -1/6*y**3 + 0 - 4*y**2 + 0*y - 1/32*y**4 + 1/240*y**5. Solve q(w) = 0.
-1, 4
Factor g**4 + 0*g**4 - g**2 - 4*g**2 + 4*g**4.
5*g**2*(g - 1)*(g + 1)
Let f(c) = c**3 - 7*c**2 + 2*c - 6. Let p be f(7). Let q be ((-4)/p)/(10/(-4)). Suppose 4/5*k + q*k**4 + 6/5*k**2 + 1/5 + 4/5*k**3 = 0. Calculate k.
-1
Let w(k) be the third derivative of k**5/6 - k**4/3 - k**3/3 - 11*k**2. Solve w(g) = 0.
-1/5, 1
Suppose -4*x = -6*x + 6. Factor -3*l**3 - 3*l**2 + 2*l**x - 2*l**2 + 7*l**2 - l.
-l*(l - 1)**2
Suppose 4*c = -c - 15. Let x(q) = 9*q. Let a(r) = -r**2 - 8*r - 1. Let b(l) = c*a(l) - 2*x(l). Factor b(y).
3*(y + 1)**2
Let b = 31 - 91/3. Suppose o + 0*o + 4 = 0, -o - 4 = 3*w. Factor w - 2/3*d**3 - 4/3*d**2 - b*d.
-2*d*(d + 1)**2/3
Let f(s) be the first derivative of -3 + 0*s**2 + 0*s + 1/2*s**6 + s**3 + 9/5*s**5 + 9/4*s**4. Suppose f(d) = 0. What is d?
-1, 0
Let j(a) = a + 11. Suppose 3 - 11 = u. Let w be j(u). Determine m, given that -1/5*m**w + 0*m**2 + 3/5*m - 2/5 = 0.
-2, 1
Suppose 0 = 4*w - 3 + 15. Let u be 2/w + (-50)/(-15). Factor -8/3 - u*g - 2/3*g**2.
-2*(g + 2)**2/3
Let h be (-23)/(-7) + -7 + 4. Suppose -2*m + 19 = -5*c, -c - 13 = -m - 4*m. Factor h - 2/7*w**m + 0*w.
-2*(w - 1)*(w + 1)/7
Let g(j) be the first derivative of -j**8/2240 - j**7/840 + j**6/1440 + j**5/240 + 4*j**3/3 + 3. Let l(m) be the third derivative of g(m). Factor l(w).
-w*(w + 1)**2*(3*w - 2)/4
Let a(t) = -21*t**3 + 165*t**2 - 108*t + 18. Let k(c) = -6*c**3 + 47*c**2 - 31*c + 5. Let z(q) = -5*a(q) + 18*k(q). Factor z(d).
-3*d*(d - 6)*(d - 1)
Let m(t) be the first derivative of -5*t**6/6 + 5*t**4/2 - 5*t**2/2 - 16. Factor m(x).
-5*x*(x - 1)**2*(x + 1)**2
Factor -2/5*m**4 + 0 + 2/5*m**3 + 0*m + 0*m**2.
-2*m**3*(m - 1)/5
Suppose -2*l + 4 = -0*l. Factor -p**l - p - p + p.
-p*(p + 1)
Let y(s) be the second derivative of 0*s**2 + 1/105*s**7 + 0*s**3 + 0 - s - 1/75*s**6 - 1/50*s**5 + 1/30*s**4. Suppose y(g) = 0. Calculate g.
-1, 0, 1
Let n(w) be the third derivative of -w**7/3780 + w**6/540 - w**5/270 - w**3/6 + 2*w**2. Let s(v) be the first derivative of n(v). What is x in s(x) = 0?
0, 1, 2
Let b be (-5)/((-45)/66) + -1. Solve -5*y**2 - 7/3*y**4 + 2/3 - b*y**3 - 1/3*y = 0 for y.
-1, 2/7
Let y(n) = -n**3 - 8*n**2 - 8*n - 3. Let s be y(-7). Let h(m) be the second derivative of 0 + 2/21*m**3 - m + 1/42*m**s + 1/7*m**2. Factor h(z).
2*(z + 1)**2/7
Let r be (-4)/(8/(-6)) + 1. Let d**3 - 2*d**4 + 2*d**r - d**4 = 0. What is d?
0, 1
Suppose -11*w + 14*w - 6 = 0. Factor 4/3 - 2*s**3 - 4/3*s**2 + w*s.
-2*(s - 1)*(s + 1)*(3*s + 2)/3
Suppose 21*t = 15*t + 36. Let c(v) be the second derivative of 1/30*v**5 + 0*v**2 - 7/90*v**t + 0 + 0*v**4 + 0*v**3 + v. Determine l so that c(l) = 0.
0, 2/7
Let g(d) = -1. Let w(b) = -2*b**2 - 14*b + 6. Let j(c) = 36*g(c) + 2*w(c). Find h such that j(h) = 0.
-6, -1
Suppose -38 = -3*y - 17. Let m(w) be the second derivative of 3/100*w**5 + 1/210*w**y + 0*w**2 + 0 + 1/60*w**4 + w + 1/50*w**6 + 0*w**3. Factor m(n).
n**2*(n + 1)**3/5
Let z(n) be the third derivative of 0 + 5/36*n**4 + 2/45*n**5 + 1/9*n**3 + 0*n - 3*n**2. Let z(p) = 0. Calculate p.
-1, -1/4
Let x(z) = z**5 - z**2 + z. Let a(c) = -6*c**5 - 10*c**4 - 12*c**3 + 8*c**2 + 10*c + 6. Let u(r) = -a(r) - 4*x(r). Find y, given that u(y) = 0.
-3, -1, 1
Let s(y) = -y**2 - 9*y + 5. Let g be s(-8). Let p = -11 + g. Let 2/3*d**3 + 4/3 + p*d**2 - 10/3*d - 2/3*d**4 = 0. Calculate d.
-2, 1
Let y be 36/(0 + -2 + 4). Suppose 2*f**3 - 14*f**2 + y*f**2 + 2 - 2*f + 2 - 8*f**2 = 0. Calculate f.
-1, 1, 2
Let m be -3 + (-21)/(-14) + (-13)/(-6). Factor -n**3 + m*n**2 + n - 2/3.
-(n - 1)*(n + 1)*(3*n - 2)/3
Let r(l) be the second derivative of 1/60*l**5 + 0*l**2 - 1/36*l**4 + 0*l**3 + 0 + 3*l. Solve r(a) = 0 for a.
0, 1
Suppose -2 = -b - 0. Factor -4*o**2 + o + 3*o**2 + 5*o**3 - b*o**4 + 5*o**2 + 4*o**4.
o*(o + 1)**2*(2*o + 1)
Let c(t) be the third derivative of 0*t**3 + 0*t + 0 + 2/15*t**6 + 0*t**4 + t**2 - 1/30*t**5 - 16/105*t**7. Determine n so that c(n) = 0.
0, 1/4
Suppose 3*c + 18 - 69 = 0. Suppose -4*o - 2*d + d + c = 0, 25 = 5*o + 5*d. Suppose 0*w + 0*w**2 - 2/5*w**o + 0 + 2/5*w**3 = 0. Calculate w.
