i). Factor d(k).
-4*k*(k + 1)**2*(7*k + 2)
Let v(b) be the first derivative of 2*b**5/15 + b**4/6 - 2*b**3/9 - b**2/3 - 7. Determine c so that v(c) = 0.
-1, 0, 1
Let f = 21 - 19. Let s be (12/(-4) - -3) + f. Let -12/5*r**4 + 0 + 0*r - 7/5*r**5 + 2/5*r**s - 3/5*r**3 = 0. What is r?
-1, 0, 2/7
Factor 6*c - 2 - c + 0*c - 3*c**2 + 2*c.
-(c - 2)*(3*c - 1)
Find x, given that -2/5 - 2/15*x**3 - 14/15*x - 2/3*x**2 = 0.
-3, -1
Let q be ((-30)/35)/(4/(-28)). Let i(c) be the second derivative of 1/24*c**4 + 0*c**2 - 1/60*c**q + 1/40*c**5 + 0*c**3 + 0 - 1/84*c**7 + c. Factor i(l).
-l**2*(l - 1)*(l + 1)**2/2
Let f = 1/6 - -1/30. Suppose 2/5*t + 0 + f*t**2 = 0. Calculate t.
-2, 0
Let l be (-1 - 16)/((-6)/30). Let f be (2/(-5))/((-68)/l). Let f*t**2 + 0 + 0*t = 0. What is t?
0
Let m(y) = y - 11. Let d be m(13). Determine x, given that 1/4*x + 1/4*x**5 - 1/2*x**3 + 1/2*x**d - 1/4 - 1/4*x**4 = 0.
-1, 1
Let l = 370 - 1471/4. Suppose -7/4*t**2 + 0 + 1/4*t**5 - 5/4*t**4 + 1/2*t + l*t**3 = 0. Calculate t.
0, 1, 2
Let f(g) = -8 + g**2 + 6 + 10 + 6 - 12*g. Let r be f(11). Let 0 - 2/5*t**r + 0*t - 2/5*t**2 = 0. Calculate t.
-1, 0
Let i be (4/5)/((-8)/(-20)). Let l be 46/8 - (-3 - -2). Find h, given that -2*h**i - 19/4*h**4 + l*h**3 + 0 + h**5 - h = 0.
-1/4, 0, 1, 2
Let b(q) be the first derivative of q**6/6 - 2*q**5/5 + 2*q**3/3 - q**2/2 + 1. Find u, given that b(u) = 0.
-1, 0, 1
Suppose 5*x - 19 - 1 = 0. Let o(j) be the first derivative of 1 + 3*j**2 + 2*j + 1/2*j**x + 2*j**3. Factor o(k).
2*(k + 1)**3
Let r = 29/2 - 14. Let z = -2/153 + 769/306. Determine p, given that -z*p - r - 2*p**2 = 0.
-1, -1/4
Suppose -12 = -4*m - 72. Let p be (-18)/m*(-20)/(-6). Suppose 8*n + 2/3*n**4 + 8/3 + p*n**3 + 26/3*n**2 = 0. Calculate n.
-2, -1
Let m(t) be the third derivative of -t**5/12 + 5*t**4/12 - 5*t**3/6 - t**2. Factor m(g).
-5*(g - 1)**2
Let l(o) = -2*o**2 - 21*o - 8. Let k be l(-10). Factor 3*t - 9/2 - 1/2*t**k.
-(t - 3)**2/2
Let q(s) = -75*s**2 - 5*s - 15. Let h(o) = -19*o**2 - o - 4. Let d(z) = 15*h(z) - 4*q(z). Determine m, given that d(m) = 0.
-1/3, 0
Let h(q) be the second derivative of 3*q**4/20 - 4*q**3/5 + 6*q**2/5 + 3*q. Factor h(k).
3*(k - 2)*(3*k - 2)/5
Suppose -4*u + 10 = -5*o, -u + 4 = o - 3. Factor 0 + 3/2*v**o + 3/2*v.
3*v*(v + 1)/2
Let z(w) = w**2 + 6*w - 5. Let t be z(-6). Let j = t + 7. Suppose -2/5*c**j + 4/5*c - 2/5 = 0. What is c?
1
Factor -2/9*s**4 - 2/3*s**2 + 0 - 8/9*s**3 + 0*s.
-2*s**2*(s + 1)*(s + 3)/9
Factor 1/8*x**5 + 0 + 0*x - 1/8*x**4 + 1/8*x**2 - 1/8*x**3.
x**2*(x - 1)**2*(x + 1)/8
Let y(b) be the second derivative of -b**4/6 - 5*b**3/3 - 4*b**2 - 12*b. Suppose y(q) = 0. Calculate q.
-4, -1
Let t(s) be the third derivative of 0 + 1/48*s**4 + 0*s + s**2 + 0*s**3 + 1/120*s**5. Factor t(y).
y*(y + 1)/2
Factor -2*o**2 + o**2 - 4*o**2 + 2*o**2 + 3*o**3 - 6*o.
3*o*(o - 2)*(o + 1)
Let y(v) be the third derivative of -2*v**7/105 + v**6/30 + v**5/15 - v**4/6 - 4*v**2. Suppose y(w) = 0. What is w?
-1, 0, 1
Factor 4/9*u - 4/9 - 1/9*u**2.
-(u - 2)**2/9
Let u = 12 + -11. Let q(c) be the first derivative of -u - 1/3*c**3 + c - c**4 + 2*c**2. Find b, given that q(b) = 0.
-1, -1/4, 1
Factor 0 + 2/11*q**3 + 8/11*q - 8/11*q**2.
2*q*(q - 2)**2/11
Find q, given that 0 + 1/3*q**5 + 4/3*q**4 + 1/3*q + 2*q**3 + 4/3*q**2 = 0.
-1, 0
Let f(k) be the first derivative of -k**6/30 + 2*k**5/25 - 2*k**3/15 + k**2/10 - 1. What is c in f(c) = 0?
-1, 0, 1
Let p = -18 - -18. Let b(g) be the third derivative of 0*g - 1/105*g**7 - 1/168*g**8 - 1/3*g**3 + 2*g**2 + 1/15*g**5 - 1/12*g**4 + p + 1/30*g**6. Factor b(q).
-2*(q - 1)**2*(q + 1)**3
Let d = 2/11 - -16/33. Let p be (10/(-4) - -3)*0. Factor -2/3*a + p - d*a**2.
-2*a*(a + 1)/3
Suppose 3*x + 4*i + 4 + 4 = 0, 5*i = 2*x - 10. Suppose x = -5*r + 10. Factor -1/4*c + 1/4*c**r + 0.
c*(c - 1)/4
Let s(h) be the third derivative of -h**6/60 + h**4/12 + 6*h**2. Find k, given that s(k) = 0.
-1, 0, 1
Let r = 8 - 4. Suppose -m - m = -r. Suppose -m*s**2 - 1 + 1 = 0. What is s?
0
Solve -8/3*y - 20/3*y**2 + 4*y**5 + 0 + 20/3*y**4 - 4/3*y**3 = 0.
-1, -2/3, 0, 1
Let t(h) be the third derivative of -9*h**5/140 + 3*h**4/14 - 2*h**3/7 + 8*h**2. Determine n so that t(n) = 0.
2/3
Let s(q) be the third derivative of q**6/600 + q**5/300 - q**4/120 - q**3/30 - 6*q**2. Factor s(z).
(z - 1)*(z + 1)**2/5
Let t(s) be the second derivative of s**5/14 - 2*s**4/21 - s**3/21 - 4*s. Factor t(k).
2*k*(k - 1)*(5*k + 1)/7
Let x(d) = -2*d**2 + 4*d - 2. Let p(r) = -r - 1. Let u(z) = -2*p(z) + x(z). Determine b, given that u(b) = 0.
0, 3
Let d(v) be the second derivative of -v**7/126 + 6*v. Factor d(r).
-r**5/3
Let v be ((-8)/(-10))/((-2)/(-5)). Factor -d**2 - 24*d + 0*d**2 + 23*d + v.
-(d - 1)*(d + 2)
Let f(z) = z**3 + 9*z**2 + 7*z - 10. Let j be f(-8). Let p be (2 - 3)/(1/j). Factor -t**2 + t**3 - t**2 + p*t**4 + 2*t - 3*t**3.
2*t*(t - 1)**2*(t + 1)
Let a(g) be the second derivative of g**5/130 - 9*g. Factor a(d).
2*d**3/13
Let i = -11 + 14. Let a(s) be the second derivative of -1/21*s**3 - 1/42*s**4 + i*s + 0 + 0*s**2. Factor a(c).
-2*c*(c + 1)/7
Let g(o) = -o**4 + o**3 - o**2 - 1. Suppose 0 = -w + 4*w - 9. Let y(n) = -7*n**4 - 5*n**3 - 3*n**2 + 8*n + 1. Let m(v) = w*g(v) - y(v). Factor m(q).
4*(q - 1)*(q + 1)**3
Suppose -12*b + 2*b + 20 = 0. Let a(o) be the second derivative of b*o + 2/27*o**3 + 1/54*o**4 + 1/9*o**2 + 0. Solve a(l) = 0.
-1
Suppose 2*f + 4*u = 0, 2 = -2*u - 0. Factor 1/2*g**3 + 1/2*g**f - g + 0.
g*(g - 1)*(g + 2)/2
Factor 2/19*h**3 + 0 + 2/19*h**2 - 4/19*h.
2*h*(h - 1)*(h + 2)/19
Let 12 - 18 + 3*z**2 + 2*z + z = 0. Calculate z.
-2, 1
Let j = -52 + 157/3. Factor -z**2 + 1/3*z - 1/3*z**3 + 2/3 + j*z**4.
(z - 2)*(z - 1)*(z + 1)**2/3
Let k be (-20)/(-9) - 4/18. Factor 0 + 3*g**k + g**2 + 3*g - 5 + 4.
(g + 1)*(4*g - 1)
Let a = 8 + -9. Let u be a/(-2) + (-2)/4. Suppose u - 1/2*j + 1/2*j**2 = 0. What is j?
0, 1
Let t = 22 + -12. Let v be (-2)/(-4) - (-15)/t. Suppose 5/4*g**v + 0 - 1/2*g = 0. Calculate g.
0, 2/5
Let v(o) be the third derivative of -o**8/84 + o**6/15 - o**4/6 - 8*o**2. Factor v(u).
-4*u*(u - 1)**2*(u + 1)**2
Let x be (0*(-2)/(-6))/4. Let z be 4 - (x - 102/(-27)). Factor 0 - 2/9*k**2 + 0*k - 4/9*k**3 - z*k**4.
-2*k**2*(k + 1)**2/9
Let x(l) = -5*l**3 - l**2 + 4*l - 2. Let b(k) = -15*k**3 - 2*k**2 + 13*k - 7. Let o(d) = 2*b(d) - 7*x(d). Factor o(j).
j*(j + 1)*(5*j - 2)
Let x(c) be the first derivative of 0*c**2 - 1/6*c**4 + 7 + 0*c**3 + 0*c. Factor x(q).
-2*q**3/3
Find u, given that -4*u + 4/9 + 9*u**2 = 0.
2/9
Let h(x) be the second derivative of x**5/8 - 5*x**4/12 + 5*x**3/12 - 10*x. Let h(u) = 0. Calculate u.
0, 1
Let q be 20/12*8/20. Let -2/9 - 4/9*v**2 - 4/9*v**3 + 2/3*v - 2/9*v**5 + q*v**4 = 0. Calculate v.
-1, 1
Factor -5*w**2 + 5*w**2 - 2*w**3 + 0*w**3 - w**4 + w**5.
w**3*(w - 2)*(w + 1)
Let r(v) = -3*v**3 + 36*v**2 - 24*v. Let s be 18/(-8) - 1/(-4). Let t(g) = g**3 - 9*g**2 + 6*g. Let q(f) = s*r(f) - 9*t(f). Find l, given that q(l) = 0.
0, 1, 2
Suppose 31 + 5*o**2 + 65*o**2 - 1 - 85*o - 15*o**3 = 0. What is o?
2/3, 1, 3
Let y(a) be the first derivative of -a**6/21 - 4*a**5/35 + a**4/7 + 8*a**3/21 - a**2/7 - 4*a/7 + 18. Let y(w) = 0. Calculate w.
-2, -1, 1
Factor -2/11*b**2 + 0 + 24/11*b.
-2*b*(b - 12)/11
Let v(x) be the third derivative of x**7/70 - x**6/20 - x**5/20 + x**4/4 + 34*x**2 + 2. Solve v(k) = 0.
-1, 0, 1, 2
Let m(o) = 4 - o - o - 5*o + 4*o**2. Let c(l) = -l**3 + l**2 - l. Let f(i) = -c(i) - m(i). Factor f(p).
(p - 2)**2*(p - 1)
Let p be ((-8)/14)/(4/(-14)). Solve 110*w**p + 13 - 5 - 112*w**2 = 0.
-2, 2
Let v(z) be the third derivative of -z**6/120 - z**5/20 + 2*z**3/3 + 18*z**2. Determine j, given that v(j) = 0.
-2, 1
Let w(f) be the first derivative of -5*f**9/13608 + f**8/945 - f**7/3780 - f**6/810 - f**3/3 + 1. Let j(q) be the third derivative of w(q). Factor j(l).
-2*l**2*(l - 1)**2*(5*l + 2)/9
Factor -1/5*i + 1/5*i**3 + 4/5*i**2 - 4/5.
(i - 1)*(i + 1)*(i + 4)/5
Let c(j) = j + 10. Let q be c(-8). Factor 5*s - 17*s - 3*s**2 + 0*s**q - 12.
-3*(s + 2)**2
Factor 10*u**3 - 4*u**3 - 2*u**4 - 96*u**2 - 30*u**2 + 98*u + 24*u**3.
-2*u*(u - 7)**2*(u - 1)
Solve 0*j**3 + 0*j + 1/4 + 1/4*j**4 - 1/2*j**2 = 0 for j.
-1, 1
Suppose 0 = 2*a - 3*x - 3, -a - 2*a + 2*x + 7 = 0. Find m, given that m**3 - 19*m**2 - 11*m**3 - 3*m**a - 2 -