d. Determine b, given that 0 + 0*b**3 + v*b**5 - 1/3*b + 2/3*b**4 - 2/3*b**2 = 0.
-1, 0, 1
Let l = 66 + -196/3. Let -1/3 - 4/3*q - 5/3*q**2 - l*q**3 = 0. Calculate q.
-1, -1/2
Let g(f) be the second derivative of -f**4/21 + 2*f**3/21 + 4*f**2/7 + 5*f. Solve g(r) = 0.
-1, 2
Let c(u) = 3*u**3 - 2*u**2 + 5*u + 3. Let m be c(4). Factor r**2 - 6*r**3 + r**2 + 6*r**4 - 185*r**5 + m*r**5.
-2*r**2*(r - 1)**3
Let y = -42 - -46. Let c(w) be the first derivative of 1/20*w**5 - 1/8*w**2 + 1 - 3/16*w**y + 0*w + 1/4*w**3. Factor c(i).
i*(i - 1)**3/4
Let v(t) be the second derivative of -t**5/80 - t**4/12 + t**3/24 + t**2/2 - 8*t. Suppose v(b) = 0. What is b?
-4, -1, 1
Let d(i) be the first derivative of -3*i**4/26 - 4*i**3/39 + i**2/13 - 1. Factor d(y).
-2*y*(y + 1)*(3*y - 1)/13
What is w in 0 - 2/7*w - 2/7*w**3 - 4/7*w**2 = 0?
-1, 0
Let m(w) be the second derivative of -1/66*w**4 - 2*w + 0*w**2 + 0 - 1/11*w**3. Factor m(q).
-2*q*(q + 3)/11
Factor -u**2 + 2*u**2 - 2*u**4 + u**4.
-u**2*(u - 1)*(u + 1)
Let x = 680 + -3398/5. Factor -2/5*b**5 + 0*b - 2/5*b**4 + 0 + x*b**2 + 2/5*b**3.
-2*b**2*(b - 1)*(b + 1)**2/5
Let k(o) = 4*o**2 + 4*o + 10. Let s(v) = -v**2 + v. Let x(f) = -k(f) - 3*s(f). Find t, given that x(t) = 0.
-5, -2
Let h(x) be the third derivative of 2/5*x**7 + 0*x - 3/28*x**8 + 0 - 8/15*x**6 + 0*x**4 + 0*x**3 + 4/15*x**5 + 6*x**2. Solve h(a) = 0.
0, 2/3, 1
Let q(m) = -6*m**3 - 5*m**2 + 9*m - 5. Let f(s) = s**3 + s**2 + 1. Let w(n) = 5*f(n) + q(n). Factor w(r).
-r*(r - 3)*(r + 3)
Let s(q) be the first derivative of q**7/4620 + q**6/396 + 2*q**5/165 + q**4/33 + q**3 - 2. Let k(i) be the third derivative of s(i). Factor k(v).
2*(v + 1)*(v + 2)**2/11
Factor -6*t**2 + 2 + 3 + 3*t - 2.
-3*(t - 1)*(2*t + 1)
Let r(l) be the first derivative of l**5/20 - l**3/12 + 3. Find y such that r(y) = 0.
-1, 0, 1
Let h(l) be the third derivative of -1/720*l**6 - 2*l**2 + 0*l + 0*l**4 + 1/3*l**3 + 1/240*l**5 + 0. Let z(b) be the first derivative of h(b). Factor z(o).
-o*(o - 1)/2
Let y = -50 - -254/5. Suppose 0*c - 21/5*c**4 - y*c**2 + 0 - 49/5*c**5 + 24/5*c**3 = 0. What is c?
-1, 0, 2/7
Let n(b) be the third derivative of 2*b**7/315 - b**5/15 + b**4/9 + 10*b**2. Factor n(l).
4*l*(l - 1)**2*(l + 2)/3
Determine d so that 1/5*d + 1/5*d**2 + 0 = 0.
-1, 0
Let q = 1 + -5. Let a be (-4)/(-3)*(-6)/q. Factor -5*f**a + 7*f**2 - f - 5*f + 4.
2*(f - 2)*(f - 1)
Determine r so that -r - 13*r**3 - 9*r - 2*r**2 - 10*r**4 - 2 - 2*r**5 - 18*r**2 - 7*r**3 = 0.
-1
Let b(w) be the first derivative of -w**5/40 + w**3/4 - 3*w**2/2 + 1. Let y(g) be the second derivative of b(g). Factor y(v).
-3*(v - 1)*(v + 1)/2
Let p(o) be the second derivative of 2*o**6/39 - 23*o**5/130 + 2*o**4/13 + 5*o**3/39 - 4*o**2/13 + 6*o. Find a, given that p(a) = 0.
-1/2, 4/5, 1
Let t**2 + 0 + 1/3*t**3 + 2/3*t = 0. Calculate t.
-2, -1, 0
Let g(l) = 4*l + 3. Let d be g(3). Let h be d/3*1 - 3. Solve 2/3*s + 2*s**h + 0 = 0 for s.
-1/3, 0
Let n(d) be the third derivative of -d**7/420 + d**6/90 + d**5/60 - d**4/6 + d**3/2 - 2*d**2. Let c(t) be the first derivative of n(t). Factor c(q).
-2*(q - 2)*(q - 1)*(q + 1)
Suppose 0 = l - 1, 5*l - 3 + 8 = 5*h. Find d, given that h + d**4 - 2 = 0.
0
Let k(b) be the second derivative of 5*b**7/42 + b**6/3 - b**5/4 - 5*b**4/6 + 10*b. Factor k(d).
5*d**2*(d - 1)*(d + 1)*(d + 2)
Let g(l) be the third derivative of -l**6/12 + 16*l**5/15 - 19*l**4/4 + 6*l**3 - 8*l**2. Find i such that g(i) = 0.
2/5, 3
Let r(c) be the third derivative of -c**5/15 - 2*c**4/3 + 8*c**2 - 2*c. Solve r(z) = 0 for z.
-4, 0
Let h(x) be the third derivative of x**5/60 - x**4/12 + x**3/6 + 12*x**2. Find k such that h(k) = 0.
1
Let z(c) = -3 - c**3 - 3 - 3*c + 3 + 2*c**2. Let i(x) = -x**3 + x**2 - 2*x - 2. Let o(r) = -3*i(r) + 2*z(r). Factor o(w).
w**2*(w + 1)
Let h(a) be the third derivative of 0*a**5 + 1/240*a**6 + 0 + 0*a - 1/420*a**7 - 2*a**2 + 0*a**3 + 0*a**4. Determine g so that h(g) = 0.
0, 1
Suppose -3*l - 4 = -4*l. Let k(n) be the second derivative of n**2 + 0 + 0*n**3 - 1/6*n**l - 3*n. Suppose k(y) = 0. What is y?
-1, 1
Let j(b) = 3*b**2 + 7*b - 4. Let o be j(-3). Suppose -8/3*x + 4*x**o + 2/3 - 8/3*x**3 + 2/3*x**4 = 0. Calculate x.
1
Let k(p) be the second derivative of p**7/420 + p**6/240 - 3*p**2/2 - p. Let s(v) be the first derivative of k(v). Factor s(d).
d**3*(d + 1)/2
Let d(v) be the second derivative of -v**7/42 + 3*v**5/20 - v**4/6 - 6*v. Find w, given that d(w) = 0.
-2, 0, 1
Suppose 0 = i - 113 + 111. Solve -4/5 + 6/5*l**i + 2/5*l = 0.
-1, 2/3
Let v(i) be the third derivative of i**7/11340 - i**6/1620 + i**5/540 - i**4/12 - 3*i**2. Let s(o) be the second derivative of v(o). Factor s(l).
2*(l - 1)**2/9
Let i(d) be the third derivative of d**6/240 + 7*d**5/60 + 49*d**4/48 + 11*d**2. Find f, given that i(f) = 0.
-7, 0
Suppose 4*k + 16 - 52 = 0. Let c = k - -12. Let q(a) = -a**2 - 5*a - 2. Let g(y) = 3*y**2 + 16*y + 6. Let h(o) = c*q(o) + 6*g(o). Factor h(d).
-3*(d + 1)*(d + 2)
Let m(j) be the third derivative of -4*j**6/135 + 28*j**5/135 - 25*j**4/108 + j**3/9 - 7*j**2. Factor m(g).
-2*(g - 3)*(4*g - 1)**2/9
Factor -57*x - 41*x**2 + 33*x - 27*x**2 - 20*x**3.
-4*x*(x + 3)*(5*x + 2)
Let j(s) be the third derivative of -3*s**2 + 1/36*s**4 + 0*s + 1/180*s**6 + 0 + 1/45*s**5 + 0*s**3. Let j(y) = 0. What is y?
-1, 0
Let g(s) = s + 1. Let b be g(1). Suppose -3*o + b*y + 5 = 0, 0*y - 3 = -3*o + 3*y. Factor 4*d**2 - 3*d - 2*d**3 - 2*d + o*d.
-2*d*(d - 1)**2
Factor -10*m**4 - 5*m**5 - 1525*m**2 + 15*m**3 + 1525*m**2.
-5*m**3*(m - 1)*(m + 3)
Let i = -106 + 194. Let y be 16/i + (-4)/22. Factor 1/4*z + 1/4*z**2 + y.
z*(z + 1)/4
Let y(h) be the first derivative of 4 + 35/12*h**3 + h - 3*h**2. Factor y(g).
(5*g - 2)*(7*g - 2)/4
Solve -32*r**3 + 0*r**2 + 28*r**3 - r**4 - 9 + 2*r**2 + 12*r = 0 for r.
-3, 1
Let s = -8584/33 - -3426/11. Factor -64/3*g**2 - 8/3*g - s*g**3 + 0 - 98/3*g**4.
-2*g*(g + 1)*(7*g + 2)**2/3
Factor -16/3*s**3 - 2*s**4 - 14/3*s**2 - 4/3*s + 0.
-2*s*(s + 1)**2*(3*s + 2)/3
Let a(i) be the first derivative of -1 + 0*i + 3/4*i**4 + 2*i**3 - 9/2*i**2. Let a(q) = 0. Calculate q.
-3, 0, 1
Suppose -v + o = v - 4, -o = 0. Let c(p) = -p**3 + 8*p**2 + 10*p - 6. Let g be c(9). Solve 3*j**4 - 4*j**4 + j**g - j**v - 3*j**3 = 0.
-1, 0
Let a = -1/20 - -11/20. Suppose -5*p + 21 = 1. Factor -a*l**5 - 1/2*l + l**3 + 0*l**p + 0 + 0*l**2.
-l*(l - 1)**2*(l + 1)**2/2
Let j(y) be the second derivative of -y**7/8820 - y**6/2520 + y**4/2 - 4*y. Let d(i) be the third derivative of j(i). Factor d(l).
-2*l*(l + 1)/7
Let g = 826 + -826. Determine l so that 0 - 2/3*l + g*l**2 + 2/3*l**3 = 0.
-1, 0, 1
Let r(w) be the third derivative of -w**8/2352 + w**7/735 - w**5/210 + w**4/168 - 14*w**2. Factor r(m).
-m*(m - 1)**3*(m + 1)/7
Let j be 1/(-35) + (-39)/(-91). Factor -18/5*n**3 + 0 + 12/5*n**2 - j*n.
-2*n*(3*n - 1)**2/5
Let c(z) be the first derivative of -z**6/2160 - z**5/720 - 2*z**3/3 + 1. Let y(b) be the third derivative of c(b). Factor y(u).
-u*(u + 1)/6
Let w(h) = -h**4 + 5*h**3 + 4*h**2 + 4*h + 4. Let d(g) = g**3 + g**2 + g + 1. Let f = 1 + -2. Let c(o) = f*w(o) + 4*d(o). Factor c(s).
s**3*(s - 1)
Determine f, given that 0 + 2/9*f**3 + 4/3*f**5 + 0*f - 10/9*f**4 + 0*f**2 = 0.
0, 1/3, 1/2
Suppose 0*u - 3 = -u. Suppose -u*o = 2*o - 15. Factor 2/3*b**o - 2/3*b + 2/3*b**2 + 0 - 2/3*b**4.
-2*b*(b - 1)**2*(b + 1)/3
Let w(k) be the first derivative of k**5 + 25*k**4/4 + 15*k**3 + 35*k**2/2 + 10*k + 6. Factor w(y).
5*(y + 1)**3*(y + 2)
Let u = -68 + 70. Let s(g) be the first derivative of 2/9*g**3 + 1/12*g**4 + 0*g + 2 + 0*g**u. Factor s(c).
c**2*(c + 2)/3
Let y(m) be the second derivative of -4*m**6/3 - 3*m**5 + 115*m**4/24 + 25*m**3/4 + 5*m**2/2 - 2*m + 2. Let y(w) = 0. What is w?
-2, -1/4, 1
Suppose -3*r + 2*f + 15 = 0, -4*r + 2*f + 13 = -3*f. Factor 2 + 4*q + 10*q**2 + 3*q**3 - 12*q - r*q**3 + 0.
-2*(q - 1)**2*(2*q - 1)
Let z(v) = 2*v. Let k be z(0). Factor k*y**4 + 1/2*y**5 - y**3 + 0*y**2 + 1/2*y + 0.
y*(y - 1)**2*(y + 1)**2/2
Let s(o) be the second derivative of -o**4/96 + o**3/12 + 5*o**2/16 + 20*o. Factor s(y).
-(y - 5)*(y + 1)/8
Let v(t) be the first derivative of t**4/36 + t**3/9 + t**2/6 + 3*t - 3. Let z(p) be the first derivative of v(p). Factor z(r).
(r + 1)**2/3
Let m(j) be the third derivative of 2*j**7/315 -