**3/39 - 24*q. Factor d(x).
-2*x*(x + 8)/13
Factor 0*t + 0 - 1/4*t**4 + t**3 - 3/4*t**2.
-t**2*(t - 3)*(t - 1)/4
Let c(i) be the third derivative of -i**6/60 + i**5/10 - i**4/4 + i**3/3 + 11*i**2. Determine r so that c(r) = 0.
1
Let h(s) = 4*s**3 - 2*s**2 - 6*s. Let k(y) = 7*y**3 - 5*y**2 - 12*y. Let d(c) = 10*h(c) - 6*k(c). Suppose d(g) = 0. What is g?
-1, 0, 6
Let m(h) be the first derivative of 2*h**3/3 - 2*h**2 - 2*h - 2. Let s(k) be the first derivative of m(k). Let n(r) = r**2. Let c(f) = n(f) - s(f). Factor c(b).
(b - 2)**2
Let g(h) be the third derivative of 0 - 9/100*h**5 + 3*h**2 + 1/5*h**3 + 0*h - 7/40*h**4. Factor g(p).
-3*(p + 1)*(9*p - 2)/5
Let w(d) be the first derivative of d**3 + 9*d**2/2 + 6*d - 2. Solve w(j) = 0 for j.
-2, -1
Suppose 2*s - 2*x + 10 = 2*x, 3*s - 17 = -2*x. Suppose 0*r + s = r. Let -8/3*g**2 - 4/3*g + 4/3*g**r + 2/3 + 2*g**4 = 0. Calculate g.
-1, 1/3, 1
Let c(t) be the third derivative of -t**7/105 - t**6/12 - 3*t**5/10 - 7*t**4/12 - 2*t**3/3 + 4*t**2. Factor c(x).
-2*(x + 1)**3*(x + 2)
Factor 12*w**3 + 36*w**2 + 3*w**4 - 3*w**3 - 30*w**2.
3*w**2*(w + 1)*(w + 2)
Suppose s - 6*s = -l + 4, -8 = -2*l - 5*s. Suppose 0 = t + t + l, 5*a - 3*t - 21 = 0. Factor 7*f + 1 + f - 6*f**2 - a.
-2*(f - 1)*(3*f - 1)
Let q be ((-4 + 2)/8)/(-1 + 0). Factor -q*r**3 + 1/4*r + 0*r**2 + 0.
-r*(r - 1)*(r + 1)/4
Let g = 35 - 30. Let u(s) be the second derivative of 0 - 5/6*s**4 + s - 2/5*s**g + 0*s**2 - 1/3*s**3. Solve u(o) = 0.
-1, -1/4, 0
Let t = 328/3 + -109. Let t*l**4 - l + l**3 - 2/3 + 1/3*l**2 = 0. Calculate l.
-2, -1, 1
Factor o**3 + o - 2*o**2 - 2*o + 2*o + 0*o**3.
o*(o - 1)**2
Suppose 0 = 4*n - 20 - 0. Factor 2*t + 4*t**5 - 3*t**3 - t**2 - 4*t**n + t**5 + t**4.
t*(t - 1)**2*(t + 1)*(t + 2)
Let u = -952/5 - -191. Factor -3/5*r**3 + 0 + 0*r + u*r**2.
-3*r**2*(r - 1)/5
Let w(f) be the second derivative of -3/20*f**5 + 0*f**2 + f + 0*f**3 + 1/12*f**4 + 0 - 1/42*f**7 + 1/10*f**6. Factor w(q).
-q**2*(q - 1)**3
Let l(i) be the second derivative of -i**6/20 + i**5/20 + i**4/8 + 5*i**2/2 + i. Let b(h) be the first derivative of l(h). Suppose b(g) = 0. Calculate g.
-1/2, 0, 1
Factor -1/5*y**2 - 121/5 - 22/5*y.
-(y + 11)**2/5
Let m(f) = 16*f + 20. Let v(w) = w**2 + 1. Let j(i) = m(i) - 2*v(i). Suppose j(p) = 0. Calculate p.
-1, 9
Let q(a) = -a**3 - 5*a**2 - 3*a - 6. Let r be q(-5). Let y = 9 - r. Factor y + 1/3*u**2 - 1/3*u**4 + 1/3*u**3 - 1/3*u.
-u*(u - 1)**2*(u + 1)/3
Let h(s) = -s**2 + 2*s + 3. Let v(y) = y**2 - 2*y - 2. Let k be ((-1)/2)/(2/(-8)). Let a(o) = k*h(o) + 3*v(o). Determine z so that a(z) = 0.
0, 2
Let t(v) be the second derivative of -3*v**5/20 - 3*v**4/4 - v**3 + 42*v. Find k, given that t(k) = 0.
-2, -1, 0
Let d(r) be the first derivative of 0*r + 6 - 5/8*r**6 - 3/16*r**4 + 0*r**2 + 6/5*r**5 - 1/2*r**3. Factor d(i).
-3*i**2*(i - 1)**2*(5*i + 2)/4
Let k be -4 + -2 + 4 + (-21)/(-9). Factor 2/3*w**4 + 0*w**2 + k*w**5 + 0*w + 1/3*w**3 + 0.
w**3*(w + 1)**2/3
Let v(g) = 2*g**4 + 29*g**3 + 54*g**2 + 43*g + 16. Let w(j) = j**4 + 10*j**3 + 18*j**2 + 14*j + 5. Let s(u) = -2*v(u) + 7*w(u). Factor s(d).
3*(d + 1)**4
Let i(g) be the first derivative of g**4/4 - g**3/2 - 2*g**2 - 3*g/2 - 20. What is d in i(d) = 0?
-1, -1/2, 3
Find u, given that 521*u + 9 - 253*u - 256*u + 3*u**2 + 0*u**2 = 0.
-3, -1
Suppose -k + 36 = 5*k. Suppose -k*t = -t. Factor t + 0*z - 2/5*z**2 - 2/5*z**3.
-2*z**2*(z + 1)/5
Let o be (-3 - (2 + -3))*2. Let h be -1 - o - (1 - 0). Factor -u - 1/4*u**h - 1.
-(u + 2)**2/4
Let a(o) = 4*o**4 - 6*o**3 + o**2 + 1. Let d(n) = 7*n**4 - 11*n**3 + 2*n**2 + n + 1. Let g(z) = 5*a(z) - 3*d(z). Factor g(f).
-(f - 2)*(f - 1)**2*(f + 1)
Let s(t) be the third derivative of t**8/1344 + t**7/168 + t**6/48 + t**5/24 + 5*t**4/96 + t**3/24 + 7*t**2. Factor s(l).
(l + 1)**5/4
Find z, given that 664*z + z**2 - 667*z + 0 - 4 = 0.
-1, 4
Suppose 4*h + 6 + 34 = 0. Let r = -29/3 - h. Factor 2/3*i + 0*i**2 - r*i**4 + 1/3 - 2/3*i**3.
-(i - 1)*(i + 1)**3/3
Let l(u) = -u**3 - 5*u**2 + u + 4. Let w be l(-5). Let c be (2 - 0) + 2 + w. Factor -2*s**c + 0*s**4 + 40*s**4 - 42*s**5 - 6*s**3.
-2*s**3*(3*s - 2)*(7*s - 2)
Let s be (3/2)/((-7)/((-28)/12)). Solve 7/4*x**2 + 1/4*x**5 + 5/4*x**4 + 0 + s*x + 9/4*x**3 = 0 for x.
-2, -1, 0
Factor 165*q**2 - 166*q**2 + 11*q + 4 - 14.
-(q - 10)*(q - 1)
Let b = 787 + -8651/11. Suppose -4/11*t**2 + 0 + 0*t - b*t**3 = 0. Calculate t.
-2/3, 0
Find d such that -1/3*d**4 + 2*d**3 + 8/3*d - 4*d**2 + 0 = 0.
0, 2
Let h(d) = -6*d**4 + 15*d**3 - 21*d**2 + 15*d. Let r(l) = 5*l**4 - 15*l**3 + 22*l**2 - 14*l. Let j(p) = -2*h(p) - 3*r(p). Factor j(c).
-3*c*(c - 2)**2*(c - 1)
Let p = 4 + -2. Suppose d - 4*r = -r - 3, -2*d - p = -4*r. Factor 1/2*a - 1/2*a**d + 1/2 - 1/2*a**2.
-(a - 1)*(a + 1)**2/2
Let s(a) be the second derivative of 19*a**4/42 + 2*a**3/21 + 47*a. Suppose s(h) = 0. Calculate h.
-2/19, 0
Let w = -2 + 3. Suppose 3*d = 0, w + 1 = x + 5*d. Factor -4*f**3 + f**x + 3*f**3 - f**4 - f**5 + 2*f**5.
f**2*(f - 1)**2*(f + 1)
Let f be (-8 - -9)/(2/10). Factor -f*g**2 - 3*g**2 + 3*g**3 + 5*g**2.
3*g**2*(g - 1)
Let u(r) be the first derivative of r**4/28 + 2*r**3/21 - r**2/14 - 2*r/7 + 9. Factor u(s).
(s - 1)*(s + 1)*(s + 2)/7
Let -16/15*h + 32/15 + 2/15*h**2 = 0. What is h?
4
Let j be (-1 - -4) + (84/(-20) - -2). Factor 0 + j*n**2 - 2*n**5 + 0*n - 18/5*n**3 + 24/5*n**4.
-2*n**2*(n - 1)**2*(5*n - 2)/5
Suppose -4*g = u + 4*u + 7, -g - 13 = 5*u. Factor -2/3*x**5 + 0 + 0*x**4 + 0*x**g + 4/3*x**3 - 2/3*x.
-2*x*(x - 1)**2*(x + 1)**2/3
Let q(n) = n**2. Let u(f) = 8*f**2 - 16. Let t(m) = 4*q(m) - u(m). Let t(k) = 0. What is k?
-2, 2
Let v = -104855/136 + 771. Let j = 275/408 - v. Factor 4/3*y**2 - 2/3 + 0*y**3 - j*y**4 + 0*y.
-2*(y - 1)**2*(y + 1)**2/3
Let f = -4 + 8. Factor -w**2 - 6 - w + 5*w + f*w**2 - w.
3*(w - 1)*(w + 2)
Let a(i) be the first derivative of -i**5/15 + 5*i**4/12 + i**3 + 2*i**2 + 5. Let g(p) be the second derivative of a(p). Find y such that g(y) = 0.
-1/2, 3
Suppose -2*o + a = -8 - 1, 3*o - 3*a = 15. Let r be 2 + -2 - (0 - 2). Factor -4*n**r + 0*n + o*n + 6*n**2.
2*n*(n + 2)
Let r(o) = 294*o**5 + 322*o**4 - 60*o**3 - 72*o**2 + 21*o + 5. Let y(q) = q + 1. Let k(i) = r(i) - 5*y(i). Find l such that k(l) = 0.
-1, -2/3, 0, 2/7
Let q(j) be the third derivative of -5*j**8/336 - 13*j**7/42 - 23*j**6/12 + 5*j**5/6 + 875*j**4/24 - 625*j**3/6 + 33*j**2. Suppose q(p) = 0. What is p?
-5, 1
Let l(k) be the third derivative of k**7/168 + k**6/80 - k**5/20 + 5*k**4/24 - k**2. Let n(s) be the second derivative of l(s). Factor n(z).
3*(z + 1)*(5*z - 2)
Let t(u) = -u**4 - 2*u**3 - 4*u**2 - 2*u - 3. Let f(q) = -4*q**4 - 7*q**3 - 15*q**2 - 7*q - 13. Let l(o) = -2*f(o) + 9*t(o). Factor l(z).
-(z + 1)**4
Let s(k) be the first derivative of k**6/180 - k**5/120 - k**4/72 + k**3/36 + k + 3. Let y(z) be the first derivative of s(z). Suppose y(a) = 0. What is a?
-1, 0, 1
Suppose 3 = 5*d - 7. Factor -4*v - d*v**2 + v - 3*v + 4*v.
-2*v*(v + 1)
Let r be (28/(-40) - -3) + 4/20. Factor 25/2*f**3 - 8*f + 2 + r*f**2.
(f + 1)*(5*f - 2)**2/2
Let m(i) be the third derivative of i**7/945 - i**6/540 - i**5/270 + i**4/108 - 3*i**2. Factor m(p).
2*p*(p - 1)**2*(p + 1)/9
Suppose -4*d = 3*f - 29, -2*d + 11 = -3*f - 8. Let -54*q**3 - 2 - d*q**5 + 22*q**3 - 26*q**2 - 6 + 40*q + 34*q**4 = 0. Calculate q.
-1, 1/4, 1, 2
Let j(g) = 8*g**2 + 3*g + 1. Let y(t) = 5*t + 1 + 2*t - 4*t + 7*t**2. Let n(a) = -5*j(a) + 6*y(a). Factor n(o).
(o + 1)*(2*o + 1)
Let m be ((-3)/12)/(6/(-24)). Let f(i) be the first derivative of -1/3*i**4 - 8/3*i + 4/3*i**2 + m - 2/15*i**5 + 2/3*i**3. Factor f(w).
-2*(w - 1)**2*(w + 2)**2/3
Let -1/2*d**2 - 81/8*d**4 + 0*d + 0 - 9/2*d**3 = 0. What is d?
-2/9, 0
Suppose -2*o - 2*o + 12 = 0. Let m(u) be the first derivative of -13/16*u**4 - 1/4*u**2 - 1/5*u**5 + 0*u - 2 - 11/12*u**o. Let m(q) = 0. Calculate q.
-2, -1, -1/4, 0
Let p = -2/225 - -152/225. Let m be (-159)/(-53) - 14/6. Solve 2/3*x**3 - 2/3*x - m*x**4 + 0 + p*x**2 = 0.
-1, 0, 1
Factor 0 + 2/3*q**2 + 0*q - 8/3*q**3.
-2*q**2*(4*q - 1)/3
Let k = -196 + 198. Let 8/5*f**2 - k*f + 2/5 = 0. What is f?
1/4, 1
Factor -8*o**2 + 4*o + 129*o**3 - 133*o**3 + 8 + 0*o**2.
-4*(o - 1)*(o + 1)*(o + 2)
Let n(b) be the second derivative of b**6/60 - b**5/6 + 2*b**4/3 - 4*b**3/3 + b**2/2 - b. Let h(g)