Let b(a) = a. Let k(z) = 2*z**2. Suppose 0 = -4*r - 7 + 3. Let s be (-21)/3 - -12 - 7. Let h(i) = r*k(i) + s*b(i). Factor h(m).
-2*m*(m + 1)
Let w(n) be the first derivative of 4*n**3/9 + 110*n**2/3 - 126. Factor w(r).
4*r*(r + 55)/3
Let c = -1199/5 - -241. Let r be 12/15*((-4)/66 - (-851)/1518). Factor r - 2*a**2 - c*a**3 - 2/5*a.
-2*(a + 1)**2*(3*a - 1)/5
Let a = -10453/20 - -523. Let z(t) be the second derivative of 0*t**2 - t + 4/15*t**6 + 1/12*t**4 + a*t**5 + 0 + 0*t**3 - 8/21*t**7. Solve z(c) = 0 for c.
-1/4, 0, 1
Let j = 92 + -88. Let q(d) be the second derivative of -4/7*d**2 + 3*d + 0 - 1/42*d**j - 4/21*d**3. Factor q(n).
-2*(n + 2)**2/7
Let f(y) be the second derivative of y**4/30 + y**3/5 + 2*y**2/5 + 56*y + 1. Solve f(l) = 0 for l.
-2, -1
Suppose 0 = -4*u - 26 + 14 + 20. Let -10/9*x**3 + 2/3*x - 8/9 + 4/3*x**u = 0. What is x?
-4/5, 1
Let t(a) = a**3 + 4*a**2 + a + 6. Let h be t(-4). Factor -g**3 + 149*g**2 - 8 - 140*g**h - 24*g + 24.
-(g - 4)**2*(g - 1)
Let n be ((-442)/1105)/(4/(-30)). Factor 7/4*m**2 - 15/4*m + 9/4 - 1/4*m**n.
-(m - 3)**2*(m - 1)/4
Suppose -4*g = 20, -3*r - 3*g + 30 = 2*r. Suppose -15*q = -r*q - 3*q. Factor 0 + q*n - 2/7*n**3 + 0*n**2 - 10/7*n**5 + 12/7*n**4.
-2*n**3*(n - 1)*(5*n - 1)/7
Let n be (-1)/6 + (-393)/18*1. Let j = 22 + n. Determine s, given that j - 2*s**5 + 5/2*s**4 + 3/2*s**3 + 1/2*s - 5/2*s**2 = 0.
-1, 0, 1/4, 1
Let a(q) be the first derivative of -q**3/18 - 7*q**2/12 + 4*q/3 + 139. Determine n, given that a(n) = 0.
-8, 1
Let b(g) be the second derivative of g**6/40 - 3*g**5/20 - 3*g**4/16 + 9*g**3/4 - g + 198. Factor b(j).
3*j*(j - 3)**2*(j + 2)/4
Let i = -12 - -15. Suppose -12 + 0 = -i*w. Determine x so that x**2 + 18*x**3 + 7*x**w + 2*x**2 - 2*x - 6*x**3 = 0.
-1, 0, 2/7
Let -2*u**5 + 0 + 3/2*u**4 + 0*u**2 + 1/2*u**3 + 0*u = 0. What is u?
-1/4, 0, 1
Let h(p) be the second derivative of -1/10*p**5 - 26*p + 4/3*p**4 + 0*p**3 + 0 + 0*p**2. Suppose h(v) = 0. Calculate v.
0, 8
Let l(n) = n**3 + 5*n**2 + 5*n - 6. Let x(c) = c**3 + 5*c**2 + 5*c - 7. Let i(w) = -3*l(w) + 2*x(w). Let a be i(-3). Solve 1/2*r - a + 1/2*r**2 = 0.
-2, 1
Factor -3/5*j + 0 + 9/5*j**2 - 9/5*j**3 + 3/5*j**4.
3*j*(j - 1)**3/5
Let j = 1207/92 + -53/4. Let m = j + 32/69. Factor 0 - m*u**4 + 1/3*u**2 + 0*u - 1/3*u**3 + 1/3*u**5.
u**2*(u - 1)**2*(u + 1)/3
Suppose -11*w + 26 = 2*w. What is q in 8/13*q**w - 10/13*q + 4/13 - 2/13*q**3 = 0?
1, 2
Let g be (-5 - 483/(-60)) + -2 + (-4)/16. Factor 4/5*n**2 + g*n - 24/5.
4*(n - 2)*(n + 3)/5
Let g(q) = q**2 + q + 1. Let b(n) = 3*n**2 - 2*n - 201 + 41*n - 15*n**2 + 0. Let r(v) = -b(v) - 9*g(v). Suppose r(p) = 0. Calculate p.
8
Suppose 2*t + 4 = 4*x, 19*t - 16*t + 6 = -x. Let x*c + 0 - 2/7*c**2 = 0. Calculate c.
0
Let y(a) be the third derivative of 1/8*a**4 - 1/70*a**7 + 1/20*a**5 + 0*a**3 - 1/40*a**6 + 0*a + 10*a**2 + 0. Suppose y(h) = 0. What is h?
-1, 0, 1
Let v(q) be the second derivative of -q**7/63 + 2*q**6/45 + q**5/6 - 5*q**4/9 - 4*q**3/9 + 8*q**2/3 + 22*q + 2. What is l in v(l) = 0?
-2, -1, 1, 2
Let x(w) be the third derivative of -1/70*w**7 + 0*w**5 + 0 + 0*w**3 + 23*w**2 + 0*w**6 + 0*w**4 + 0*w. Factor x(t).
-3*t**4
Let i(m) = m**3 - 5*m**2 + 3*m + 7. Let t be i(4). Suppose o + 0*o - t = 0. Determine v, given that 2/7*v**o + 0 - 2/7*v + 0*v**2 = 0.
-1, 0, 1
Let j = 551 - 1649/3. Factor -j*p**4 + 8/3*p**3 + 2/9*p**5 + 0 - 16/9*p**2 + 0*p.
2*p**2*(p - 2)**3/9
Let a be (1 + 1)/(2/4). Suppose a*z = 11 + 1. What is w in 4 - 1 + 0 + 4*w**z - 3*w**2 - 3*w - w**3 = 0?
-1, 1
Factor 1/3*f**2 - 34/3*f + 289/3.
(f - 17)**2/3
Let u(z) be the second derivative of 7*z**4/3 - 50*z**3 - 44*z**2 + 23*z. Factor u(k).
4*(k - 11)*(7*k + 2)
Let k(a) be the second derivative of -a**6/150 + 9*a**5/50 + 107*a**4/60 + 6*a**3 + 46*a**2/5 + 125*a. Factor k(r).
-(r - 23)*(r + 1)*(r + 2)**2/5
Let k(o) = o**4 + o**2 - o. Let w(t) = -t**5 + 10*t**4 - 13*t**3 + 16*t**2 - 8*t. Let i(l) = -4*k(l) + w(l). Let i(f) = 0. What is f?
0, 1, 2
Suppose 0 = 5*u - u + 2*x - 4, -x = 4*u - 8. Let v(o) be the second derivative of 2*o + 0 - 1/20*o**4 - 27/10*o**2 + 3/5*o**u. Factor v(m).
-3*(m - 3)**2/5
Let p(l) = 4*l**3 - 107*l**2 - 230*l + 5. Let a(z) = -z**2 - 2*z - 1. Let g(f) = 5*a(f) + p(f). What is h in g(h) = 0?
-2, 0, 30
Suppose 5*q - i - 142 = 0, 4*i - 27 = -q + 14. Determine n, given that -5 + q - 51 + 14*n**2 - 78*n - 5*n**2 = 0.
-1/3, 9
Let g = 71 - 39. Suppose 5*z + g - 32 = 0. Factor -2/5*m + 4/5*m**2 + z - 2/5*m**3.
-2*m*(m - 1)**2/5
Let m(l) be the second derivative of -l**8/4200 + l**6/300 - l**5/150 - l**3 - 19*l. Let p(y) be the second derivative of m(y). Factor p(k).
-2*k*(k - 1)**2*(k + 2)/5
Let x = 547/6 + -91. Let o(k) be the first derivative of -4/3*k**3 + 1 + 1/2*k**2 - 4/5*k**5 + 0*k + 3/2*k**4 + x*k**6. Solve o(s) = 0 for s.
0, 1
Suppose 3*w = -2*s + 13 - 11, 0 = 3*s - 3. Factor 3/8*t**4 + 1/8*t**2 + w*t + 0 - 3/8*t**3 - 1/8*t**5.
-t**2*(t - 1)**3/8
Let i(u) = -2*u - 2. Let z be i(1). Let k(n) = -n**2. Let m(y) = 4 + 5*y**2 + 3*y - 5*y + y - 3*y. Let q(f) = z*k(f) - m(f). Let q(t) = 0. What is t?
2
Let 3/4*v**3 - 7/4*v - 3/4 + 7/4*v**2 = 0. What is v?
-3, -1/3, 1
Let m(h) be the second derivative of -h**9/9072 + h**7/420 - h**6/135 + h**5/120 - 22*h**3/3 - 20*h. Let r(t) be the second derivative of m(t). Factor r(p).
-p*(p - 1)**3*(p + 3)/3
Let p(w) be the third derivative of -w**8/672 + w**7/140 - w**6/80 + w**5/120 - 6*w**2 + 2. Suppose p(h) = 0. Calculate h.
0, 1
Let k be (-8)/32 + 182/(-8). Let x(g) = -g**2 - 21*g + 50. Let i be x(k). Find d such that 3/2*d**i + 0*d**3 + 0*d**2 + 0*d + 0 = 0.
0
Let f(a) be the second derivative of a**7/126 + a**6/180 - 11*a**5/120 + 11*a**4/72 - a**3/12 + 15*a + 4. Determine d, given that f(d) = 0.
-3, 0, 1/2, 1
Solve 1/3 - 1/6*b**3 + 0*b**2 + 1/2*b = 0.
-1, 2
Suppose q - 6 = -2*q. Suppose 0 = j + g - 5, -2*j + g = j + 1. Factor f**3 + f**q + f - 2*f + 0*f - j.
(f - 1)*(f + 1)**2
Suppose -8*u = -6*u + 2*h, -2*h = 5*u. Factor u*x + 6/7*x**3 - 2/7*x**2 + 2/7*x**5 + 0 - 6/7*x**4.
2*x**2*(x - 1)**3/7
Let t(p) = 4*p + 11 - 3*p + 2*p + 5*p. Let j be t(10). Factor -j - 4*k**2 + 4*k**3 + 91.
4*k**2*(k - 1)
Factor -2/7*a**4 - 20/7*a**3 + 0*a + 0 + 22/7*a**2.
-2*a**2*(a - 1)*(a + 11)/7
Solve -6*m**2 - 176*m + 49 + 11 - 6*m**2 + 0*m**2 = 0 for m.
-15, 1/3
Let m(r) be the second derivative of -r**5/4 + 10*r**4 - 120*r**3 - 490*r + 1. Factor m(n).
-5*n*(n - 12)**2
Let x be 10/4 - 4/8. Let s = -8 - -12. Suppose -u**4 + 0*u**2 - 6*u**3 + x*u**s + 9*u**2 = 0. Calculate u.
0, 3
Factor 67 - 21 + 7*b - 26 + 61*b + 5*b**2 - 55 - 2*b**3.
-(b - 7)*(b + 5)*(2*b - 1)
Let l(m) = -5*m**5 - 8*m**4 - m**3 + 2*m. Let g(r) = -6*r**5 - 9*r**4 + 3*r. Let i(z) = -z**2 - 2*z + 1. Let h be i(1). Let c(d) = h*g(d) + 3*l(d). Factor c(o).
-3*o**3*(o + 1)**2
Factor -344*y + 2084 + 244*y**2 + 10*y**3 + 26*y**3 - 2020.
4*(y - 1)*(y + 8)*(9*y - 2)
Let n = 31/770 + 2/385. Let m(g) be the second derivative of 1/110*g**5 + 0 - n*g**4 - 1/33*g**3 + 1/165*g**6 + 2/11*g**2 - g. What is r in m(r) = 0?
-2, -1, 1
Let p(n) be the second derivative of n**5/60 - 5*n**4/18 + n**3/2 + 67*n. Factor p(g).
g*(g - 9)*(g - 1)/3
Let a(p) be the second derivative of 7*p**4/8 + 5*p**3/2 + 9*p**2/4 + 42*p - 2. Determine x so that a(x) = 0.
-1, -3/7
Let z = -1/250 + -3647/750. Let a = z + 31/5. Factor 2/3*r**4 - 2*r**2 + 0*r**3 + 0 + a*r.
2*r*(r - 1)**2*(r + 2)/3
Let c(s) be the third derivative of -s**7/504 + s**6/48 + s**5/6 - 7*s**4/12 + 16*s**2. Let r(g) be the second derivative of c(g). Let r(f) = 0. What is f?
-1, 4
Let j(g) be the first derivative of g**8/3360 - g**7/1680 - g**6/720 + g**5/240 - 13*g**3/3 + 11. Let q(h) be the third derivative of j(h). Solve q(t) = 0.
-1, 0, 1
Let r be 228/24*1/((-1)/(-2)). Determine k so that -37*k + 16 + 4*k**2 + 72*k - r*k = 0.
-2
Let v(b) = b**2 + b + 1. Let n(u) = -6*u**2 - 11*u - 1. Let j(i) = n(i) + v(i). Factor j(c).
-5*c*(c + 2)
Let t = 29/15 + -523/30. Let f = 17 + t. Factor f*v**4 + 3/2*v**3 + 0 + 1/2*v**2 + 1/2*v**5 + 0*v.
v**2*(v + 1)**3/2
Suppose -92*r**2 - 1 + 6*r - 2 + 89*r**2 = 0. What is r?
1
Let n(r) = -r**3 - 6*r**2 - 4. Let u be n(-6). Let c(v) = -6*v**2 - 189*v - 1359. Let x(m) = -3*m**2 - 94*m - 679. Let f(t) = u*c(t) + 9*x(t). Factor f(q).
-3*(q + 15)**2
Let q(i) b