= -23 - 1. Factor 3/5*t**2 - 3/5*t**3 + 0*t - 3/5*t**r + 0 + 3/5*t**5.
3*t**2*(t - 1)**2*(t + 1)/5
Factor -107*s + 3 + 107*s - 3*s**2.
-3*(s - 1)*(s + 1)
Let r(j) be the third derivative of 0*j**5 + 0*j + 0*j**3 + 1/210*j**7 + 1/60*j**6 + 0*j**4 + 0 - j**2. Factor r(l).
l**3*(l + 2)
Factor -6/5*t**2 + 0*t + 0 + 3/5*t**3.
3*t**2*(t - 2)/5
Factor 0 + 8/5*j**4 + 0*j + 0*j**2 - 8/5*j**3 - 2/5*j**5.
-2*j**3*(j - 2)**2/5
Let b(n) be the first derivative of -175*n**6/6 + 74*n**5 - 195*n**4/4 - 20*n**3/3 + 10*n**2 - 35. Suppose b(r) = 0. Calculate r.
-2/7, 0, 2/5, 1
Let x(k) = -20*k**2 + 72*k - 432. Let h(b) = -7*b**2 + 24*b - 144. Let d(w) = -17*h(w) + 6*x(w). Let d(z) = 0. What is z?
12
Let x = 13/14 - -23/126. Suppose 8/9 - 32/9*d + 34/9*d**2 - x*d**3 = 0. Calculate d.
2/5, 1, 2
Let f(r) = -17*r**5 - 23*r**4 - 37*r**3 - 3*r**2. Let l(k) = -8*k**5 - 12*k**4 - 18*k**3 - 2*k**2. Let u(c) = -3*f(c) + 7*l(c). Factor u(j).
-5*j**2*(j + 1)**3
Let u(m) be the first derivative of -2*m**6/33 + 2*m**5/11 - 3*m**4/22 - 2*m**3/33 + m**2/11 - 9. Determine f, given that u(f) = 0.
-1/2, 0, 1
Let j(v) = -4*v**3 - 4*v**2 - 4*v - 2. Let f(n) = 21*n**3 + 19*n**2 + 19*n + 10. Let w(r) = -4*f(r) - 22*j(r). Factor w(a).
4*(a + 1)**3
Let k be 11/275*10/8. Let d(a) be the second derivative of k*a**5 + a + 0*a**2 + 0*a**3 - 1/12*a**4 + 0. Factor d(y).
y**2*(y - 1)
Factor 4/7*c**2 + 10/7*c**3 + 2/7*c**5 + 0 + 8/7*c**4 + 0*c.
2*c**2*(c + 1)**2*(c + 2)/7
Let x(h) = -3*h**2 - 6*h + 9. Let w = 1 + 0. Let p(n) = -n + 1. Let o(q) = w*x(q) - 3*p(q). Factor o(c).
-3*(c - 1)*(c + 2)
Let r = 89/33 - 15/11. Determine w so that 1/3*w**2 + r + 4/3*w = 0.
-2
Factor -7/3*t**2 + 2/3*t + 8/3*t**3 + 0 - t**4.
-t*(t - 1)**2*(3*t - 2)/3
Suppose m + 22 - 73 = 0. Let k be (-4)/9 + 34/m. Let k*w - 2/9*w**3 + 2/9*w**4 - 2/9*w**2 + 0 = 0. Calculate w.
-1, 0, 1
Let y(l) be the second derivative of l**6/105 - 11*l**5/70 + 6*l**4/7 - 16*l**3/21 - 64*l**2/7 - 12*l. Find a such that y(a) = 0.
-1, 4
Suppose 3/5*r**3 + 1/5*r**5 - 1/5*r**2 + 0*r + 0 - 3/5*r**4 = 0. What is r?
0, 1
Suppose 3*k = 4*k - 3*h + 10, 4*h = 5*k + 6. Factor -2*w**3 + 4*w**3 + 4*w**3 - 2*w**3 + 1 + 9*w**k + 6*w.
(w + 1)**2*(4*w + 1)
Let k(o) be the third derivative of -o**8/560 + o**7/140 - o**6/120 + 2*o**3/3 - o**2. Let d(a) be the first derivative of k(a). Solve d(j) = 0 for j.
0, 1
Let j(o) be the second derivative of -3*o - 1/3*o**3 + 4/105*o**6 + 0 + 1/10*o**5 + 2/7*o**2 - 1/7*o**4. Find t such that j(t) = 0.
-2, -1, 1/4, 1
Let d(s) = 8 + 4*s + 7*s - 1 - 5*s**2. Let o(w) = -3*w**2 + 6*w + 4. Let v(c) = 4*d(c) - 7*o(c). Factor v(j).
j*(j + 2)
Let c(p) be the second derivative of 5*p + 3/4*p**4 + 0*p**2 + 1/10*p**6 - 1/2*p**3 + 0 - 9/20*p**5. Factor c(a).
3*a*(a - 1)**3
Let r(q) be the third derivative of q**6/120 + q**5/60 - q**4/6 - 2*q**3/3 + 45*q**2. Find g, given that r(g) = 0.
-2, -1, 2
Let j(o) be the first derivative of o**4/18 + 10*o**3/27 + 8*o**2/9 + 8*o/9 - 2. Factor j(h).
2*(h + 1)*(h + 2)**2/9
Suppose 6 = 3*t, -2*l + t = 2*t - 20. Suppose -l*q = -10*q + 3. Factor -6/5*c**2 - 1/5 - 4/5*c - 4/5*c**q - 1/5*c**4.
-(c + 1)**4/5
Factor -4/3*z**2 + 8/3 - 4/3*z.
-4*(z - 1)*(z + 2)/3
Let d = -9/4 + 11/4. Determine g, given that 0 + d*g**2 - 1/2*g = 0.
0, 1
Let c(p) be the second derivative of p**6/10 - 3*p**5/10 + p**4/4 + 14*p. Suppose c(s) = 0. What is s?
0, 1
Suppose 5*l = 4*n - 54, n - 4*l - 6 = 2. What is t in 5*t + 5*t - 14*t - 28*t**2 - n*t**5 - 52*t**4 - 60*t**3 = 0?
-1, -1/4, 0
Find o such that -1 + 1 - 4*o**5 + 4*o**4 - 12*o**3 - 20*o**4 = 0.
-3, -1, 0
Factor k**2 - 3*k**2 - k**2 + 6*k.
-3*k*(k - 2)
Find a such that -4/5*a**2 + 0 + 1/5*a = 0.
0, 1/4
Let c(m) = -11*m**4 + m**3 - 10*m**2 - 13*m - 9. Let l(i) = 5*i**4 + 5*i**2 + 6*i + 4. Let g(x) = -4*c(x) - 9*l(x). Let g(f) = 0. Calculate f.
-2, -1, 0
Suppose -3*i - 1 = 8. Let u(w) = -5*w**4 - w**3 + 8*w**2 - 5*w - 3. Let h(q) = 10*q**4 + 3*q**3 - 17*q**2 + 11*q + 7. Let l(o) = i*h(o) - 7*u(o). Factor l(x).
x*(x - 1)*(x + 1)*(5*x - 2)
Factor -3*a**2 - 4*a**2 + 4*a**2 + 6 - a - 2*a.
-3*(a - 1)*(a + 2)
Solve -129 + 6*d**3 - 191 - d**3 + 240*d + 75*d**2 = 0 for d.
-8, 1
Let l be 2 + (-9)/(3 + -6). Let f(b) be the first derivative of -1/3*b**6 + 0*b**l - 4/3*b**3 + 3/2*b**4 + 2 + 0*b + 0*b**2. Factor f(v).
-2*v**2*(v - 1)**2*(v + 2)
Let i(w) = 7*w**3 - 5*w**2 + 3*w + 5. Let t(p) = 4*p**3 - 3*p**2 + 2*p + 3. Let d(o) = 3*i(o) - 5*t(o). Factor d(j).
j*(j - 1)*(j + 1)
Let r(n) = 5*n**4 + 3*n**3 - 5*n**2 + 3. Let s(m) = -16*m**4 - 10*m**3 + 16*m**2 - 10. Let f(o) = 20*r(o) + 6*s(o). What is p in f(p) = 0?
-1, 0, 1
Let q = -203/4 + 51. Let v = -16 - -33/2. Determine t so that v*t - 1/4*t**2 - q = 0.
1
Let g = -465 + 469. Determine o so that 2/7*o**3 + 2/7*o**g + 0 - 2/7*o - 2/7*o**2 = 0.
-1, 0, 1
Factor 4*d**3 - 2*d**3 - 2*d**4 + 12*d**5 + 12*d**4.
2*d**3*(2*d + 1)*(3*d + 1)
Let c(l) = l**3 - 3*l**2 + 2*l - 3. Let d = -6 - -9. Let y be c(d). Find w such that 9*w**2 + 2*w + w**y - 13*w**2 + w**3 = 0.
0, 1
Let z(l) be the first derivative of 9/25*l**5 - 2 + 12/5*l**3 - 3/2*l**4 + 3/5*l - 9/5*l**2. Factor z(v).
3*(v - 1)**3*(3*v - 1)/5
Determine j so that -6*j + 29*j + 27*j + 45*j**3 + 105*j**2 + 45*j + 5*j**4 + 30 = 0.
-6, -1
Factor 3/2*f**2 - 3/4*f - 3/2*f**4 + 3/4*f**5 + 0*f**3 + 0.
3*f*(f - 1)**3*(f + 1)/4
Let u = 1977/524 + -3/131. Let o(m) be the first derivative of -u*m**2 + 1 - m - 4*m**3 + 2*m**4. Factor o(z).
(z - 2)*(4*z + 1)**2/2
Let x(o) = o + 2*o - o**3 - o - 5 - o. Let h(w) = w**3 - w + 3. Let s(l) = 5*h(l) + 3*x(l). Factor s(c).
2*c*(c - 1)*(c + 1)
Suppose 323 = 4*h + 315. Factor -2/7*s + 0 - 2/7*s**h.
-2*s*(s + 1)/7
Let d(s) be the third derivative of -s**10/43200 + 11*s**9/241920 - s**8/40320 - s**5/10 - 9*s**2. Let l(g) be the third derivative of d(g). Factor l(p).
-p**2*(2*p - 1)*(7*p - 2)/4
Suppose 29*a + 36*a**2 - 13*a**2 + 6 + 12*a + 44*a**4 + 7*a**5 + 71*a**2 + 96*a**3 = 0. What is a?
-3, -1, -2/7
Let 31 - 1 - 12 + 2*v**2 - 12*v = 0. Calculate v.
3
Suppose 0 = 5*h - 2 - 83. Let g = h - 16. Factor -g - 1/2*t**2 + 3/2*t.
-(t - 2)*(t - 1)/2
Let h(b) be the second derivative of -b**7/525 + b**6/150 - b**5/150 - b**2/2 + 5*b. Let d(k) be the first derivative of h(k). Let d(q) = 0. What is q?
0, 1
Factor 2*q**2 + 1/6*q**5 + 0 - 6*q + 35/6*q**3 - 2*q**4.
q*(q - 6)**2*(q - 1)*(q + 1)/6
Determine w so that 0 + 1/4*w**2 + 0*w = 0.
0
Let d(r) be the first derivative of r**4/8 - r**3/9 - r**2/12 + 39. Suppose d(y) = 0. What is y?
-1/3, 0, 1
Suppose 4*f - 3*f = -2*i - 1, -f = -i - 2. Let d(c) be the first derivative of f + 0*c**2 + 1/3*c**3 + 0*c. Find g, given that d(g) = 0.
0
Let i(p) = p**3 - 10*p**2. Let c be i(10). Let a(z) be the third derivative of c*z**3 + 0 + 1/36*z**4 + 0*z - 1/180*z**5 - z**2. Factor a(o).
-o*(o - 2)/3
Let x be 2/8 + 0*(-9 - -10). Factor -1/2*p + x*p**2 + 1/4.
(p - 1)**2/4
Let s(p) be the first derivative of -p**6/30 + p**5/10 - p**3/3 + p**2/2 + p - 1. Let f(l) be the first derivative of s(l). Suppose f(r) = 0. What is r?
-1, 1
Determine s, given that 1/8*s**2 - 5/8*s**4 + 1/2 + 3/2*s - 3/2*s**3 = 0.
-2, -1, -2/5, 1
Let i(h) be the third derivative of -h**7/840 - h**6/120 - h**5/40 - h**4/24 + h**3/2 - 2*h**2. Let n(b) be the first derivative of i(b). Factor n(s).
-(s + 1)**3
Let q = 1/32 + 11/672. Let s(i) be the third derivative of 0*i + 4/21*i**3 - 3*i**2 - q*i**4 + 1/210*i**5 + 0. Determine c so that s(c) = 0.
2
Let r = 33 - 22. Let u = r - 8. Suppose u*a + 9/2 + 1/2*a**2 = 0. Calculate a.
-3
Let g = 2 + 0. Suppose 31 = 5*v + 11. Factor -3*z**v + 5*z**g - z**2 - z**2.
-3*z**2*(z - 1)*(z + 1)
Let w be 716/(-320) + 2 + (-1)/(-4). Let s(u) be the second derivative of 1/24*u**4 + w*u**5 + 0 - 1/4*u**2 - 4*u - 1/24*u**3. Factor s(g).
(g - 1)*(g + 1)*(g + 2)/4
Factor -9/4*h**3 - 3/2 + 3/4*h + 3*h**2.
-3*(h - 1)**2*(3*h + 2)/4
Let z(x) = -x**4 + x**3 + 8*x**2 - 6*x + 3. Let j(m) = -2*m + m**2 + 0*m**2 + m - 2 + 3. Let q(a) = 5*j(a) - z(a). Let q(u) = 0. What is u?
-1, 1, 2
Let p be (-4)/((-32)/6) - 0. Suppose -2*r + 2 = -2. Find c, given that p*c - 1/4 - 1/2*c**r = 0.
1/2, 1
Let v(g) be the second derivative of -g**4/18 - 3*g. Factor v(m).
-2*m**2/3
Let y(s) be the first derivative of 6*s**5/5 - 27*s**4/20 - 3*s**3/5 + 3*s**2/5 + 32. Det