 - 8*x**3 - 13*x**2 + 3*x. Let i(k) = -5*k**4 + 7*k**3 + 12*k**2 - 2*k. Let p(t) = 2*g(t) + 3*i(t). Factor p(n).
-5*n**2*(n - 2)*(n + 1)
Let f(t) = -1 - t**2 + 0*t + 8*t - 4 + 0. Let l be f(7). Factor 0 + 1/3*r**l - 2/3*r.
r*(r - 2)/3
Let s(q) = -q**3 + 17*q**2 - 16*q. Let f = 39 + -23. Let p be s(f). Factor 2/9*z + 0*z**2 + p - 2/9*z**3.
-2*z*(z - 1)*(z + 1)/9
Let x(m) = -3*m**4 + 6*m**3 + 5*m**2 - 8*m - 16. Let s(t) = 12*t**4 - 24*t**3 - 21*t**2 + 33*t + 63. Let u(o) = -4*s(o) - 15*x(o). Factor u(r).
-3*(r - 2)**2*(r + 1)**2
Suppose -z**2 - 8/7 - 1/7*z**3 - 2*z = 0. Calculate z.
-4, -2, -1
Let l be 11 + -15 + 3/(9/16). What is q in 2*q + 2/3*q**2 + l = 0?
-2, -1
Factor 2*x**2 - 9*x**2 + 4*x**2 - 2*x**2 + 10*x - 5*x**3.
-5*x*(x - 1)*(x + 2)
Let i(v) be the third derivative of -v**2 + 0*v**3 + 0*v**5 + 0*v + 1/112*v**8 + 0 + 1/8*v**4 - 1/20*v**6 + 0*v**7. Factor i(x).
3*x*(x - 1)**2*(x + 1)**2
Let d(a) = 3*a**3 + 12*a**2 + 12*a - 2. Let p(y) = 12*y**3 + 48*y**2 + 48*y - 9. Let i(k) = -9*d(k) + 2*p(k). Factor i(t).
-3*t*(t + 2)**2
Suppose 14 = m - 0*m - 5*b, 8 = 3*m + 2*b. Let a(i) = -m*i**3 + 0*i + 0*i - 2*i**4. Let o(t) = -4*t**4 - 9*t**3. Let c(d) = -13*a(d) + 6*o(d). Factor c(g).
2*g**3*(g - 1)
Suppose -9*r - 5*r - 2*r = 0. Let c(m) be the second derivative of m + r + 2/27*m**4 - 1/27*m**3 + 4/135*m**6 - 1/15*m**5 + 0*m**2 - 1/189*m**7. Factor c(y).
-2*y*(y - 1)**4/9
Suppose 4*w - 12 - 13 = -5*g, 2*w = -3*g + 15. Let u(j) be the second derivative of 0 - 2*j - 1/9*j**3 + 1/30*j**g + 0*j**2 + 0*j**4. Solve u(d) = 0 for d.
-1, 0, 1
Let l(h) = h**2 + h + 2. Let f be l(0). Find b such that -4*b**f + b**4 + b**3 + 4*b**2 = 0.
-1, 0
Let 6*m + 5*m**2 - 12*m**2 + 3*m**2 + m**2 - 3 = 0. Calculate m.
1
Suppose -m - 4*m = -4*b + 14, -m - 10 = b. Let i(h) = h**2 + 5*h - 6. Let n be i(m). Find q such that -4/9 + n*q**2 - 2/9*q**3 + 2/3*q = 0.
-2, 1
Let n = 151 - 146. Let s(g) be the second derivative of 1/2*g**3 - 3/20*g**n + 2*g + 0*g**4 + 0*g**2 + 0. Suppose s(l) = 0. Calculate l.
-1, 0, 1
Let i(c) = -2*c**5 - 7*c**4 - 2*c**3 - 3. Let o(m) = -16 - 36*m**4 - 3*m**3 - 7*m**5 - 3*m**5 - 7*m**3. Let g(j) = -16*i(j) + 3*o(j). Factor g(a).
2*a**3*(a + 1)**2
Let l = 364 - 2544/7. Factor 6/7*a - l - 2/7*a**2.
-2*(a - 2)*(a - 1)/7
Let o be 0 - 11/(-5) - 2. Let y(a) be the first derivative of 1 + o*a**2 - 1/10*a**4 + 0*a + 0*a**3. Factor y(n).
-2*n*(n - 1)*(n + 1)/5
Factor 1/3*u**2 + 10*u + 75.
(u + 15)**2/3
Factor -6*m**4 - m**4 + 18*m**5 - 2*m**2 - 2*m**4 + 3*m**4 - 10*m**3.
2*m**2*(m - 1)*(3*m + 1)**2
Suppose 2*p = -15 + 5. Let b be (2/(-18))/(p/30). Factor 0 + 2/3*v**2 - b*v.
2*v*(v - 1)/3
Let i be 2/3 - (-448)/(-1176). Factor -4/7 - i*j**2 + 6/7*j.
-2*(j - 2)*(j - 1)/7
Let m(t) = -t + 6. Let d be m(0). Suppose -8*k**2 + 10*k + d*k**3 - 2*k**3 - 2*k**3 - 4 = 0. Calculate k.
1, 2
Let b(g) = g**2 + g - 1. Let a(c) = c**2 + 4*c - 6. Let l(t) = 1. Let u(f) = -a(f) - 3*l(f). Let d(r) = -2*b(r) - u(r). Factor d(z).
-(z - 1)**2
Let k = 63 + -249/4. Suppose 0*j - j**4 + k*j**3 + 0 + 1/4*j**2 = 0. What is j?
-1/4, 0, 1
Let v be ((480/126)/10)/((-2)/(-3)). Solve -v + 2/7*s**3 - 6/7*s**2 - 10/7*s + 2/7*s**4 = 0.
-1, 2
Let s(h) be the third derivative of h**6/780 - h**5/390 - 3*h**2. Determine w, given that s(w) = 0.
0, 1
Suppose -9*c + 22 = -7*c. Suppose z - a - 9 = 0, 0 = z + 4*a + c. Let 2/3*k**3 + 0 - 8/9*k**2 - 8/9*k + 8/9*k**4 + 2/9*k**z = 0. Calculate k.
-2, -1, 0, 1
Let p(y) be the first derivative of y**3/27 - 2*y**2/9 + 4*y/9 + 20. Factor p(v).
(v - 2)**2/9
Let v(g) be the second derivative of -g**6/225 - g**5/15 - 5*g**4/18 + 25*g. What is n in v(n) = 0?
-5, 0
Let w(a) be the third derivative of 0*a - 1/54*a**4 + 0 - 5*a**2 + 1/27*a**3 + 1/270*a**5. Factor w(l).
2*(l - 1)**2/9
Let g(y) be the second derivative of -y**7/133 + 11*y**6/285 + 3*y**5/190 - 13*y**4/38 + 40*y**3/57 - 12*y**2/19 - 10*y. Let g(c) = 0. Calculate c.
-2, 2/3, 1, 3
Factor -3*w**2 - 2*w**3 + 3*w**5 + 3*w**5 + 4*w**3 - 10*w**4 + 5*w**2.
2*w**2*(w - 1)**2*(3*w + 1)
Let o = -27 - -31. Let q(j) be the second derivative of 0 - 1/24*j**o + 0*j**2 + 2*j + 0*j**3. What is p in q(p) = 0?
0
Suppose -4*v + 2*x = -0*x - 24, 4*x = 5*v - 36. Find a, given that 9*a**v - a**3 - 6*a**2 - 5*a**3 - 4*a**5 + 7*a**2 = 0.
0, 1/4, 1
Suppose -5*s + 4*q - 2*q - 112 = 0, 39 = -2*s - 5*q. Let h(a) = a**2. Let k(t) = 12*t**2 - 3*t. Let d(g) = s*h(g) + 2*k(g). Factor d(l).
2*l*(l - 3)
Let t be 2 - -2*(-2 + (-44)/(-32)). Factor t*w**2 - 1/4*w**4 - 1 + 1/2*w**3 - w.
-(w - 2)**2*(w + 1)**2/4
Solve -13*f + 6*f**4 + 93*f + 50*f**2 + 70*f**3 + 2*f**4 - 32 + 124*f**2 = 0.
-4, -1, 1/4
Let x(f) be the third derivative of 1/12*f**4 + 0*f - 1/15*f**5 + 1/60*f**6 - 3*f**2 + 0 + 0*f**3. Factor x(m).
2*m*(m - 1)**2
Let q = 32 - 158/5. Suppose -3*k + 4*n + 12 = 2*n, 5 = -5*k - 5*n. Find o, given that q*o**k + 2/5*o + 0 = 0.
-1, 0
Let p = 23 + -20. Factor -4*d**p - 8*d**2 + 10*d**2 + 2*d**3 - 2*d**4 + 4*d - 2*d**3.
-2*d*(d - 1)*(d + 1)*(d + 2)
Let d(g) be the second derivative of -27*g**5/40 + 3*g**4/4 - g**3/4 + 11*g. Suppose d(w) = 0. Calculate w.
0, 1/3
Let -7*c - 17*c + 9*c + 5*c**2 = 0. What is c?
0, 3
Suppose 3*q + 3*u + 4 = 1, -2*q + 3*u = -18. Factor -5*a + 6*a**3 - a - q*a**5 + 3*a.
-3*a*(a - 1)**2*(a + 1)**2
Let a be -5 + 6 - (6 - 7). Factor 1/2*s**3 - 1/4*s**a + 0*s - 1/4*s**4 + 0.
-s**2*(s - 1)**2/4
Let d(a) be the third derivative of a**6/780 + a**5/130 + a**4/52 + a**3/39 + 7*a**2. Factor d(z).
2*(z + 1)**3/13
Let v = -1 + 16. Suppose 0*r + 5*r - v = 0. Factor -3*m**r - 4*m**2 - 6*m**3 + 3*m**3.
-2*m**2*(3*m + 2)
Let i = -167/15 - -59/5. Find c, given that -1/3*c**2 + i*c + 0 - 1/3*c**3 = 0.
-2, 0, 1
Let f(l) = 15*l**3 + 37*l**2 + 8*l - 52. Let v(u) = -10*u**3 - 25*u**2 - 5*u + 35. Let w(a) = 5*f(a) + 8*v(a). Factor w(y).
-5*(y - 1)*(y + 2)**2
Let c = -583/510 - -20/17. Let j(g) be the second derivative of -g - c*g**6 - 1/2*g**4 - 1/2*g**2 + 2/3*g**3 + 0 + 1/5*g**5. Factor j(f).
-(f - 1)**4
Let d = 77/6 + -38/3. Let o(a) be the second derivative of -1/10*a**5 + 0*a**2 - 1/15*a**6 - 2*a + 0*a**3 + 1/21*a**7 + 0 + d*a**4. Factor o(g).
2*g**2*(g - 1)**2*(g + 1)
Let k(c) be the first derivative of c**7/147 - c**6/35 + 3*c**5/70 - c**4/42 - 2*c + 2. Let h(v) be the first derivative of k(v). Solve h(q) = 0 for q.
0, 1
Let w(z) be the third derivative of 0*z + 1/20*z**5 + 1/112*z**8 + 0*z**3 + 3/40*z**6 + z**2 + 0*z**4 + 0 + 3/70*z**7. Factor w(o).
3*o**2*(o + 1)**3
Let c(i) = -3*i - 15. Let m be c(-6). What is g in 7*g**5 - 28*g**2 + 0*g**3 + 6*g**m + 4*g**4 - 2*g - 6*g + 19*g**4 = 0?
-2, -2/7, 0, 1
Suppose -21 = -u - 6*u. Suppose u = -2*n + 11. Factor 1/4*s**3 + 0 + 0*s - 1/4*s**5 - 1/4*s**n + 1/4*s**2.
-s**2*(s - 1)*(s + 1)**2/4
Determine w, given that 19*w**2 + 20 + 0*w - 27*w - 18 + 6*w = 0.
2/19, 1
Find p, given that -p**4 + p**4 - 5*p**5 + 10*p**2 - 15*p - 13 + 3 + 20*p**3 = 0.
-1, 1, 2
Let x = 12 + -8. Let h(f) = f. Let k be h(3). Determine v, given that -k*v**3 - x*v**3 - 5*v**2 - 2*v + 4*v = 0.
-1, 0, 2/7
Let p(t) = -t**2 + 4. Let f be p(0). Let i(h) be the second derivative of 0*h**3 + 1/105*h**6 + 1/42*h**f + 2*h + 0 + 1/35*h**5 + 0*h**2. Solve i(a) = 0.
-1, 0
Factor -2*z**2 + 11*z**2 + 9*z + 6*z**2 - 6*z.
3*z*(5*z + 1)
Let y(i) be the third derivative of -i**7/11340 + i**5/540 + i**4/12 - i**2. Let l(h) be the second derivative of y(h). Suppose l(s) = 0. What is s?
-1, 1
Let k(t) be the third derivative of t**8/480 + t**7/105 + t**6/120 - t**5/30 + t**4/12 - t**2. Let z(n) be the second derivative of k(n). Factor z(c).
2*(c + 1)**2*(7*c - 2)
Determine a so that 0*a + 0 - 2/3*a**2 = 0.
0
Factor 0 + 0*t**4 + 1/3*t + 1/3*t**5 + 0*t**2 - 2/3*t**3.
t*(t - 1)**2*(t + 1)**2/3
Let m = -27 + 41. Let s be (20/(-70))/((-6)/m). Let 2/3*j**2 + s*j + 0 = 0. What is j?
-1, 0
Let k be (-6)/(-15) + 27/(-5). Let j = 7 + k. Solve 0*o + 2/5*o**j + 0 - 2/5*o**3 = 0 for o.
0, 1
Suppose 9 = -2*c + 5*c. Let b(g) be the third derivative of 1/40*g**6 + 1/80*g**5 + 0 - 1/48*g**4 - g**2 + 1/120*g**7 + 0*g + 0*g**c. Factor b(h).
h*(h + 1)**2*(7*h - 2)/4
Suppose 3*x + 4*o = 6*o - 4, -4*x + o = -3. Let p(c) be the third derivative of 0 + 0*c**4 - x*c**2 + 0*c - 1/60*c**6 + 1/30*c**5 + 0*c**3. Factor p(a).
-2*a**2*(a - 1)
Let k be (-26)/(-3