ive of 5/21*p**4 + k*p**2 + 0 + 3/7*p**3 + 2*p. Factor c(i).
2*(2*i + 1)*(5*i + 2)/7
Let i be (2*2/(-4))/(-1). Let w = 1 + i. Suppose t**3 + 0*t**w - t - 3*t**2 + t**4 + 2*t**2 = 0. Calculate t.
-1, 0, 1
Factor -16*n**2 + 0*n**3 - 24*n**4 - 2 + 10*n**4 + 9*n + n**5 + 8*n**4 + 14*n**3.
(n - 2)*(n - 1)**4
Let x(z) = 4*z**4 - 15*z**3 + 8*z**2 - 3*z. Let n(d) = -12*d**4 + 44*d**3 - 24*d**2 + 8*d. Let k(f) = -3*n(f) - 8*x(f). Factor k(i).
4*i**2*(i - 2)*(i - 1)
Let m(p) = p**4 - p**2 - p - 1. Let o(w) = -w**5 + 10*w**4 + w**3 - 10*w**2 - 11*w - 11. Let c(x) = 22*m(x) - 2*o(x). Factor c(k).
2*k**2*(k - 1)*(k + 1)**2
Solve -m**2 + 2*m**2 - 4*m + 0 + 2 + 2 = 0 for m.
2
Let k be (-1)/4 - 17/(-4). Factor 2*p**4 + p**k + 2*p**4 - 4*p**4 + p**5.
p**4*(p + 1)
Let n = 11/30 + -1/30. Factor n*g**2 - 1/3*g + 0.
g*(g - 1)/3
Suppose 3*s + 1 = -2*m + 7*m, 3*m + 4*s = 18. Factor 11*j**2 + 13*j**m - 26*j**2 - 6*j.
-2*j*(j + 3)
Suppose -20 = -5*n + 5*u, -u - 2*u = -5*n + 12. Let 0*f**3 + 0 + 0*f**2 + n*f + 1/3*f**4 = 0. Calculate f.
0
Factor -2/19*i**2 - 8/19*i - 8/19.
-2*(i + 2)**2/19
Let q = 32 - 287/9. Let v(i) be the first derivative of q*i**2 - 1 + 1/18*i**4 - 4/27*i**3 + 0*i. Suppose v(k) = 0. Calculate k.
0, 1
Let d be -5 + 1596/160 + 6/(-16). Factor -22/5*a**2 - d*a - 6/5 - a**3.
-(a + 1)*(a + 3)*(5*a + 2)/5
Suppose 4*r - 5*u = -17, -3*r - u - 9 = -4*u. Let f = 326/7 + -1297/28. Factor f + 1/4*x**r - 1/2*x.
(x - 1)**2/4
Let n(m) = 2*m**2 - 20*m + 53. Let u be n(5). Suppose 2*s + 6*j - 4*j = 4, -2*s + 8 = 4*j. Factor 1/4*k + s - 1/4*k**4 - 1/4*k**u + 1/4*k**2.
-k*(k - 1)*(k + 1)**2/4
Let h be -4 + 0/3 - -3. Let r = 6 + h. Factor 0*s + 3/5*s**3 - 3/5*s**r + 0 + 3/5*s**2 - 3/5*s**4.
-3*s**2*(s - 1)*(s + 1)**2/5
Let y be 5/(-2 - (0 + -3)). Factor -1/4*v**3 - 1/4*v**4 + 1/4*v**2 + 0*v + 0 + 1/4*v**y.
v**2*(v - 1)**2*(v + 1)/4
Let q = -12 - -27. Let p be 2/(-4)*(-10)/q. Determine x, given that 0 + 0*x**2 - p*x**4 + 0*x + 0*x**3 = 0.
0
Let h = -10 + 10. Let j(q) be the third derivative of 1/315*q**7 + 1/180*q**6 + 0*q + 0*q**3 - 2*q**2 + 0*q**5 + h*q**4 + 0. Factor j(w).
2*w**3*(w + 1)/3
Let q(h) = 25*h**4 + 126*h**3 + 185*h**2 + 82*h + 12. Let n(r) = -174*r**4 - 882*r**3 - 1296*r**2 - 573*r - 84. Let b(f) = 2*n(f) + 15*q(f). Factor b(t).
3*(t + 2)**2*(3*t + 1)**2
Let f be (-3)/(-2)*4/3. Factor 6*r + f*r**3 + 23*r**2 - 2*r - 17*r**2.
2*r*(r + 1)*(r + 2)
Let s = 1266 - 46836/37. Let x = 20/333 + s. Let x*p**2 + 2/9 - 4/9*p = 0. What is p?
1
Let g(s) = s**2 - s - 1. Let c(v) = -7*v**3 - 13*v**2 - 14*v - 2. Let h(o) = c(o) - 6*g(o). Factor h(z).
-(z + 1)*(z + 2)*(7*z - 2)
Suppose -4*x = q - 15, -5*x + 9 + 12 = -q. Let j be (-2 - (-9)/3) + q. Determine y, given that 0 + 0*y**2 + j*y - 1/2*y**3 = 0.
0
Suppose 21 = -4*f + 9. Let o(b) = -b**2 - 4*b + 1. Let q be o(f). Factor -2*n**2 + q + 4*n**2 - n**2 + 4*n.
(n + 2)**2
Let j(m) be the third derivative of m**5/20 - 3*m**4/8 - 34*m**2. Find f, given that j(f) = 0.
0, 3
Let r(y) = -1. Let v(z) = z**2 + 2*z + 1. Let j(h) = r(h) + v(h). Let j(k) = 0. What is k?
-2, 0
Let x(n) = -n**2 + 13*n. Let p be x(13). Factor 1/2*w**3 + 0 + 0*w**2 + p*w.
w**3/2
Find u, given that -8/5 + 28/5*u**3 - 28/5*u + 4*u**4 - 12/5*u**2 = 0.
-1, -2/5, 1
Let o(l) be the first derivative of l**4/4 - l**3/3 - l**2 + 2*l - 4. Let u be o(2). Factor n + 1 + 1/4*n**u.
(n + 2)**2/4
Let z(t) be the third derivative of t**6/210 + 13*t**5/105 - 29*t**4/42 + 10*t**3/7 + 8*t**2. Find p, given that z(p) = 0.
-15, 1
Let g(s) be the second derivative of 0 + 4/33*s**3 + 2/55*s**5 + 1/11*s**4 + 5*s + 1/165*s**6 + 1/11*s**2. Factor g(b).
2*(b + 1)**4/11
Let g(t) be the first derivative of -2*t**3/3 - t**2 - 12. Factor g(h).
-2*h*(h + 1)
Let c(u) be the first derivative of -u**8/4200 - u**7/2100 + u**6/900 + u**5/300 + u**3 - 2. Let d(g) be the third derivative of c(g). Factor d(k).
-2*k*(k - 1)*(k + 1)**2/5
Suppose 7*i = 2*i. Suppose i = -0*d + d - 3. Factor -k - 2*k**4 - 6*k + 4*k**d + 2 + 3*k.
-2*(k - 1)**3*(k + 1)
Let w(u) = 5*u**3 - 40*u**2 - 5*u + 5. Let q(b) = 5*b**3 - 40*b**2 - 4*b + 4. Let s(f) = -5*q(f) + 4*w(f). Factor s(n).
-5*n**2*(n - 8)
Let p = -2/67 + 71/134. What is w in 1/2 + 0*w - p*w**2 = 0?
-1, 1
Suppose 0*q + 2*q = -5*x - 4, -4*q = 8. Let m(k) be the third derivative of 0*k + 1/120*k**5 + x - 1/24*k**4 + 1/12*k**3 - 2*k**2. Factor m(u).
(u - 1)**2/2
Let s = -7/43 - -393/301. Find p, given that 0 - 6/7*p**3 - s*p - 16/7*p**2 = 0.
-2, -2/3, 0
Let k(o) be the second derivative of 4*o + 0*o**2 + 16/189*o**7 + 0*o**4 + 0*o**3 + 1/90*o**5 + 0 - 8/135*o**6. Let k(y) = 0. What is y?
0, 1/4
Suppose 3*x - 15 = -3*u, 5*u - 27 = x - 2. Let j = -1 + 1. Factor -2/3*i**5 + j*i - 2/3*i**4 + 2/3*i**3 + 2/3*i**2 + x.
-2*i**2*(i - 1)*(i + 1)**2/3
Let w(l) be the first derivative of -l**6/1260 + l**5/420 - 2*l**3/3 - 3. Let o(f) be the third derivative of w(f). Factor o(m).
-2*m*(m - 1)/7
Let l(i) = -i**3 - 11*i**2 + 11*i - 7. Let o be l(-12). Let y = 11/2 - o. Determine d, given that 0 + 1/2*d + 0*d**2 - y*d**3 = 0.
-1, 0, 1
Suppose -2*x = 3*q + 16, 3*q + 4*x = q - 24. Let g = 2 - q. Factor 3*c**g - 2*c**4 + 4*c**3 + 0*c**3 + 6*c**2 + 4*c + 1.
(c + 1)**4
Find j, given that 5*j**5 + 1 + 13*j**4 + 5*j**2 - 1 - 18*j**4 - 5*j**3 = 0.
-1, 0, 1
Suppose 2*o - 4*q = 4*o + 8, 4 = -3*o - 4*q. Let r(x) be the first derivative of -2 - 1/3*x**6 + 0*x + 3/2*x**o + 2*x**2 + 10/3*x**3 - 2/5*x**5. Factor r(n).
-2*n*(n - 2)*(n + 1)**3
Let f = -146 + 149. Let i(x) be the first derivative of 5/4*x**2 + 1/2*x + f + 3/8*x**4 + 7/6*x**3. Let i(r) = 0. What is r?
-1, -1/3
Let 5/3*p**3 - 5/3*p + p**4 - 5/3*p**2 + 2/3 = 0. Calculate p.
-2, -1, 1/3, 1
Let c = 3 + 0. Suppose 3 + 2*q**c + q**3 - 3*q**2 + 0*q**3 - 3*q = 0. What is q?
-1, 1
Let b(h) = -13*h**4 + h**3 - 5*h**2 + 17*h - 9. Let u(y) = -3*y**4 - y**2 + 4*y - 2. Let n(v) = -4*b(v) + 18*u(v). Factor n(q).
-2*q*(q - 1)*(q + 1)*(q + 2)
Let d(c) be the first derivative of -c**4/2 - 4*c**3/3 + c**2 + 4*c - 5. Solve d(y) = 0 for y.
-2, -1, 1
Suppose t + 6 + 3 = 0. Let u = t + 11. Factor -4*d + 5*d - 2*d - 2*d**2 + 5*d - u*d**3.
-2*d*(d - 1)*(d + 2)
Let k(b) = b**2 - 1. Let i be k(-1). Let a be (0 + i)*4/(-8). Factor a + 1/3*l + 0*l**2 - 1/3*l**3.
-l*(l - 1)*(l + 1)/3
Let s(c) = 5*c - 11. Let h(o) = -9*o + 21. Let k(j) = 4*h(j) + 7*s(j). Let m be k(4). Factor -2*g**2 - g**4 + 3*g**2 - g**5 + 2*g**m - g**3.
-g**2*(g - 1)*(g + 1)**2
Let m(s) be the first derivative of 1 + 0*s**2 + 0*s + 2/3*s**3. Factor m(c).
2*c**2
Let m be 10/3 - (-4)/(-12). Determine z, given that 62*z - 66*z + 4*z**3 + 0*z**m = 0.
-1, 0, 1
Let k(q) be the first derivative of -2*q**5/45 - q**4/9 + 2*q**3/9 + 4*q**2/9 - 8*q/9 - 5. Factor k(l).
-2*(l - 1)**2*(l + 2)**2/9
Let c be 2/6*(3 - 2/6). Let v(w) be the first derivative of 8/9*w - c*w**2 - 3 + 2/27*w**3 + 1/6*w**4. Find l such that v(l) = 0.
-2, 2/3, 1
Suppose q - 4*n + 7 + 1 = 0, -3*q - 2*n + 18 = 0. Let k(g) be the first derivative of 2 + 0*g**2 + 0*g**q + 1/6*g**3 - 1/4*g - 1/20*g**5. Factor k(r).
-(r - 1)**2*(r + 1)**2/4
Let a be ((-3)/18*-3)/(9/72). Factor 0 - 2/5*v**5 + 0*v**2 + 0*v**a + 0*v**3 + 0*v.
-2*v**5/5
Factor 0*p + 0 - 2/3*p**4 + 1/3*p**3 + 0*p**2.
-p**3*(2*p - 1)/3
Determine c so that 3*c - 3*c - 14*c**5 + 22*c**2 + 14*c**3 - 4*c**5 + 4*c - 22*c**4 = 0.
-1, -2/9, 0, 1
Let v(m) = m**2. Let x(w) = -3 + 0*w - w + 0. Let n be x(0). Let t(b) = -4*b**2 + b. Let h(a) = n*v(a) - t(a). Determine p so that h(p) = 0.
0, 1
Let m(j) = 2*j**2 - 3*j. Suppose 4*q - 6 = 2. Let i be m(q). Factor 1/2*f**5 - 2*f**4 + 0*f + 0*f**2 + i*f**3 + 0.
f**3*(f - 2)**2/2
Let u(y) be the first derivative of -2/3*y**3 + 1/3*y**2 - 2/3*y**4 + 0*y + 1. Factor u(i).
-2*i*(i + 1)*(4*i - 1)/3
Let k be 0 - (-2 + 1) - 0. Factor -3*j + k + 3 + 0 + j**2 - 2.
(j - 2)*(j - 1)
Let m(g) = -g**2. Let r(o) = 9*o**2 - 2*o - 4. Let b(x) = 3*m(x) + r(x). Determine s, given that b(s) = 0.
-2/3, 1
Let g(h) be the third derivative of -2*h**7/525 - h**6/75 + h**5/25 + 2*h**4/15 - 8*h**3/15 + 33*h**2. Determine r so that g(r) = 0.
-2, 1
Let k(b) be the second derivative of 5*b + 1/20*b**4 + 0*b**2 + 0 - 3/10*b**3. Factor k(o).
3*o*(o - 3)/5
Let o(n) be the second derivative of n**5/150 + n**4/90 - 10*n. Factor o(m).
2*m**2*(m + 1)/15
Let i(x) be the 