20 - 3*w**4/8 - 4*w**2 - 4*w. Factor j(t).
3*t*(t + 1)*(2*t - 3)
Factor -3*u - u**5 + 7*u**2 + 9/2*u**4 + 1/2 - 8*u**3.
-(u - 1)**4*(2*u - 1)/2
Let i be (-731)/(-258) + (-2)/(-12). Find p such that 1/2*p**i - p**2 + 0 + 1/2*p = 0.
0, 1
Let s(y) be the third derivative of -y**6/160 + 11*y**5/40 - 121*y**4/32 + 43*y**2. Factor s(u).
-3*u*(u - 11)**2/4
Let n(w) be the third derivative of -w**6/960 + w**4/16 + w**3/3 + 16*w**2. Solve n(d) = 0 for d.
-2, 4
Let y(d) = 8*d**5 + 14*d**4 + 24*d**3 - 7*d**2 - 5*d - 5. Let n(t) = t**5 - t**4 + t**3 + t - 1. Let u(c) = 5*n(c) - y(c). Find f, given that u(f) = 0.
-5, -1, 0, 2/3
Suppose -4*j = -0*j - 4*w + 28, 0 = -4*w - 4. Let y be 6 - j/(-6)*3. Factor 0*o + 0 - 1/4*o**y + o**5 + 7/4*o**4 + 1/2*o**3.
o**2*(o + 1)**2*(4*o - 1)/4
Suppose 4 = 2*t - 4. Let j(s) be the second derivative of s - 1/24*s**3 + 1/80*s**5 - 1/8*s**2 + 0 + 1/48*s**t. Find h, given that j(h) = 0.
-1, 1
Let m = -848/21 + 122/3. Factor -24/7*n**2 + m*n**5 + 26/7*n**3 + 8/7*n - 12/7*n**4 + 0.
2*n*(n - 2)**2*(n - 1)**2/7
Let w = -79 + 79. Factor w*s - 3/4*s**5 + 0 - 5/4*s**3 + 1/4*s**2 + 7/4*s**4.
-s**2*(s - 1)**2*(3*s - 1)/4
Let b = -453/7 + 65. Factor -b*w**2 + 4/7*w - 2/7.
-2*(w - 1)**2/7
Factor -7*q**3 + q**2 + 7*q - q**2 + 2 - 2*q**2.
-(q - 1)*(q + 1)*(7*q + 2)
Let f be (-4)/(-18) + (-4)/18. Factor 0*v**2 + f*v + 0*v - v**2.
-v**2
Suppose -2*k**2 + 4*k - 9 + 9 = 0. Calculate k.
0, 2
Let g(c) be the second derivative of -11*c**4/72 + c**3/18 + 10*c. Factor g(a).
-a*(11*a - 2)/6
Let v be -3 + 2 - -1 - -11. Let x = -11 + v. Find i such that -1/3*i + 1/3*i**5 + x + 2/3*i**2 + 0*i**3 - 2/3*i**4 = 0.
-1, 0, 1
Let j(q) be the second derivative of -q**9/3780 - q**8/420 - q**7/126 - q**6/90 + q**4/6 + 6*q. Let m(t) be the third derivative of j(t). Factor m(u).
-4*u*(u + 1)**2*(u + 2)
Suppose 3*g = -2*t - 6, 3*g = g - 3*t + 1. Let x be ((-4)/(-1 + 3))/g. Factor 1/2*h**2 + 1/2*h - x*h**3 - 1/2.
-(h - 1)**2*(h + 1)/2
Factor 218*m**2 + 22*m**4 - 38*m**2 - 3 - 3*m**5 + 57 + m**5 - 162*m - 92*m**3.
-2*(m - 3)**3*(m - 1)**2
Let b(h) be the second derivative of -3*h**5/50 + 2*h**4/15 - h**3/15 - 3*h. Determine o so that b(o) = 0.
0, 1/3, 1
Let v(g) = -g + 4. Let q be v(0). Factor -q + 1 + 12*u + 8*u**2 - 5.
4*(u + 2)*(2*u - 1)
Suppose -6 = -2*q - 0*q. Factor -2*m**4 + 5*m**2 - 11*m + 0*m**q + 4 + m + m**2 + 2*m**3.
-2*(m - 1)**3*(m + 2)
Let s = -10 + 14. Suppose -5*u - 3*l + s*l = -21, 0 = 3*u - 5*l - 17. Solve 2*y**4 + 5*y + 24*y**u - 18*y**3 + y - 2*y**2 - 10*y**5 - 2*y = 0 for y.
-2/5, 0, 1
Let t(r) = r**2 - r - 1. Let u be t(-1). Solve -u - 1/4*w**2 - w = 0 for w.
-2
Let -x**3 - 39 + 26 + 17 - 3*x**2 = 0. What is x?
-2, 1
Let t(n) be the first derivative of 2/3*n**3 + 4 - 3*n**2 + 4*n. Solve t(m) = 0 for m.
1, 2
Let h be (-11)/((-22)/6) + 0/(-2). Let w(i) be the first derivative of 0*i**h + 4/7*i + 1/14*i**4 - 3/7*i**2 + 1. Factor w(g).
2*(g - 1)**2*(g + 2)/7
Let n(u) be the first derivative of 0*u + 0*u**2 + 1/24*u**6 - 1/12*u**3 + 1/20*u**5 - 1/16*u**4 + 4. Factor n(b).
b**2*(b - 1)*(b + 1)**2/4
Let n(z) be the second derivative of z + 1/63*z**7 + 0*z**3 + 1/10*z**5 + 0 - 1/15*z**6 + 0*z**2 - 1/18*z**4. Factor n(a).
2*a**2*(a - 1)**3/3
Let q(i) be the first derivative of -i**7/840 + i**6/120 - i**5/60 + i**3 + 4. Let x(m) be the third derivative of q(m). Factor x(o).
-o*(o - 2)*(o - 1)
Let u(l) be the first derivative of -3*l**4/4 + 9*l**2/2 + 6*l + 6. Factor u(d).
-3*(d - 2)*(d + 1)**2
Let s be (-13 - -13) + 40/(-21) - -2. Let m(h) be the third derivative of -s*h**3 + 0*h - 1/84*h**4 + 1/210*h**5 + 0 - 2*h**2. Suppose m(n) = 0. What is n?
-1, 2
Let m(t) = -t**2 + 9*t - 9. Let y be m(6). Let v be -9*(1 + (-12)/y). Let -14*k**4 - v*k**5 - 5*k + 20*k**2 + k - 4*k**2 - 4*k**3 - 2 + 11*k**5 = 0. What is k?
-1, -1/4, 1
Solve 4/3*p - 4/3*p**3 + 1 - 1/3*p**4 - 2/3*p**2 = 0 for p.
-3, -1, 1
Factor -12*l**2 - 84*l - 98 - 53 + 4.
-3*(2*l + 7)**2
Let v = 86 - 55. Let n = v - 61/2. Let -1/2*r + n*r**3 + 1/2*r**4 - 1/2*r**2 + 0 = 0. What is r?
-1, 0, 1
Factor -2/3*g**5 + 0 - 2*g**3 + 2*g**4 + 0*g + 2/3*g**2.
-2*g**2*(g - 1)**3/3
Let o(s) be the second derivative of 2*s - 1/144*s**6 + 0 + 0*s**2 + 0*s**4 - 1/120*s**5 + 1/6*s**3. Let x(z) be the second derivative of o(z). Factor x(t).
-t*(5*t + 2)/2
Let l(w) be the second derivative of -w**7/252 - w**6/90 - w**5/120 + 18*w. Factor l(z).
-z**3*(z + 1)**2/6
Let x(h) be the first derivative of 2*h**5/5 - 7*h**4/6 + 10*h**3/9 - h**2/3 - 12. Suppose x(c) = 0. Calculate c.
0, 1/3, 1
Find x, given that 2*x + 3 + x + 0*x + 3*x + 3*x**2 = 0.
-1
Suppose 34*u = 32*u + 4. What is a in 2*a**2 + a + 0*a**3 + 2 - 3*a**u - a**3 - 1 = 0?
-1, 1
Suppose -2*p - 3*p - 10 = 0. Let v be 1/p*20/(-2). Determine r, given that -v*r**5 + 2 + 11*r**4 - 13*r + 11*r**4 + 32*r**2 - 52*r**3 + 14*r**3 = 0.
2/5, 1
Let t(y) be the first derivative of 11/8*y**2 - 1/2*y - 4/3*y**3 + 7/16*y**4 + 2. Solve t(b) = 0.
2/7, 1
Let a = 7 - 3. Let h(r) be the third derivative of r**2 + 0 - 1/120*r**5 + 0*r**3 + 0*r + 1/96*r**a + 1/480*r**6. Factor h(w).
w*(w - 1)**2/4
Find m, given that 12/5*m + 3/5*m**2 + 12/5 = 0.
-2
Let b(l) be the third derivative of -l**7/504 + l**6/60 - l**5/30 + l**4/6 + l**2. Let m(y) be the second derivative of b(y). Determine u so that m(u) = 0.
2/5, 2
Let v(d) be the second derivative of -40*d**7/21 - 4*d**6/3 + 23*d**5/4 + 5*d**4/2 - 15*d**3/2 + d. Factor v(a).
-5*a*(a + 1)**2*(4*a - 3)**2
Let c(p) = -12*p + 2 + 3 - 6*p**2 + 9*p. Let w(l) = -l**2 + 1. Let g(x) = -c(x) + 5*w(x). Solve g(n) = 0.
-3, 0
Solve 19/2*h**4 - 7/2*h**5 + 1/2*h**2 - 15/2*h**3 + 0 + h = 0 for h.
-2/7, 0, 1
Let v(x) be the third derivative of 4*x**2 + 0*x**3 - 1/120*x**6 + 0*x - 1/24*x**4 + 1/30*x**5 + 0. Find j such that v(j) = 0.
0, 1
Solve -2 - 1/3*k + 1/3*k**2 = 0 for k.
-2, 3
Suppose 5*b - 21 = -l - 6, 5*b + 5*l - 15 = 0. Factor 4*o**b - 2*o**3 + 1 - 9*o - o**5 + o**4 - 2*o**2 + 8*o.
-(o - 1)**3*(o + 1)**2
Let d(k) = -k**2 + 5*k - 2. Let b be d(4). What is o in 3 + o**2 + 0*o**b - 2 + 3*o - o = 0?
-1
Let b(q) = 9 + 7*q**3 - 2*q - q**2 - 15 - 4*q**2. Let i(a) = -15*a**3 + 11*a**2 + 4*a + 13. Let y(u) = -13*b(u) - 6*i(u). Solve y(o) = 0 for o.
-2, 0, 1
Let b = 355/812 + -1/116. Let 3/7*v**2 + 0*v - b = 0. What is v?
-1, 1
Let b = 64 - 61. Factor -1/3*m**5 - 2/3*m**2 + 1/3*m + 2/3*m**4 + 0*m**b + 0.
-m*(m - 1)**3*(m + 1)/3
Let a(f) = -2*f**2 + 4*f + 1. Let g(b) = b**2 - b - 1. Let p(i) = a(i) + 3*g(i). Suppose p(q) = 0. What is q?
-2, 1
Let c(k) = 12*k**3 - 4*k**2 - 19*k - 10. Let h(d) = -4*d**3 + d**2 + 6*d + 3. Let o(b) = 4*c(b) + 14*h(b). Factor o(y).
-2*(y - 1)*(y + 1)*(4*y + 1)
Let g = 8 + -6. Let a(i) = -i + 3. Let u be a(0). Determine h, given that u*h**2 - 4*h**4 - 2*h**3 - 4*h**g + 3*h**4 = 0.
-1, 0
Let i(y) be the first derivative of y**8/112 + y**2 + 2. Let h(j) be the second derivative of i(j). Let h(u) = 0. Calculate u.
0
Suppose 0*k = 3*k - 27. Let j be k/45 + (-2)/(-10). Factor 4/5*g**2 - 2/5*g**5 + j*g + 0 + 0*g**3 - 4/5*g**4.
-2*g*(g - 1)*(g + 1)**3/5
Solve -4/3*s + 0*s**2 + 0 + 49/3*s**3 = 0.
-2/7, 0, 2/7
Suppose 0 = i + c - 0*c + 7, c = -3. Let r be (-2)/(-4)*(i + 10). Determine l, given that 0 + 2/7*l**5 - 4/7*l**2 + 4/7*l**4 + 0*l**r - 2/7*l = 0.
-1, 0, 1
Let f(l) be the second derivative of l**6/180 - l**5/40 + 10*l. Solve f(y) = 0.
0, 3
Let w be (-77)/(-120) - 18/30. Let m(y) be the second derivative of 0*y**3 - w*y**4 + 0*y**2 + 1/60*y**6 + 1/84*y**7 + 2*y - 1/40*y**5 + 0. Factor m(k).
k**2*(k - 1)*(k + 1)**2/2
Let u = 0 - -2. Let v = -4 - -4. Find n such that v*n**3 - n**3 + 3*n**3 - 14 + 12 + u*n**2 - 2*n = 0.
-1, 1
Let q(l) be the second derivative of 0*l**3 + 1/48*l**4 - 1/8*l**2 - 2*l + 0. Factor q(v).
(v - 1)*(v + 1)/4
Let i be (-14)/(-4) - (-2)/4. Let a(o) be the second derivative of 0*o**2 + 0*o**3 - 2*o + 1/30*o**5 - 1/18*o**i + 0. Find l such that a(l) = 0.
0, 1
Factor 1/3*k**2 - 1/3*k - 1/3 + 1/3*k**3.
(k - 1)*(k + 1)**2/3
Let x(b) be the first derivative of -7*b**5 + 50*b**4 + 95*b**3/3 - 100*b**2 - 60*b - 19. Determine o so that x(o) = 0.
-1, -2/7, 1, 6
Let k = -12 - -14. Let m be (30/(-4))/(-4 - k). Factor 3/4*a - m*a**2 + 1/2.
-(a - 1)*(5*a + 2)/4
Suppose 0 = -3*j - 0*j. Let h be (-3 - (-4 + 2))*j. Factor 0*y**4 