8 + g**7/35 + g**6/20 + g**5/30 - 2*g**2. Factor l(w).
2*w**2*(w + 1)**3
Suppose -5*t + t + 5*p + 14 = 0, 3*t - p = 5. Let q be 2 + (-1 + 2 - t). Factor -2*j - 2*j + 2*j - 2*j**q.
-2*j*(j + 1)
Factor -v**2 + 4*v**2 - 2*v**3 - 2*v + v**2.
-2*v*(v - 1)**2
Find f, given that -4*f**3 + 8 + 12*f**2 - 16*f + 1/2*f**4 = 0.
2
Let n(f) be the first derivative of -3*f**4/16 + 5*f**3/4 - 3*f**2/2 + 59. Factor n(v).
-3*v*(v - 4)*(v - 1)/4
Let f be -6*((-217)/756 + 1/4). Factor -2/3*j**4 + 2/3*j**3 + 0*j + 2/9*j**5 + 0 - f*j**2.
2*j**2*(j - 1)**3/9
Let n = 84 - 80. Factor 1/2*h**3 + 0*h**2 + 0 + 0*h + 1/2*h**n.
h**3*(h + 1)/2
Factor 0 - 23/2*y**4 - 7/2*y**5 - y - 13/2*y**2 - 27/2*y**3.
-y*(y + 1)**3*(7*y + 2)/2
Let k be 2 + -2 - (-13)/91. Suppose 1/7*d**3 - 1/7*d**2 + k - 1/7*d = 0. What is d?
-1, 1
Let g(w) = w**2 + 11*w + 4. Let a(o) = o**2 + 10*o + 4. Let d(k) = 7*a(k) - 6*g(k). Solve d(b) = 0.
-2
Let i(w) be the second derivative of w**7/3780 + w**6/810 + w**5/540 + w**3/2 - 3*w. Let x(c) be the second derivative of i(c). Factor x(t).
2*t*(t + 1)**2/9
Let n(a) be the third derivative of a**7/1470 + a**6/840 - a**5/140 - 5*a**4/168 - a**3/21 - 14*a**2. Suppose n(t) = 0. Calculate t.
-1, 2
Let n(k) be the first derivative of 3/2*k**2 - 4 + 0*k**3 + 0*k - 3/16*k**4. Find i, given that n(i) = 0.
-2, 0, 2
Let t(g) be the third derivative of g**5/300 + g**4/60 + g**3/30 + 2*g**2. Suppose t(y) = 0. What is y?
-1
Let k(f) be the second derivative of -1/8*f**2 + 1/12*f**3 - 1/20*f**5 + 0 + 3*f + 1/16*f**4 - 1/30*f**6. Factor k(p).
-(p + 1)**2*(2*p - 1)**2/4
Let 2/7 - 4/7*g**2 + 2/7*g**4 + 0*g + 0*g**3 = 0. Calculate g.
-1, 1
Let j(v) be the first derivative of 2*v**5/25 - v**4/10 - 3. Factor j(f).
2*f**3*(f - 1)/5
Let s = -183 + 1283/7. Factor 2/7*z + 0 + 2/7*z**2 - s*z**4 - 2/7*z**3.
-2*z*(z - 1)*(z + 1)**2/7
Let s be (-6)/9*(-9)/2. Let h be 4/3*(-9)/(-6). Factor 2*k**2 - h*k**2 - k**2 - k**s.
-k**2*(k + 1)
Let b(m) be the first derivative of -m**4/10 + 2*m**3/15 + 2*m**2/5 - 15. Factor b(p).
-2*p*(p - 2)*(p + 1)/5
Factor 18/5*w**3 + 0 + 2*w**4 + 4/5*w + 14/5*w**2 + 2/5*w**5.
2*w*(w + 1)**3*(w + 2)/5
Let m(s) = -s**3 - 6*s**2 + 5*s - 10. Let l be m(-7). Let i(j) = j**2 + 10*j + 9. Let c(p) = p. Let n(f) = l*c(f) - i(f). Factor n(a).
-(a + 3)**2
Let x(u) be the third derivative of u**8/84 - u**6/10 + 2*u**5/15 + 11*u**2. Factor x(y).
4*y**2*(y - 1)**2*(y + 2)
Let s = 19 - 10. Determine a, given that -a**4 + 2 - 2*a + s*a - 3*a - 4*a**3 - a**4 = 0.
-1, 1
Let b = 1/274 - -64/1233. Let t(n) be the second derivative of 0 + 0*n**3 + 1/30*n**5 + b*n**4 + 0*n**2 + 2*n. Factor t(g).
2*g**2*(g + 1)/3
Suppose 2*v - 90 = 2*d, -4*d - 4*v + 135 = -7*d. Let s be (-231)/d - 1/(-5). Determine c, given that -2/3 + 6*c**4 + s*c**2 + 12*c**3 - 4/3*c = 0.
-1, -1/3, 1/3
Let z be (9/(-15))/(2/(-20)). Suppose -x = -z - 8. Factor -4 + x*d + 0*d**3 - 2*d**3 - 8*d.
-2*(d - 1)**2*(d + 2)
Let w be -2 - 2 - -3 - -6. Suppose -5*k + 0*b - 5 = w*b, -k = -4*b - 4. Determine j, given that -3/4*j**3 + 1/4*j**4 + 3/4*j**2 + k - 1/4*j = 0.
0, 1
Let x be 1 + -6 + (-5762)/(-1118). Factor 4/13*y - x*y**2 - 2/13.
-2*(y - 1)**2/13
Let s = -11 - -15. Factor -7*t**2 - 2*t**2 - 54 - 6*t + 3*t**s + 54.
3*t*(t - 2)*(t + 1)**2
Factor -4/5*u**2 - 2/5 - 2/5*u**5 - 4/5*u**3 + 6/5*u + 6/5*u**4.
-2*(u - 1)**4*(u + 1)/5
Let h(s) be the third derivative of 1/336*s**8 - 1/105*s**7 + 1/30*s**5 - 3*s**2 + 0*s**3 + 0*s + 0 + 0*s**6 - 1/24*s**4. Solve h(o) = 0.
-1, 0, 1
Suppose 1/4*c**2 + 3/4*c + 0 = 0. Calculate c.
-3, 0
Suppose -9*u + 18 = -3*u. Suppose -34 = -5*s + 2*c, -2*s + 3 - 1 = 5*c. Suppose s*n**u + 3*n - 2*n**4 - 1/2 - 13/2*n**2 = 0. What is n?
1/2, 1
Let i be (-2 - (-18)/10)/((-4)/10). Factor i*z - 1/4 - 1/4*z**2.
-(z - 1)**2/4
Let d(w) be the first derivative of w**4/6 - 2*w**3/3 + 1. Solve d(n) = 0.
0, 3
Factor -2/5*g - 4/5*g**2 + 0*g**3 + 4/5*g**4 + 2/5*g**5 + 0.
2*g*(g - 1)*(g + 1)**3/5
Suppose 2*x = -h - 1 - 0, -h - 4*x - 5 = 0. Suppose -4*y = -20, h*j - y - 1 = -0. What is d in -1/6*d - 1/6*d**j + 1/3 = 0?
-2, 1
Let z be (0 + 12)*7/14. Suppose -v - 2*v + z = 0. Factor -3*m**3 + 0*m**3 + v*m**3.
-m**3
Factor 0*x**3 + 7*x**3 - 3*x**3 + 15*x**2 - 16 - 3*x**2.
4*(x - 1)*(x + 2)**2
Let c = -14 - -16. Let l(t) be the second derivative of -1/80*t**5 - 3*t + 0 + 1/24*t**3 + 1/8*t**c - 1/48*t**4. Solve l(h) = 0 for h.
-1, 1
Let h(t) be the second derivative of -t**8/30240 + t**7/3780 - t**6/1080 + t**5/540 - t**4/6 - t. Let q(w) be the third derivative of h(w). Factor q(a).
-2*(a - 1)**3/9
Let z be -6 - -8 - (-9 - -1). Let g be (-21)/(-52) + z/(-65). Suppose -3/4*x**3 - 1/4*x + g - 5/4*x**2 = 0. What is x?
-1, 1/3
Let y(p) be the second derivative of 7*p**6/75 - 37*p**5/50 + 59*p**4/30 - 7*p**3/3 + 6*p**2/5 - 16*p. Determine a so that y(a) = 0.
2/7, 1, 3
Let -7*d**2 - 2*d + 5*d**2 - 2*d - 2 + 0*d = 0. What is d?
-1
Let x(l) = -4*l - 1. Let j be x(-2). Let p(g) be the third derivative of -1/630*g**j + 0 + 0*g + 0*g**3 + g**2 + 0*g**6 + 1/36*g**4 + 1/60*g**5. Factor p(y).
-y*(y - 2)*(y + 1)**2/3
Factor 2/15*t**4 - 8/15*t**3 + 0*t + 8/15*t**2 + 0.
2*t**2*(t - 2)**2/15
Suppose 44/3*z - 8*z**2 - 8 + 4/3*z**3 = 0. What is z?
1, 2, 3
Factor 4/5*w - 8/5*w**3 + 4/5*w**5 + 0*w**4 + 0*w**2 + 0.
4*w*(w - 1)**2*(w + 1)**2/5
Suppose 2*m = -a + 5, -3*a + 5*m + 5 = m. Suppose -3*b**3 + 4*b**3 - 6*b + 3*b**a - 4 - 2*b**3 = 0. What is b?
-1, 2
Let g be 3/((-9)/24*1). Let h be (-20)/(-8) + 4/g. Find o such that 1/4*o**3 + 1/2*o**h + 0 - 1/4*o**4 + 0*o = 0.
-1, 0, 2
Let m be 11/4 - (-4)/16. Factor 8 - 6*h + 5*h**2 - m*h**2 - 2*h.
2*(h - 2)**2
Suppose -80*c**4 - 9*c**5 + 20*c**2 + 45*c**2 - 15*c**3 + 29*c**5 - 20*c = 0. Calculate c.
-1, 0, 1/2, 4
Let u(y) = y**3 - 9*y**2 + 8*y - 4. Let p be u(8). Let s(o) = -8*o**2 - 2*o - 5. Let w(g) = 3*g**2 + g + 2. Let j(x) = p*s(x) - 11*w(x). Factor j(a).
-(a + 1)*(a + 2)
Suppose 3 = -w + 5. Find a such that 4*a - 10*a**w - 7*a - a = 0.
-2/5, 0
Factor 2/3*j**5 + 2*j**3 + 2*j**4 + 0 + 0*j + 2/3*j**2.
2*j**2*(j + 1)**3/3
Factor 0 + 5*v**3 - 5/3*v**2 + 0*v - 5*v**4 + 5/3*v**5.
5*v**2*(v - 1)**3/3
Let b(n) be the second derivative of -n**4/66 + 4*n**3/33 - 4*n**2/11 + 5*n. Solve b(c) = 0 for c.
2
Let w = 5/203 + 747/2639. Factor 0 + 14/13*v**2 - w*v.
2*v*(7*v - 2)/13
Let o(y) = -3*y**3 + 25*y**2 - 19*y - 5. Let k(a) = a - 3. Let t be k(5). Let n(v) = -4*v**3 + 24*v**2 - 18*v - 6. Let x(d) = t*o(d) - 3*n(d). Factor x(c).
2*(c - 2)**2*(3*c + 1)
Let -4*x**2 + 0 - 8/7*x + 16/7*x**3 = 0. Calculate x.
-1/4, 0, 2
Let d(m) be the third derivative of m**5/60 + 7*m**4/24 - 2*m**3/3 + 2*m**2. Let g(p) = -p**2 - 6*p + 3. Let v(h) = 4*d(h) + 5*g(h). Let v(x) = 0. Calculate x.
-1
Let j = -8 + 13. Suppose -3*a + 13 = j*p, -3*a + 7*a = 4. Suppose 14/5*q**p - 18/5*q + 4/5 = 0. Calculate q.
2/7, 1
Factor -9/7*p + 0 - 3/7*p**2.
-3*p*(p + 3)/7
Let j(u) = -u**2 - 11*u + 13. Let i be j(-11). Suppose -3 - i = -4*n. Find v such that 1/4*v**3 + 0*v**2 - 1/2*v**n + 1/4*v**5 + 0 + 0*v = 0.
0, 1
Suppose -2/13*p**5 + 8/13*p + 2/13*p**4 + 18/13*p**3 + 22/13*p**2 + 0 = 0. Calculate p.
-1, 0, 4
Let s = 17 - 15. Let q(a) be the first derivative of 0*a**2 - 34/15*a**5 + 0*a + 4/9*a**3 + 1/2*a**4 - s + 4/3*a**6. Find j, given that q(j) = 0.
-1/4, 0, 2/3, 1
Suppose -2*g + 0*g + 5*q + 7 = 0, -2 = 3*g + 5*q. Factor 1 + 0 - g - 2*l**2.
-2*l**2
What is f in -24/5*f**2 - 9/5*f**5 - 12*f**3 - 42/5*f**4 + 0 + 0*f = 0?
-2, -2/3, 0
Suppose -21 = -4*f + 27. Let s be ((-14)/(-3))/(f/9). Find i such that -1/2 - s*i - 4*i**2 + 8*i**3 = 0.
-1/4, 1
Let d be 10/24*(11 - 12/4). Let c = 0 + 2. Factor d*h**c + 2/3*h + 0.
2*h*(5*h + 1)/3
Let p = 26 + -22. Let q(f) be the first derivative of -1/4*f**p + 1 + 0*f - f**3 - f**2. Let q(t) = 0. What is t?
-2, -1, 0
Factor 2/9*y**2 + 2/9*y + 0.
2*y*(y + 1)/9
Let z(h) be the third derivative of h**8/168 - h**7/15 + 3*h**6/20 + 9*h**5/10 - 9*h**4/2 - 33*h**2. Factor z(p).
2*p*(p - 3)**3*(p + 2)
Let x(k) be the third derivative of -k**8/168 + 11*k**7/420 - 3*k**6/80 + k**5/120 + k**4/48 + 8*k**2. Factor x(p).
-p*(p - 1)**3*(4*p + 1)/2
Let l(f) = 9*f**2 + 51*f + 18. Let h(u) = 10*u**2 + 51*u + 18. Let s(m) = -6*h(m) + 5*l(m). Factor s(t).
-3*(t + 3)*(5*t + 2)
Let r(x) = 7*x**2 - 2*x - 4. Let u(n) = -13*n**2 