e of 4*i**6/3 + 12*i**5/5 - 2*i**4 + 4. Factor t(p).
4*p**3*(p + 2)*(2*p - 1)
Suppose -12 = 4*c - 5*s, -2 = 3*c + 5*s - 28. Let n be (-4)/((7/(14/(-20)))/1). Factor 4/5 - 2/5*h**c + n*h.
-2*(h - 2)*(h + 1)/5
Let t(k) be the third derivative of -k**9/45360 - k**8/20160 + k**7/7560 + k**6/2160 - k**4/12 + 2*k**2. Let j(q) be the second derivative of t(q). Factor j(h).
-h*(h - 1)*(h + 1)**2/3
Determine j so that -6/5*j**2 + 0*j - 12/5*j**4 + 3*j**3 + 0 + 3/5*j**5 = 0.
0, 1, 2
Suppose -7 + 16 = 2*h - a, -3*h - 6 = 5*a. Let x(p) be the second derivative of 0 + p + 0*p**4 + p**h - 2/5*p**5 + p**2. Factor x(q).
-2*(q - 1)*(2*q + 1)**2
Suppose 0 = -3*i + 6, -4*l - i + 31 = 149. Let s be 16/l*6/(-8). Factor 4/5 + 2*u + 6/5*u**2 - s*u**4 - 2/5*u**3.
-2*(u - 2)*(u + 1)**3/5
Let d(u) = u**3 + 12*u**2 + 9*u - 16. Let s be d(-11). Factor 3*o + 4*o**3 + 5*o + s*o**3 - 24*o**2.
2*o*(o - 2)*(5*o - 2)
Let a = -19940 + 2313019/116. Let k = 2/29 - a. Factor -1/4*v**3 + 1/4 - k*v**2 + 1/4*v.
-(v - 1)*(v + 1)**2/4
Let r(k) be the second derivative of -k**6/45 + k**5/15 + 2*k**4/9 - 8*k**3/9 - 9*k. Determine g, given that r(g) = 0.
-2, 0, 2
Let z(p) = 7*p**3 - 4*p**2 - 3*p. Let h(w) = w**3 - w. Let t(r) = 4*h(r) - z(r). Factor t(v).
-v*(v - 1)*(3*v - 1)
Let z be 6*65/(-156)*4/(-5). Find j, given that 1/3 - 1/2*j + 1/6*j**z = 0.
1, 2
Determine c so that -6 + 18*c + 20*c - 6*c**4 + 9*c**5 + 12*c**2 + 21*c - 18*c**3 - 50*c = 0.
-1, 2/3, 1
Let r = -45 - -47. Factor -1/4*p + 1/4*p**r + 0.
p*(p - 1)/4
Let l(w) = -w**3 + 1. Let d be l(2). Let t(j) = -j - 4. Let m be t(d). Let -16*s**m + 2 - 4*s**5 - 12*s**2 + 10*s**4 + 16*s**5 + 0 + 4*s = 0. Calculate s.
-1, -1/3, 1/2, 1
Let m(l) = 2*l - 4. Let v(t) = -t**3 - 4*t**2 - 5*t - 3. Let p be v(-3). Let i be m(p). Determine k so that 2 + 1/2*k**2 - i*k = 0.
2
Let f(s) = 7*s - 1 + 3*s**2 - 2*s + 1 - s**3. Let o be f(4). Find r, given that -2*r**o - 7*r**4 - 2*r**2 - 6*r**3 + 3*r**4 - 2*r**5 = 0.
-1, 0
Let z(u) be the first derivative of u**6/105 - u**4/21 + u**2/7 - 4*u - 4. Let v(n) be the first derivative of z(n). Let v(g) = 0. What is g?
-1, 1
Suppose -1 = 3*w + 2*r, 6*w - 5*r = w + 40. Factor -9*b - w - 27/4*b**2.
-3*(3*b + 2)**2/4
Find y, given that -4/5*y + 0 + 11/5*y**3 - 7/5*y**5 + 12/5*y**2 - 12/5*y**4 = 0.
-2, -1, 0, 2/7, 1
Let u(p) be the first derivative of -4*p**2 - 4*p + 2 + p**3 + p**3 + 1 - 4*p. Suppose u(s) = 0. Calculate s.
-2/3, 2
Let c(y) be the third derivative of y**5/30 - y**4/4 - y**2. Let g(d) = 7*d + 6 - 2*d**2 - 3 - 3. Let j(z) = -3*c(z) - 2*g(z). Factor j(p).
-2*p*(p - 2)
Let r(l) be the second derivative of -3*l**6/80 - l**5/6 - 13*l**4/48 - l**3/6 - 3*l**2/2 + 3*l. Let j(p) be the first derivative of r(p). Factor j(o).
-(o + 1)**2*(9*o + 2)/2
Let a be -6*(15/6 - 3). Let k be (-14)/(-4*a/2). Let 0 - k*i**3 + 0*i - 2/3*i**2 = 0. Calculate i.
-2/7, 0
Let a(z) = 4*z - 5. Let i be 35/15 + (-1)/3. Let d be a(i). Factor 3/4*q**2 + 1/4*q**d + 0*q - 1.
(q - 1)*(q + 2)**2/4
Let p be (1/6)/((-33)/176*-2). Factor 2/3*a - 2/9*a**2 - p.
-2*(a - 2)*(a - 1)/9
Let d(u) = u**2 - 8*u + 10. Let n be d(7). Factor -3 + 3 + 2*t**4 + 2*t**n.
2*t**3*(t + 1)
Let k(v) be the first derivative of 1/12*v**4 + 3/2*v**2 - 1/2*v**3 - 1/180*v**5 - 4 + 0*v. Let n(d) be the second derivative of k(d). Factor n(h).
-(h - 3)**2/3
Let a(z) be the third derivative of 0*z**3 + 2*z**2 - 1/27*z**4 + 0*z - 2/27*z**7 + 1/180*z**6 - 7/216*z**8 + 2/27*z**5 + 0. Factor a(n).
-2*n*(n + 1)**2*(7*n - 2)**2/9
Find o such that 7*o**3 + 0*o**4 - 6*o**3 + 0*o**4 - 2*o**4 + o**2 = 0.
-1/2, 0, 1
Let m(n) be the third derivative of n**8/378 - n**7/105 + n**6/90 - n**5/270 - n**2 + 27*n. Find z such that m(z) = 0.
0, 1/4, 1
Let n be 11 + -2 - (1 + -2). Factor n*x**2 + 9*x**3 + 4*x - 2*x - 2 - 5*x**3 - 2.
2*(x + 1)*(x + 2)*(2*x - 1)
Let q(y) be the second derivative of -y**5/5 - y**4 - 2*y**3 - 2*y**2 + 3*y. Factor q(d).
-4*(d + 1)**3
Factor -3*i**2 - 2*i**2 + 20*i**2 + 5*i**3 + 10*i.
5*i*(i + 1)*(i + 2)
Let a be (-15)/(-7) + (-4)/28. Factor 0*p + 4*p - 5*p**a - p + 32*p**2 + 48*p**4 + 72*p**3.
3*p*(p + 1)*(4*p + 1)**2
Suppose 44 + q**2 - q - 40 - 3*q = 0. Calculate q.
2
Let g = 6 + -2. Suppose g*f**3 - 4 - 7*f**2 + 2*f + 0*f**3 + 5 = 0. What is f?
-1/4, 1
Factor 2/3*d - 2/3*d**2 + 0.
-2*d*(d - 1)/3
Solve -2/5*t**4 - 4/5*t**3 + 6/5*t**2 + 0 + 0*t = 0.
-3, 0, 1
Let c(f) be the third derivative of -f**5/60 - f**4/3 - 8*f**3/3 - 12*f**2. Determine a so that c(a) = 0.
-4
Let z(i) be the second derivative of 0*i**4 + 0 - 1/60*i**5 - 4*i + 1/6*i**3 + 1/3*i**2. Factor z(p).
-(p - 2)*(p + 1)**2/3
Suppose 3*t = 2*k - 6 + 1, 3*k = -3*t + 15. Solve t - 1/2*z - 1/2*z**2 = 0.
-2, 1
Let f(b) be the first derivative of -2*b**3/15 + 6*b**2/5 - 24. Find j, given that f(j) = 0.
0, 6
Let k(z) be the first derivative of -2*z**5/45 + 2*z**4/9 + 10*z**3/27 + 23. Determine n so that k(n) = 0.
-1, 0, 5
Factor -16*d**2 + 3*d - 12*d**2 + 3*d + 2*d + 12*d**3.
4*d*(d - 2)*(3*d - 1)
Let r(j) be the first derivative of -j**5/30 + j**4/24 - 6. Suppose r(x) = 0. Calculate x.
0, 1
Suppose -2*k - 57 = -5*k. Let t = 21 - k. Factor 14/3*h + 4/3 + 6*h**t + 10/3*h**3 + 2/3*h**4.
2*(h + 1)**3*(h + 2)/3
Let k = 18 - 18. Let 2*l**4 - 4*l + k*l**4 + l**3 + 5*l**3 - 2 - 2*l**3 = 0. Calculate l.
-1, 1
Let v(l) be the first derivative of 7*l**4/4 - 6*l**3 - 6*l**2 + 5*l - 9. Let x(s) be the first derivative of v(s). Determine c, given that x(c) = 0.
-2/7, 2
Factor 0*p + 2 - 3/2*p**2 + 1/2*p**3.
(p - 2)**2*(p + 1)/2
Let f(p) = -p**2 - 8*p - 9. Let r be f(-6). Let v = 9/20 + -1/5. Factor v + 1/4*k**4 - k**r - k + 3/2*k**2.
(k - 1)**4/4
Let t(b) be the third derivative of b**6/840 - 3*b**5/35 + 18*b**4/7 - 288*b**3/7 - b**2 + 4*b. Factor t(r).
(r - 12)**3/7
Let j(k) be the third derivative of -k**7/1680 + k**6/480 - k**4/96 + k**3/48 + 4*k**2 - 8*k. Determine t, given that j(t) = 0.
-1, 1
Suppose -5*t = -0*t - 25. Suppose j = -0*j - 4, 4*m - t*j - 32 = 0. Factor -c**3 + m*c**4 + c**4 + 3*c**3 + 2*c**5.
2*c**3*(c + 1)**2
Let d(z) = z**2 - z - 1. Let g(f) = -3*f - 21. Let h(u) = -3*d(u) - g(u). Factor h(n).
-3*(n - 4)*(n + 2)
Let l(v) be the second derivative of v**4/6 - 7*v**3/3 + 30*v. Solve l(u) = 0 for u.
0, 7
Factor 4/7*i + 0 - 10/7*i**2.
-2*i*(5*i - 2)/7
Let w = -18 + 75/4. Let 1/2*a + 0 - w*a**2 = 0. What is a?
0, 2/3
Let n(a) be the second derivative of -a**4/138 + 4*a**3/23 - 36*a**2/23 - a + 9. Suppose n(q) = 0. What is q?
6
Factor -17*s - 27*s + 21 + 10*s**2 - 5.
2*(s - 4)*(5*s - 2)
Factor 2*m**2 + 2/9*m**3 - 32/9 + 4/3*m.
2*(m - 1)*(m + 2)*(m + 8)/9
Let z(g) = 6*g + 1. Let d be z(1). Let a = d + -5. Determine p, given that 2*p**3 + 0*p**3 - 3 + 1 - 2*p + 2*p**a = 0.
-1, 1
Suppose 2*q - 3 = -y + 6, -4*y - 3*q + 21 = 0. Suppose -y*i - 2 = 4*x, 3*i + 2*x = 6 - 4. Factor -m**4 + i + 0*m + 5*m + 3*m**2 + m**3 - 2*m**3.
-(m - 2)*(m + 1)**3
Let y(d) be the first derivative of -3*d**7/280 - d**6/24 - d**5/20 - 2*d**3/3 - 1. Let w(h) be the third derivative of y(h). Factor w(c).
-3*c*(c + 1)*(3*c + 2)
Let l(m) be the second derivative of -m**6/195 + m**4/78 + 7*m. Find q, given that l(q) = 0.
-1, 0, 1
Solve 1728/5*b + 252/5*b**2 - 84/5*b**5 - 1564/5*b**3 + 432/5 + 676/5*b**4 = 0.
-2/3, -2/7, 3
Suppose -14*r = -5*r - 27. Let a(p) be the second derivative of -1/20*p**5 + 0*p**2 + 0*p**4 + 0*p**r + p + 0 - 1/30*p**6. Factor a(c).
-c**3*(c + 1)
Let m = -40/17 + 474/187. Factor -4/11*q**3 + 0 + m*q**2 + 0*q + 2/11*q**4.
2*q**2*(q - 1)**2/11
Let f(a) be the second derivative of -2*a**6/45 + a**5/15 + a**4/9 - 2*a**3/9 + 7*a. Factor f(i).
-4*i*(i - 1)**2*(i + 1)/3
Suppose 2*j - 5*z - 19 = 0, j = 3*j - z - 7. Factor -5 - 2*g + 4*g**j + 0*g + 2*g**3 + 1.
2*(g - 1)*(g + 1)*(g + 2)
Factor -4/5*c**3 + 4/5*c + 2/5*c**2 + 1/5*c**4 - 3/5.
(c - 3)*(c - 1)**2*(c + 1)/5
Let w(r) be the first derivative of 0*r**2 + 0*r**5 + 0*r**3 - 1/10*r**4 + 2 + 0*r + 1/15*r**6. What is y in w(y) = 0?
-1, 0, 1
Let i(t) be the first derivative of 1/5*t**2 - 1/10*t**4 - 5 - 2/25*t**5 - 4/5*t + 2/5*t**3. Find f, given that i(f) = 0.
-2, -1, 1
Suppose 69*u = 74*u. Factor 0*x + u + 0*x**2 + 1/2*x**3.
x**3/2
Let w(t) = -2*t**5 - 2*t**4 + 4*t**3. Let x = -12 - -8. Let c(p) = p**5 + p**4 - 3*p**3. Let j(n) = x*c(n) - 3*w(n). Factor j(q).
2*q*