)*(q + 2)*(7*q + 2)/7
Let b be (84/(-350))/((-12)/160). Let s be -11*(0 - 8/10). Factor -18/5*k**4 - b*k - 2/5 - 48/5*k**3 - s*k**2.
-2*(k + 1)**2*(3*k + 1)**2/5
Factor -2/5*h + 0 - 1/5*h**2.
-h*(h + 2)/5
Let o(c) be the second derivative of c**5/30 - c**4/9 - c**3/9 + 2*c**2/3 - 7*c. Factor o(j).
2*(j - 2)*(j - 1)*(j + 1)/3
Let w(v) = -8*v**2 + 10*v - 2. Let x(j) = 17*j**2 - 20*j + 2 + 2 - j. Let u(l) = 5*l**2 + 1. Let b be u(1). Let p(k) = b*x(k) + 13*w(k). What is r in p(r) = 0?
1
Factor 23*a**3 - 8*a**3 - 5*a**5 - 53 - 10*a**2 + 53.
-5*a**2*(a - 1)**2*(a + 2)
Let n(w) = 5*w**3 + 9*w**2 + 2*w. Let h(t) = -10*t**3 - 19*t**2 - 4*t. Let y(f) = -2*h(f) - 5*n(f). Factor y(x).
-x*(x + 1)*(5*x + 2)
Find h such that -6/7*h**3 + 4/7 + 6/7*h - 2/7*h**2 - 2/7*h**4 = 0.
-2, -1, 1
Factor 279 - 2*k - 3*k + k**2 - 273.
(k - 3)*(k - 2)
Let -3/5*p**4 - 6/5*p**3 + 0 - 3/5*p**2 + 0*p = 0. What is p?
-1, 0
Let v(z) be the second derivative of 0 + 0*z**2 - 1/24*z**4 + 1/24*z**3 - 2*z + 1/80*z**5. Factor v(b).
b*(b - 1)**2/4
Let n(t) be the third derivative of -t**8/131040 - t**7/16380 - t**6/4680 + 7*t**5/60 + 2*t**2. Let f(i) be the third derivative of n(i). Factor f(x).
-2*(x + 1)**2/13
Let a(w) be the first derivative of -w**3/21 - 2*w**2/7 + 5*w/7 + 12. Factor a(m).
-(m - 1)*(m + 5)/7
Let g be (-6)/18 + 4874/1326. Let a = -2/221 + g. What is v in 1/3 + 10/3*v**2 + 5/3*v**4 - a*v**3 - 1/3*v**5 - 5/3*v = 0?
1
Suppose 0*w = 4*m - w + 1, -3*m - w = -1. Let a(h) be the second derivative of -h**2 + 0 - h + 1/6*h**4 + m*h**3. Solve a(g) = 0.
-1, 1
Let l(k) be the third derivative of k**5/150 - 4*k**2. Factor l(b).
2*b**2/5
Let j(s) = 5*s**2 + s. Let u be j(1). Solve 99*v**3 - u + 51*v**4 - 7*v**5 + 69*v**2 + 16*v**5 - 6 = 0.
-2, -1, 1/3
Let r = 2 - -2. Factor 5*a + a**2 - 2*a + 0*a - 2*a**3 - a - a**r.
-a*(a - 1)*(a + 1)*(a + 2)
Suppose 2*d - 3*c = c + 20, -2*d + 3*c + 16 = 0. Let h(n) be the second derivative of -4/21*n**3 - 4/7*n**d + 0 - 1/42*n**4 + n. Factor h(x).
-2*(x + 2)**2/7
Factor 37*r**5 - 6*r**2 - 40*r**5 + 3*r**2 + 3*r**4 + 3*r**3.
-3*r**2*(r - 1)**2*(r + 1)
Let t(n) be the second derivative of -1/10*n**5 + 0*n**2 + 0 - 1/6*n**3 - 3*n - 1/4*n**4. Factor t(p).
-p*(p + 1)*(2*p + 1)
Let m be (21/9 + -3)/(16/(-6)). Let d = -2/67 - -75/268. Let 1/4 - d*q**2 + m*q - 1/4*q**3 = 0. What is q?
-1, 1
Suppose 0*q + q = -11. Let o = 11 + q. What is s in 0*s**4 + 1/2*s + 0*s**2 + 1/2*s**5 + o - s**3 = 0?
-1, 0, 1
Let o be (-20)/48 - (0 - 4/6). Solve 1/4 + o*x**4 + 1/2*x**3 - 1/2*x**2 - 1/4*x - 1/4*x**5 = 0 for x.
-1, 1
Let f(y) = -y**2 + 4*y - 1. Let j be f(3). Suppose -j*r + 3*r = 0. Factor -2/9*q**2 + 0 + r*q.
-2*q**2/9
Let d(m) be the third derivative of -m**4/12 - m**3 - 2*m**2. Let b be d(-5). Factor t**3 + 5*t**b + t**5 + 3*t**4 - 6*t**4 + 0*t**5.
t**3*(t + 1)**2
Solve 2/13*x**2 - 2/13*x - 2/13 + 2/13*x**3 = 0 for x.
-1, 1
Let j(t) = -t**3 - 15*t**2 - 3*t**3 + 31*t**2 + 5*t**3 - t - 13. Let z be j(-16). Factor -1/4*b**z + 0 + 1/2*b - 1/4*b**2.
-b*(b - 1)*(b + 2)/4
Let p be ((-88)/154)/(-2 - (-24)/14). Let r(d) be the second derivative of -d**2 + 0 + p*d + 1/12*d**4 + 1/6*d**3. Factor r(z).
(z - 1)*(z + 2)
Let g(m) be the third derivative of 4*m**2 + 0 + 0*m - 1/120*m**6 + 0*m**5 + 1/24*m**4 + 0*m**3. Factor g(u).
-u*(u - 1)*(u + 1)
Let s(a) be the third derivative of -a**5/180 - a**4/72 + 9*a**2. Factor s(r).
-r*(r + 1)/3
Let o(x) be the first derivative of x**7/280 - x**6/60 + x**5/40 + 4*x**3/3 + 2. Let y(j) be the third derivative of o(j). Suppose y(w) = 0. Calculate w.
0, 1
Let a = 146535/28 + -5234. Let p = a + 6/7. Factor p - 1/4*w**2 + 0*w.
-(w - 1)*(w + 1)/4
Let s(u) be the second derivative of 0*u**3 - 1/9*u**4 + 4*u + 0 + 0*u**2 - 1/30*u**5. Let s(x) = 0. Calculate x.
-2, 0
Let g(p) = -4*p**4 + 2*p**3 + 5*p**2 - 5*p. Let a(n) = n**4 - n**2 + n. Let b(o) = 15*a(o) + 3*g(o). Solve b(s) = 0 for s.
-2, 0
Let c(u) be the third derivative of -u**9/60480 + u**8/6720 - u**7/2520 + u**5/60 - 2*u**2. Let o(d) be the third derivative of c(d). Factor o(y).
-y*(y - 2)*(y - 1)
Let p = 14 + -11. Let t(q) be the second derivative of 0*q**5 + 1/15*q**6 + 0*q**2 - 2*q + 0 + 1/21*q**7 + 0*q**p + 0*q**4. Determine o, given that t(o) = 0.
-1, 0
Let r(s) be the second derivative of -s**5/80 - s**4/12 - s**3/8 - 12*s. Suppose r(g) = 0. Calculate g.
-3, -1, 0
Determine b so that 2/9*b**3 + 0 + 0*b**2 - 2/9*b = 0.
-1, 0, 1
Suppose 0 = -95*g + 99*g - 16. Let a(u) be the third derivative of 0*u**3 + 0*u - 1/420*u**6 + 3*u**2 - 1/84*u**g + 0 - 1/105*u**5. What is h in a(h) = 0?
-1, 0
Let d(w) = -8*w**5 + 4*w**4 - w**3 + 5*w. Let m(t) = 9*t**5 - 6*t + t**3 - t**3 - 3*t**4. Let r(i) = -6*d(i) - 5*m(i). Solve r(g) = 0.
0, 1, 2
Let v(u) be the second derivative of u**8/1008 + u**7/315 - u**5/90 - u**4/72 + 3*u**2/2 - 3*u. Let o(r) be the first derivative of v(r). Factor o(f).
f*(f - 1)*(f + 1)**3/3
Let m(r) be the second derivative of -r**9/60480 + r**8/26880 + r**7/10080 - r**6/2880 + r**4/2 + r. Let f(g) be the third derivative of m(g). Factor f(z).
-z*(z - 1)**2*(z + 1)/4
Let u(c) be the second derivative of -3*c**4/20 - c**3/10 + 6*c**2/5 - 7*c. Suppose u(r) = 0. Calculate r.
-4/3, 1
Let r(w) be the third derivative of -w**7/1050 - w**6/600 + w**5/150 + 8*w**2. Factor r(p).
-p**2*(p - 1)*(p + 2)/5
Let d be (1/(-5))/(2/(-5)). Let s = 0 - -2. Let 0 + d*o**s - 1/2*o = 0. Calculate o.
0, 1
Factor 0 - 2/7*k**4 - 12/7*k**3 + 0*k - 10/7*k**2.
-2*k**2*(k + 1)*(k + 5)/7
Let l(b) = -6*b**4 - 51*b**3 + 15*b**2 - 21. Let k(i) = i**4 + 10*i**3 - 3*i**2 + 4. Let r(x) = -21*k(x) - 4*l(x). Factor r(m).
3*m**2*(m - 1)**2
Determine y so that 0*y**3 - 4/3*y**5 + 0 - 8/3*y**4 + 4/3*y + 8/3*y**2 = 0.
-1, 0, 1
Let q(v) be the third derivative of -v**6/240 + v**5/60 - v**4/48 + 4*v**2. Let q(d) = 0. What is d?
0, 1
Suppose -s + 3*s - 16 = 0. Suppose -4*z = -2*z - s. Factor 2*g**z - 2*g**3 - 4*g**2 + 0*g**4 + 0*g**3.
2*g**2*(g - 2)*(g + 1)
Let i(t) be the third derivative of 0 + 0*t**3 - 1/40*t**4 - 1/100*t**5 - 2*t**2 + 0*t. Factor i(w).
-3*w*(w + 1)/5
Let k(q) be the first derivative of 5 + 1/15*q**3 + 0*q**2 - 1/5*q. Factor k(y).
(y - 1)*(y + 1)/5
Suppose 0 = 3*a + 2*a, -5 = -v - 3*a. Factor -3*w**5 - 4*w**4 + 4*w**2 - 2*w + 2*w**v + 5*w**5 - 2*w**5.
2*w*(w - 1)**3*(w + 1)
Let g be (-1)/2*24/2. Let f(q) = 5*q**2 - q - 6. Let h(d) = 9*d**2 - 2*d - 11. Let z(o) = g*h(o) + 11*f(o). Factor z(p).
p*(p + 1)
Solve -33*f**3 + 12 - 96*f + 131*f**2 - 114*f**3 + 100*f**2 = 0 for f.
2/7, 1
Let w(z) = -z**3 + 10*z**2 - 4*z. Let b(p) = -p**3 + p**2 - p. Let y(x) = 4*b(x) - w(x). Factor y(u).
-3*u**2*(u + 2)
Factor 0 + 8/5*c + 72/5*c**2 + 162/5*c**3.
2*c*(9*c + 2)**2/5
Let w(i) be the second derivative of -i**4/84 + i**3/42 - 21*i. Suppose w(u) = 0. Calculate u.
0, 1
Let x(j) = -j + 0 + 0. Let u(i) = 2*i**3 + 4*i**2. Suppose 0 = m - 0*m - 2. Let k(v) = m*x(v) - u(v). Factor k(a).
-2*a*(a + 1)**2
Suppose 6*b - 9 - 3 = 0. Factor 2/9*c**b + 2/9 - 4/9*c.
2*(c - 1)**2/9
Let m(k) = k - 1. Let h(r) = r**2 + 3*r + 4. Let x(t) = -3*h(t) - 3*m(t). Factor x(p).
-3*(p + 1)*(p + 3)
Suppose -8/7*t**2 - 4/7 - 2/7*t**3 - 10/7*t = 0. Calculate t.
-2, -1
Suppose s + 2*s = 18. Suppose -3*h - t = -s, 7*t - 3*t + 2 = h. Find f, given that 1/3*f**h + 1/3 - 2/3*f = 0.
1
Let n(f) be the second derivative of f**5/4 + 5*f**4/3 + 5*f**3/2 + 6*f. Factor n(k).
5*k*(k + 1)*(k + 3)
Let k(r) be the first derivative of 3/8*r**2 + 1/4*r + 1/4*r**3 + 1/16*r**4 + 2. Solve k(h) = 0.
-1
Let l = 78/7 + -305/28. Factor 3/4*j**2 - l*j**4 - 1/4*j - 1/2 + 1/4*j**3.
-(j - 2)*(j - 1)*(j + 1)**2/4
Suppose 16*h = 5*h + 22. Factor 0*g + 0 - 1/5*g**h - 1/5*g**4 - 2/5*g**3.
-g**2*(g + 1)**2/5
Let v be (-768)/75*15/(-54). Let a = v - 22/9. Factor -2/5*b**2 + 0 - a*b.
-2*b*(b + 1)/5
Let w(f) = -f**2 + 1. Let g(k) = k**2 + 2*k - 6. Let s(j) = -g(j) - 5*w(j). Let o be s(1). What is r in -3*r**o + 4*r**3 + 0*r**4 + r**4 = 0?
-1, 0
Suppose -2*f + 2 = -2. Factor 2 - 5*p**f + 2*p + p**2 + 2*p**2 + 2.
-2*(p - 2)*(p + 1)
What is x in -7 + 3 + 7*x**4 - 16*x - 16*x**3 - 11*x**4 - 24*x**2 = 0?
-1
Let t = -15 + 15. Solve -6*d**4 + 10*d**4 + d - d**3 - 5*d**4 + d**2 + t*d**3 = 0.
-1, 0, 1
Let r(n) = n + 3. Let a be r(0). Let b be 3*-1 + 2 + 25. Solve 49*i**a + 3 - 1 + 2