3 + 1/6*r**4. Factor o(z).
-2*z*(z - 1)*(z + 1)**2
Let c be -33*(-2 + 3)/(-3). Find q, given that 1 + c*q**3 + 2*q + 15*q**4 + 15*q**3 + 13*q**2 - 1 = 0.
-1, -2/5, -1/3, 0
Let q be 8/(-5) + 0 + 2. Suppose -2*a + 4*v + 18 = 0, 3*v = -a - 0 - 6. Factor 2/5 + 6/5*d**2 + q*d**a + 6/5*d.
2*(d + 1)**3/5
Let w(u) be the second derivative of 0*u**2 + 1/120*u**6 + 0 + 1/48*u**4 + 1/40*u**5 + 2*u + 0*u**3. Determine i, given that w(i) = 0.
-1, 0
Let g(c) be the first derivative of c**4/36 + c**3/9 + c + 3. Let s(z) be the first derivative of g(z). Let s(a) = 0. What is a?
-2, 0
Suppose -15 = i - 6*i. Factor -4*y**3 - 3*y**3 + 3*y**i + 4 + 6*y - 2*y**3 - 4*y**2.
-2*(y - 1)*(y + 1)*(3*y + 2)
Let l(o) = -2*o**4 - 2*o**3 + 3*o. Let b = -2 - 2. Let j = b + 7. Let d(g) = 5*g**4 + 5*g**3 - 8*g. Let w(f) = j*d(f) + 8*l(f). Factor w(r).
-r**3*(r + 1)
Let o(d) be the second derivative of 2/33*d**3 - 1/165*d**6 - 1/55*d**5 + 7*d + 1/66*d**4 + 0*d**2 + 0. Find p such that o(p) = 0.
-2, -1, 0, 1
Let n(w) be the first derivative of 189*w**4/16 - 59*w**3/4 - 3*w**2 + 3*w - 7. Find j, given that n(j) = 0.
-2/7, 2/9, 1
Let u be (0 - -3) + (-19)/7. Suppose -2*t = -3*t - 5*p + 22, 28 = 4*t + 5*p. Let -u + 2/7*r**t + 0*r = 0. Calculate r.
-1, 1
Factor 9 - 2923*k**2 - 4*k**3 + 19 + 2943*k**2 + 52*k.
-4*(k - 7)*(k + 1)**2
Let m(q) be the second derivative of -q**4/4 + 3*q**3/2 - 5*q. Factor m(v).
-3*v*(v - 3)
Suppose -2*m + 3 - 1 = 0. Solve 0 + 2*a - 4*a**2 - m + 3*a**2 = 0.
1
Let a(x) be the second derivative of x**6/30 - x**5/10 - x**4/12 + x**3/3 + x. Factor a(o).
o*(o - 2)*(o - 1)*(o + 1)
Factor -14*z + 10 + z**2 - 12 + 13*z.
(z - 2)*(z + 1)
Suppose -2*d - 18 = -3*m, m + 3*d - 7 = -3*m. Suppose -3*z + m = -z. Factor 2/3*o + 0*o**z + 0 - 2/3*o**3.
-2*o*(o - 1)*(o + 1)/3
Let w(i) be the second derivative of -1/3*i**4 - 1/42*i**7 + 0 - 1/6*i**3 + 1/10*i**5 + 4*i + 1/15*i**6 + i**2. Factor w(r).
-(r - 2)*(r - 1)**2*(r + 1)**2
Suppose 3*g + g + 144 = 0. Let s be (9/g)/(2/(-6)). Determine w so that -s*w + 1/4 + 3/4*w**2 - 1/4*w**3 = 0.
1
Suppose 2/13*o**4 + 6/13*o**3 + 2/13*o + 6/13*o**2 + 0 = 0. Calculate o.
-1, 0
Let f(x) = -x**2 + 6*x + 1. Let v be f(4). What is i in -i**2 - 2*i**3 - v*i - 5*i**3 + 4*i**3 + 3 + 10*i**2 = 0?
1
Suppose 5*d - 15 = -5. What is n in 2/5*n**3 + 2/5*n**d - 2/5*n - 2/5 = 0?
-1, 1
Factor 0*x**3 - 12*x**2 - 3/4*x**5 + 12*x + 0 + 3*x**4.
-3*x*(x - 2)**3*(x + 2)/4
Let w(h) be the second derivative of -h**8/336 - h**7/105 + h**5/30 + h**4/24 + 3*h**2/2 - h. Let r(v) be the first derivative of w(v). Factor r(n).
-n*(n - 1)*(n + 1)**3
Suppose -8*d = d - 54. Let u(o) be the second derivative of o + 7/2*o**3 - 9/4*o**4 + 3/4*o**5 - 3*o**2 - 1/10*o**d + 0. Factor u(q).
-3*(q - 2)*(q - 1)**3
Let 0*k**3 + 18/5*k + 22/5*k**2 - 8/5*k**4 + 4/5 = 0. What is k?
-1, -1/2, 2
Let y(j) be the first derivative of 2*j**6/3 + 4*j**5/5 - 2*j**4 - 8*j**3/3 + 2*j**2 + 4*j + 14. Factor y(l).
4*(l - 1)**2*(l + 1)**3
Let u(z) be the third derivative of z**8/336 + z**7/210 - z**6/40 - z**5/60 + z**4/12 + 11*z**2. Factor u(d).
d*(d - 1)**2*(d + 1)*(d + 2)
Let y = 3148/5 - 620. Factor y*c + 12/5 + 3*c**2 - 21/5*c**3.
-3*(c - 2)*(c + 1)*(7*c + 2)/5
Let n(b) be the second derivative of 1/9*b**3 + b + 1/36*b**4 + 0 + 1/6*b**2. Factor n(z).
(z + 1)**2/3
Let r(w) be the third derivative of -7*w**5/180 + w**4/8 - w**3/9 - 33*w**2. Determine f, given that r(f) = 0.
2/7, 1
Let r = -5461/5 + 1093. Factor 0*u**3 + r*u + 0 - 4/5*u**5 + 8/5*u**4 - 8/5*u**2.
-4*u*(u - 1)**3*(u + 1)/5
Suppose -4 = -2*p - 2*p. Let h be 20/(-30) + (-16)/(-6). Factor p - j + 1/4*j**h.
(j - 2)**2/4
Let n be ((-309)/(-206))/((-9)/(-2)). Factor -1/3*o**3 - 1/3 + 1/3*o**2 + n*o.
-(o - 1)**2*(o + 1)/3
Suppose 55*k - 41*k = 0. Factor 0 + k*a + 0*a**2 + 2/9*a**5 + 0*a**4 - 2/9*a**3.
2*a**3*(a - 1)*(a + 1)/9
Suppose -k = -3*a + 1, -5*k - 3*a - 13 = 10. Let s be k/8 - 13/(-18). Factor -2/9*r**2 - s*r + 4/9.
-2*(r - 1)*(r + 2)/9
Factor 0*g - 1/7*g**4 + 0 + 0*g**2 + 1/7*g**3.
-g**3*(g - 1)/7
Solve -6*q**3 + 5*q**4 - 5 - 2*q - 8*q + 16*q**3 = 0.
-1, 1
Let i = 2/635 + -251/120015. Let j(g) be the third derivative of 0*g**3 - g**2 + 0*g + 1/180*g**6 - 1/135*g**5 - i*g**7 + 0 + 0*g**4. Let j(a) = 0. Calculate a.
0, 1, 2
Let c(m) be the third derivative of m**7/7560 - m**6/1080 - m**4/12 + 4*m**2. Let l(n) be the second derivative of c(n). Factor l(i).
i*(i - 2)/3
Let i(k) = -3*k + 33. Let t be i(10). Let s(n) be the second derivative of -3/2*n**2 + 1/4*n**4 - 9/4*n**t + 4*n + 0 + 27/40*n**5. Factor s(x).
3*(x - 1)*(x + 1)*(9*x + 2)/2
Let i(s) = -17*s**4 + 41*s**3 - 49*s**2 + 16*s. Let q(x) = 8*x**4 - 20*x**3 + 24*x**2 - 8*x. Let k(g) = 4*i(g) + 9*q(g). Find j, given that k(j) = 0.
0, 1, 2
Let t(p) be the first derivative of 14*p**5/3 + 4*p**4 + 8*p**3/9 + 5. Factor t(g).
2*g**2*(5*g + 2)*(7*g + 2)/3
Suppose 3*s + 7 = -y - 0, -3*s - 2*y - 8 = 0. Let g be (-16)/40*s*2. Let 2*m**2 + 16/5*m**3 + 0 + g*m**4 + 2/5*m = 0. Calculate m.
-1, -1/2, 0
Suppose 0*r + 6*r - 24 = 0. What is h in 0 - 18*h + 16*h - 4*h**r + 1 + 2*h**3 + 3*h**4 = 0?
-1, 1
What is q in -769 + 4*q**3 + 4*q**2 + 769 + 2*q**2 - 2*q**4 = 0?
-1, 0, 3
Factor 1/5*a - 1/5*a**2 + 1/5 - 1/5*a**3.
-(a - 1)*(a + 1)**2/5
Let k(z) be the second derivative of z**4/18 - 2*z**3/9 + 3*z. Solve k(l) = 0 for l.
0, 2
Let v(y) = 9*y**2 + 21*y. Let r(t) = -8*t**2 - 20*t. Let b(h) = 5*r(h) + 4*v(h). Solve b(g) = 0.
-4, 0
Let h(o) = 17*o**3 + o**2. Let i be h(-1). Let a = -10 - i. Factor j**2 + 3*j**4 + 9*j + 2*j**2 - 9*j**3 - a + 0*j**2.
3*(j - 2)*(j - 1)**2*(j + 1)
Let g(b) = -b - 12. Let d be 2 - -16*(2 - 3). Let q be g(d). Solve 4/5 + 2*m + 4/5*m**q = 0 for m.
-2, -1/2
Let t = -1416 - -2913/2. What is i in 3 + 39/2*i + t*i**2 + 21/2*i**4 + 69/2*i**3 = 0?
-1, -2/7
Let a(z) = -3*z**2 + 17*z + 5. Let p(k) = -2*k**2 + 16*k + 6. Let b(i) = -4*a(i) + 5*p(i). Factor b(c).
2*(c + 1)*(c + 5)
Let c be 79/(-120) + (-2)/(-3). Let z(o) be the third derivative of -1/60*o**5 + 0 + 2*o**2 + 0*o**3 + 0*o + c*o**6 + 0*o**4. Factor z(q).
q**2*(q - 1)
Factor -c + 5 + 3*c**2 - 4*c**2 - 3*c.
-(c - 1)*(c + 5)
Factor 0 + 2/7*d**2 + 2/7*d.
2*d*(d + 1)/7
Let v(o) = o**2 - 2*o. Let c be v(3). What is n in -2*n**3 - 2*n - 5*n**3 + 5*n**2 + 4*n**c = 0?
0, 2/3, 1
Suppose -8 = 3*q - 20. Factor -3*l**4 + 1 + 4*l - l**3 - 7*l**3 + q*l**3 + 2*l**2.
-(l - 1)*(l + 1)**2*(3*l + 1)
Let t(a) be the third derivative of a**10/50400 - a**8/2240 + a**7/840 + a**5/30 - 4*a**2. Let h(n) be the third derivative of t(n). Find i such that h(i) = 0.
-2, 0, 1
Let m(o) be the third derivative of -o**9/10584 + o**8/5880 + o**7/2940 - o**6/1260 + o**3/3 - 3*o**2. Let i(j) be the first derivative of m(j). Factor i(z).
-2*z**2*(z - 1)**2*(z + 1)/7
Let f(t) be the second derivative of 4*t + 1/12*t**4 - 1/20*t**5 + 0*t**3 + 0 + 0*t**2. What is i in f(i) = 0?
0, 1
What is p in 3*p**3 - 12*p**2 + 8*p + 8*p - 4*p = 0?
0, 2
Let q(m) be the first derivative of 0*m - 22/3*m**3 - 138/5*m**5 + m**2 + 2 + 12*m**6 + 43/2*m**4. Find s, given that q(s) = 0.
0, 1/4, 1/3, 1
Suppose 1 = -z + 17. Let p be ((-3)/(-4))/(6/z). Factor -1/4*g**3 + 0 + 1/4*g**5 + 1/4*g**4 - 1/4*g**p + 0*g.
g**2*(g - 1)*(g + 1)**2/4
Let f be (-288)/(-60) - (3 - -1). Let 2/5 + f*x + 2/5*x**2 = 0. What is x?
-1
Let o be (31/9 + -3)/(30/9). Factor 0 - o*i - 2/15*i**2.
-2*i*(i + 1)/15
Let x(a) = -a**3 - 2*a**2 + 3*a + 2. Let u(c) = -3*c**3 - 7*c**2 + 10*c + 7. Let m(g) = 4*u(g) - 14*x(g). Determine i, given that m(i) = 0.
-1, 0, 1
Let j = -10 - -15. Factor -4*f**j + 3*f**5 + 0*f**3 - f + 2*f**3.
-f*(f - 1)**2*(f + 1)**2
Factor 3 - 4*g**2 - 2*g**2 + 0*g + g + 2*g.
-3*(g - 1)*(2*g + 1)
Let v(s) be the first derivative of -7*s**3/27 - 2*s**2/3 + 4*s/9 - 16. Factor v(d).
-(d + 2)*(7*d - 2)/9
Let o = 85 - 169/2. Let q(a) be the third derivative of 4/5*a**5 + 0*a - 2*a**2 + o*a**3 + a**4 + 0. Let q(p) = 0. What is p?
-1/4
Let l(g) be the third derivative of -g**5/300 - g**4/60 + g**3/10 - 8*g**2. Factor l(k).
-(k - 1)*(k + 3)/5
Let k(w) be the first derivative of w**4/14 - 18*w**3/7 + 243*w**2/7 - 1458*w/7 + 7. What is m in k(m) = 0?
9
Let d(y) be the second derivative of -4/33*y**3 + 4/11*y**2 + 1/66*y**4 + y + 0. Let d(r) = 0. Calculate r.
2
Factor -6*z**3 + 2*z**2 - z + z**4 + 112 +