*w**4 - 4*w - 2/5*w**5 - 6*w**3 - 1 + r*w**2. Let t(q) = 0. What is q?
1, 2
Let w(d) be the third derivative of d**7/840 - d**6/120 + d**5/48 - d**4/48 + 7*d**2. Factor w(i).
i*(i - 2)*(i - 1)**2/4
Let r(a) be the second derivative of 1/3*a**3 + 0 + a - 1/1080*a**6 + 0*a**2 - 1/360*a**5 + 0*a**4. Let u(o) be the second derivative of r(o). Factor u(d).
-d*(d + 1)/3
Let q = 64 - 64. Let m(n) be the second derivative of -1/36*n**4 + 0*n**2 + n + q + 1/9*n**3. Factor m(j).
-j*(j - 2)/3
Suppose -3*p = 2*v + v, 5*v = 5*p + 30. Suppose 2 = u - 6. Factor 11*z + 0*z**2 + u - 2 - v*z**2 - 8*z.
-3*(z - 2)*(z + 1)
Suppose -3*g + 4*t + 13 = 0, 9 = 4*g - 4*t - 7. Find s, given that s**4 + 36*s**5 + 8*s**2 + 7*s**4 - 2*s - 12*s**g - 38*s**5 = 0.
0, 1
Let u = 1 + 5. Suppose -l - u = -3*l. Suppose 1/3*i + 0*i**2 - 1/3*i**l + 0 = 0. Calculate i.
-1, 0, 1
Let o be 1/(-3 - (-21)/6). Suppose 4*q = o*q. Find w such that -4/3*w + q + 2/3*w**2 = 0.
0, 2
Let r(g) be the first derivative of 5*g**6/24 - g**5/2 + 5*g**3/6 - 5*g**2/8 + 21. Find i, given that r(i) = 0.
-1, 0, 1
Let a(i) be the third derivative of i**7/1050 - i**6/600 - i**5/100 + i**4/120 + i**3/15 + 2*i**2. Factor a(h).
(h - 2)*(h - 1)*(h + 1)**2/5
Let i(k) be the third derivative of k**6/90 + 11*k**5/270 + k**4/27 - k**3/27 - 2*k**2 + 7. Factor i(n).
2*(n + 1)**2*(6*n - 1)/9
Suppose 0 = -3*a + y - 5*y + 32, -y = -4*a + 11. Find s such that 1/3 - 64/3*s**5 + 47/3*s**2 + 4*s + 52/3*s**3 - 16*s**a = 0.
-1, -1/4, 1
Let s = -13569/910 + 7/130. Let b = -922/63 - s. Solve -20/9*r - b - 50/9*r**2 = 0.
-1/5
Let u = 46/5 - 9. Factor -u*v**4 + 0 + 0*v + 1/5*v**2 - 1/5*v**5 + 1/5*v**3.
-v**2*(v - 1)*(v + 1)**2/5
What is n in -37*n - 16 + 6*n**2 - 5*n**2 + 15*n + 137 = 0?
11
Suppose 0*q + q = -2*q. What is j in -25/4*j**5 + q*j**2 + 0*j - 1/4*j**3 - 5/2*j**4 + 0 = 0?
-1/5, 0
Let b(v) be the third derivative of -v**7/210 + v**6/120 + v**5/20 - 5*v**4/24 + v**3/3 + 40*v**2. Find l, given that b(l) = 0.
-2, 1
Let a be 3/12 + (-106)/(-24). Let b = a - 4. Solve b*u + 2/3*u**2 + 0 - 2/3*u**4 - 2/3*u**3 = 0 for u.
-1, 0, 1
Solve c + 7*c - 2 + 4*c**2 + 2 = 0.
-2, 0
Let u(b) be the first derivative of 98*b**5/85 + 7*b**4/2 + 12*b**3/17 - 44*b**2/17 + 16*b/17 - 38. Solve u(p) = 0 for p.
-2, -1, 2/7
Suppose -a - 2*d = 2 - 1, -3*a + d + 11 = 0. Factor 2*r**2 + r - 10*r + 4 + a*r.
2*(r - 2)*(r - 1)
Let p(k) = -k**3 - 13*k**2 - k - 4. Let w be p(-13). Let q be (-56)/105 + 12/w. Factor 3/5*n**2 + 0*n - q - 1/5*n**3.
-(n - 2)**2*(n + 1)/5
Let a(m) be the second derivative of m**7/189 - 4*m**6/135 + m**5/15 - 2*m**4/27 + m**3/27 - 11*m. Suppose a(v) = 0. What is v?
0, 1
Suppose 6*h - 2*h = -12. Let x = 5 + h. Factor -d - d**x - 6 + 6.
-d*(d + 1)
Let r(i) be the third derivative of 0*i**3 + 0*i**4 + 0 - 3*i**2 + 1/120*i**5 + 0*i. Solve r(z) = 0.
0
Let i(n) = -45*n - 92 + 13*n - 33*n + 2*n**2. Let z(m) = m**2 - 22*m - 31. Let l(y) = -4*i(y) + 11*z(y). Find r, given that l(r) = 0.
-3
Let g(k) = -9*k + 1. Let p be g(-1). Let w be 6/p*(-5)/(-1). Factor 2*s - 2*s - 3*s**2 + 2*s**w + 2 - s - 2*s.
(s - 2)*(s + 1)*(2*s - 1)
Let t(p) = p**2 - p + 4. Suppose -3*z + 2*z + 6 = 0. Let m(n) = -2*n**2 - 6 - 15 + z*n - 4*n**2. Let k(u) = -6*m(u) - 33*t(u). Factor k(o).
3*(o - 2)*(o + 1)
What is j in -49/2*j**3 + 2*j - 19*j**2 + 4 - 15/2*j**4 = 0?
-2, -1, -2/3, 2/5
Let r(x) be the third derivative of x**8/504 + x**7/45 + 19*x**6/180 + 5*x**5/18 + 4*x**4/9 + 4*x**3/9 + 9*x**2. Factor r(j).
2*(j + 1)**3*(j + 2)**2/3
Let d(a) be the second derivative of a**4/48 - a**3/4 + 9*a**2/8 + 4*a. Let d(r) = 0. Calculate r.
3
Let d(j) = 4*j**4 + 8*j**3 - j**2 - 5. Let h(t) = -4*t**4 - 8*t**3 + 2*t**2 + 6. Let l(y) = 6*d(y) + 5*h(y). Solve l(i) = 0 for i.
-1, 0
Let a(p) be the first derivative of p**5/40 + p**4/8 + p**3/6 - 7. Let a(i) = 0. What is i?
-2, 0
Let r(z) = -8*z**2 + 15*z - 17. Let a(n) = -33*n**2 + 60*n - 69. Let h(v) = 5*a(v) - 21*r(v). Factor h(f).
3*(f - 4)*(f - 1)
Factor -4/3*m**3 - 1/3*m**4 + 4/3*m + 1 - 2/3*m**2.
-(m - 1)*(m + 1)**2*(m + 3)/3
Let g(y) be the first derivative of -1/22*y**4 + 0*y + 2/11*y**2 + 3 - 2/33*y**3. Factor g(f).
-2*f*(f - 1)*(f + 2)/11
Let d(g) be the first derivative of 0*g**2 + 0*g - 4/9*g**3 - 1/15*g**5 - 5 - 1/3*g**4. Find m such that d(m) = 0.
-2, 0
Let m(s) be the second derivative of 9*s**5/20 + 7*s**4/4 + 5*s**3/2 + 3*s**2/2 - 11*s. Solve m(g) = 0.
-1, -1/3
Let i = -20 + 15. Let k = i + 5. Factor 0*r + k + 2/3*r**2.
2*r**2/3
Let f(q) be the second derivative of -3*q**4/10 + q**3/2 + 39*q. Determine h, given that f(h) = 0.
0, 5/6
Factor -3*q**2 + 3/2*q**4 + 3/2*q**5 - 3*q**3 + 3/2 + 3/2*q.
3*(q - 1)**2*(q + 1)**3/2
Let d(u) = -u**4 - u**3 - u**2 - u - 1. Let r(x) = -6*x**4 + 4*x - 2*x**3 + x - 8*x**2 - 9*x - 4 - 1. Let y(o) = 5*d(o) - r(o). Suppose y(k) = 0. What is k?
0, 1
Factor 0*q**2 + 20*q**2 - 4*q - 36*q**5 - 48*q**4 - 4*q**2 + 8*q**3.
-4*q*(q + 1)**2*(3*q - 1)**2
Factor 6*g**2 + 2*g**4 - 8*g**2 + 2*g - 2*g**3 + 0*g**2.
2*g*(g - 1)**2*(g + 1)
Solve -8 - 3 - 13*z - z**2 + z = 0.
-11, -1
Let h = -22/5 + 49/10. Let f be ((-2)/12)/((-54)/405). Find s, given that 1/4*s**4 + 9/4*s**2 + f*s**3 + 7/4*s + h = 0.
-2, -1
Let d = 2 + 8. Factor 5*c + 0*c**2 - 4*c**3 - c - 6 + d - 4*c**2.
-4*(c - 1)*(c + 1)**2
Let n(b) be the second derivative of -1/30*b**3 + 1/50*b**5 - b - 1/210*b**7 + 0*b**6 + 0*b**2 + 0 + 0*b**4. Suppose n(h) = 0. Calculate h.
-1, 0, 1
Let m(z) be the first derivative of 6*z**5/25 - 2*z**4/5 - 2*z**3/15 + 2*z**2/5 + 8. Find j such that m(j) = 0.
-2/3, 0, 1
Let i be 3/4*1232/330. Let 4/5 + 2*f**2 + i*f = 0. What is f?
-1, -2/5
Let r be (-8 - -1)*20/12. Let q = 12 + r. Factor 0*x**3 + 0 + 1/3*x**4 + 0*x - q*x**2.
x**2*(x - 1)*(x + 1)/3
Suppose 13 = o + 5*x, 5*o - 4*x = 2 + 5. Let q(d) be the second derivative of -1/24*d**o + 2*d + 0 + 1/48*d**4 + 0*d**2. Factor q(n).
n*(n - 1)/4
Find j such that -j**3 - 4/7*j - 16/7*j**2 + 0 = 0.
-2, -2/7, 0
Let a(w) be the second derivative of -w**4/4 + w**3 - w. Factor a(r).
-3*r*(r - 2)
Let l(s) be the first derivative of s**4/12 - 2*s**3/9 - 7*s**2/6 - 4*s/3 - 17. Factor l(q).
(q - 4)*(q + 1)**2/3
Factor 3/4*g + 3/4*g**2 + 0.
3*g*(g + 1)/4
Let v(a) be the first derivative of -a**6 + 2*a**5 - a**4/6 - 14*a**3/9 + 2*a**2/3 + 10. Solve v(b) = 0.
-2/3, 0, 1/3, 1
Let d(k) be the third derivative of -k**7/945 - k**6/108 - 7*k**5/270 - k**4/36 + 22*k**2. Factor d(v).
-2*v*(v + 1)**2*(v + 3)/9
Let k be ((-2)/(-4)*-8)/(-11). Factor 0 + k*d + 2/11*d**2.
2*d*(d + 2)/11
Determine x, given that 0*x**3 + 48*x**2 + 66*x**2 - 2*x**3 - 128*x**2 - 24 - 32*x = 0.
-3, -2
Let h(l) = 12*l**4 + 8*l**3 - 9*l**2 - 8*l - 3. Let z(n) = 60*n**4 + 40*n**3 - 46*n**2 - 40*n - 14. Let q(j) = -14*h(j) + 3*z(j). Factor q(f).
4*f*(f - 1)*(f + 1)*(3*f + 2)
Let c(p) be the first derivative of 0*p - 1/6*p**4 - 1 - 4/27*p**3 + 1/9*p**2. Factor c(o).
-2*o*(o + 1)*(3*o - 1)/9
Suppose 0 = 2*f - 6 + 2. Determine g, given that 1 + 1 + g**f - 2 + g = 0.
-1, 0
Suppose -5*n = -19 + 144. Let o be ((-4)/n)/(12/30). Solve 2/5*z**4 + 0*z + 0*z**3 - 4/5*z**2 + o = 0.
-1, 1
Let g be (-6)/(-2) + -1 + 1. Let k(p) = p**2 - 8*p - 8. Suppose 4*n - 1 = 15. Let o(a) = -2*a**2 + 8*a + 7. Let y(x) = g*k(x) + n*o(x). Let y(f) = 0. What is f?
-2/5, 2
Let b(w) be the third derivative of -2*w**7/105 + w**6/15 + w**5/15 - w**4/3 + 25*w**2. Factor b(d).
-4*d*(d - 2)*(d - 1)*(d + 1)
Let i = 67279/5 + -13391. Let -72/5*a + 16/15 + i*a**2 - 486/5*a**3 = 0. Calculate a.
2/9
Suppose -2 = 2*y + t - 11, -2*t = -y - 3. Let q(k) = -k**2 + 5*k - 4. Let b be q(y). Factor -2/3*z + 1/3*z**b + 1/3.
(z - 1)**2/3
Let p(o) be the third derivative of -o**9/1680 + o**8/448 - o**7/840 - o**6/240 - o**4/6 - 8*o**2. Let d(r) be the second derivative of p(r). Factor d(h).
-3*h*(h - 1)**2*(3*h + 1)
Let u(n) = -3*n**3 - 18*n**2 - 23*n - 8. Let s(f) = 5*f**3 + 35*f**2 + 45*f + 15. Let p(l) = 2*s(l) + 5*u(l). Factor p(b).
-5*(b + 1)**2*(b + 2)
Let s be (-18)/(-8) + 9/(-36). Let l = -3 + 6. Factor 8 - k**l - 9*k - s*k - k + 6*k**2.
-(k - 2)**3
Factor 4*r**2 - 2 - 3*r**2 + r**2.
2*(r - 1)*(r + 1)
Let s(f) be the first derivative of f**6/6 + 4*f**5/5 + 5*f**4/4 + 2*f**3/3 + 6. Factor s(p).
p**2*(p + 1)**2*(p + 2)
Let h(n) = -10*n**2 - 3*n. Let i(f) = 3*f**2 + 