t o be (-42)/9*(3 + 46/(-14)). Let c be (1*17/(-1))/(-3). Determine y so that o + c*y**2 + 5/3*y**3 + 16/3*y = 0.
-2, -1, -2/5
Suppose 5*y - 4 = -2*p, -34*p + 10 = -29*p + 2*y. Let 1/2 + 1/2*o**p - o = 0. What is o?
1
Suppose -10*n = -14*n + 4. Let o = n + 3. Factor -2/11*a**o + 2/11*a**3 - 2/11*a + 0 + 2/11*a**2.
-2*a*(a - 1)**2*(a + 1)/11
Suppose j = 3*j. Suppose 0 = 2*b + 2*b - 8. Suppose -q**5 - 4*q**2 + j*q**5 + q**3 + 3*q**b + q**4 = 0. What is q?
-1, 0, 1
Factor 0 + 3/4*u**3 - 3/2*u**2 + 0*u.
3*u**2*(u - 2)/4
Let b = -15 - -18. Find f, given that 6*f + 2 - 8*f**3 - 6 + 5*f**3 + f**b = 0.
-2, 1
Suppose -2345*h = -2344*h - 3. Factor 3/5*u**4 + 6/5 - 9/5*u**2 - 3/5*u + 3/5*u**h.
3*(u - 1)**2*(u + 1)*(u + 2)/5
Suppose p - 2*f + 8 = -2*p, -p - 8 = -2*f. Let p - k**4 - 3*k - 7*k + 6*k + 3*k**2 - 4 + 2*k**3 = 0. What is k?
-1, 2
Let l be 159/6 + (-3)/(-6). Let t be l/(-18) - (-2 - 0). Suppose -t*b**2 + 1/2*b + 0 = 0. What is b?
0, 1
Let q(m) be the first derivative of m**3/7 + 5. Factor q(w).
3*w**2/7
Let k(q) be the first derivative of 6 + 1/2*q**2 + 2*q - 1/3*q**3. Factor k(f).
-(f - 2)*(f + 1)
Let g(i) = 2*i**3 + 4*i**2 - 2*i + 2. Let y be -2 - -1 - (-4 - -1). Let k(n) = 4*n**3 + 9*n**2 - 5*n + 5. Let x(h) = y*k(h) - 5*g(h). Factor x(b).
-2*b**2*(b + 1)
Let n(g) be the first derivative of g**5/48 + g**4/24 - g**3/24 - g**2 + 2. Let s(x) be the second derivative of n(x). Let s(l) = 0. What is l?
-1, 1/5
Suppose -3*g = 2*y + y - 6, 0 = 3*g - 2*y + 4. Let k = 4 + g. Factor -4*v**k + 4*v**3 - 2*v**3 + 0*v**4 + 2*v**4.
-2*v**3*(v - 1)
Let n(y) be the third derivative of y**8/560 + y**7/140 + y**6/120 - y**3/6 - 4*y**2. Let j(a) be the first derivative of n(a). Factor j(x).
3*x**2*(x + 1)**2
Factor -2*s**2 - 98 + 3*s + s**2 + 96.
-(s - 2)*(s - 1)
Let m(t) be the first derivative of -2*t**3/21 + 10*t**2/7 - 50*t/7 - 20. Suppose m(n) = 0. Calculate n.
5
Let f(b) be the first derivative of -b**7/105 - b**6/75 + b**5/50 + b**4/30 + b + 1. Let g(t) be the first derivative of f(t). Factor g(q).
-2*q**2*(q - 1)*(q + 1)**2/5
Factor 0 - 15/4*l**3 + 5/4*l**4 + 5/2*l**2 + 0*l.
5*l**2*(l - 2)*(l - 1)/4
Factor 2*u**3 + u**2 + 9*u**2 - 2*u + 0*u**2 - 10 + 0*u**3.
2*(u - 1)*(u + 1)*(u + 5)
Let p(a) be the second derivative of 7*a - 1/6*a**4 + 0 + 0*a**3 + 0*a**2. Factor p(q).
-2*q**2
Let p(m) be the first derivative of -8*m**3/3 - 23*m**2/2 - 27*m + 5. Let n(q) = q**2 + q. Let x(g) = -5*n(g) - p(g). Factor x(y).
3*(y + 3)**2
Let j be 3/(-165) - 2/(0 - 10). What is n in 0 + 0*n + j*n**2 = 0?
0
Let q(z) be the second derivative of z**6/240 - z**5/80 + 4*z**3/3 - 4*z. Let a(g) be the second derivative of q(g). Factor a(f).
3*f*(f - 1)/2
Let d = -36 - -38. Let -2/7*c**d - 8/7*c - 8/7 = 0. What is c?
-2
Suppose 2*g + 16 = -2*g. Let z(k) = k**2 + 3*k + 1. Let r(m) = -m**2 - 2*m - 1. Let w = -10 - -5. Let c(f) = g*z(f) + w*r(f). Factor c(u).
(u - 1)**2
Suppose -4*k + m - 15 = 0, -2*k + 0*m - 15 = -3*m. Let n be k/33*2*-2. Let -2/11*z + 2/11*z**2 - n = 0. What is z?
-1, 2
Let d(m) be the first derivative of -2*m**3/27 - m**2/3 + 8*m/9 + 10. Factor d(h).
-2*(h - 1)*(h + 4)/9
Factor -o**5 + 5*o**5 - 4*o**3 + 3*o**2 + o**4 - 4*o**2.
o**2*(o - 1)*(o + 1)*(4*o + 1)
Let i be (-2)/(-4) + 4353/(-6). Let d = 2921/4 + i. Determine f, given that -33/4*f**3 + 21/4*f**4 + 0 - d*f**2 + 27/4*f**5 + 3/2*f = 0.
-1, 0, 2/9, 1
Suppose 0 = 2*r - 14*r + 48. Let q(k) be the first derivative of 2*k**2 + 0*k**3 + 2*k - 3 - k**r - 2/5*k**5. Factor q(n).
-2*(n - 1)*(n + 1)**3
Let r = -17 + 20. Let v(h) be the second derivative of 1/105*h**6 - 1/42*h**4 + 0 + 0*h**2 - 2*h + 1/21*h**r - 1/70*h**5. Factor v(o).
2*o*(o - 1)**2*(o + 1)/7
Suppose 0 = 26*i - 22*i - 20. Let m(b) be the first derivative of -1 + 37/6*b**3 + 2*b + 5*b**2 + 15/4*b**4 + 9/10*b**i. Factor m(f).
(f + 1)**2*(3*f + 2)**2/2
Let q(x) be the third derivative of 1/480*x**6 + 5*x**2 + 0*x + 1/80*x**5 + 1/24*x**3 + 0 + 1/32*x**4. Factor q(h).
(h + 1)**3/4
Let g(z) be the second derivative of 2/3*z**3 + 0 + 1/42*z**7 + 1/5*z**6 + z**4 + 0*z**2 + 13/20*z**5 + 3*z. Find t such that g(t) = 0.
-2, -1, 0
Let c(k) be the third derivative of 17*k**7/70 + k**6/4 + 7*k**4/8 - 6*k**2. Let n(b) = 5*b**4 + 3*b**3 + 2*b. Let w(g) = -2*c(g) + 21*n(g). Factor w(m).
3*m**3*(m + 1)
Let c(o) be the first derivative of -5*o**3/3 + 30*o**2 - 180*o - 24. Suppose c(w) = 0. Calculate w.
6
Let x be 630/(-39) + 2/13. Let n be 3/(-4) + (-12)/x. Factor n*b - 1/2*b**3 + 0 - 1/4*b**4 - 1/4*b**2.
-b**2*(b + 1)**2/4
Let z(m) be the second derivative of 0*m**3 - 1/7*m**2 + 1/42*m**4 + 3*m + 0. Factor z(p).
2*(p - 1)*(p + 1)/7
Determine u so that 1/2*u**3 - 108 + 54*u - 9*u**2 = 0.
6
Let b = -843 - -1689/2. Determine q so that b*q**2 + 6 - 6*q = 0.
2
Let i(j) be the first derivative of 3*j**5/5 + 2*j**4 + 7*j**3/3 + j**2 - 7. Factor i(s).
s*(s + 1)**2*(3*s + 2)
Let f(i) be the first derivative of i**8/2016 - i**7/630 + i**6/720 - 3*i**2/2 - 1. Let d(u) be the second derivative of f(u). Find c such that d(c) = 0.
0, 1
Suppose 6 - 26 = 5*x. Let w(k) = 9*k**2 - 19*k + 6. Let c(a) = -9*a**2 + 18*a - 6. Let v(p) = x*c(p) - 3*w(p). Factor v(n).
3*(n - 1)*(3*n - 2)
Let h(v) be the first derivative of -v**8/1120 + v**7/560 + v**6/240 - v**5/80 - 2*v**3/3 - 2. Let r(i) be the third derivative of h(i). Factor r(x).
-3*x*(x - 1)**2*(x + 1)/2
Factor -2/3*z + 2/3*z**2 - 1/6*z**3 + 0.
-z*(z - 2)**2/6
Let n be 12/(-10) - (0 - 2). Find f, given that -2/5*f**2 + n*f - 2/5 = 0.
1
Suppose 3*u - 8*u = -5*o - 35, -4*u + 30 = -3*o. Let x be (-1)/2*0/u. Let -2/3*g**4 - 2/3*g**2 - 4/3*g**3 + 0*g + x = 0. What is g?
-1, 0
Find w such that 2/11*w**2 - 6/11*w + 4/11 = 0.
1, 2
Let w(u) = 3*u**3 - 81*u**2 + 60*u + 18. Let r(x) = x**3 - 23*x**2 + 17*x + 5. Let g(k) = -18*r(k) + 5*w(k). Factor g(n).
-3*n*(n - 2)*(n - 1)
Determine j so that -18*j + 9 - 13*j**2 + 6*j + 16*j**2 = 0.
1, 3
Let q(z) be the first derivative of -z**3 - 9*z**2/2 + 7*z + 1. Let i(y) = -y**2 - y + 1. Let p(o) = -5*i(o) + q(o). What is l in p(l) = 0?
1
Find m, given that 0 + 4/5*m**2 - 2/5*m - 2/5*m**3 = 0.
0, 1
Let v(g) be the second derivative of g**6/240 - g**5/80 + g**4/96 - 4*g. Let v(z) = 0. Calculate z.
0, 1
Let 21*q**2 + 2*q - 21*q**4 - 7*q**3 + q**3 + 4*q = 0. What is q?
-1, -2/7, 0, 1
Let m(h) be the second derivative of -h**5/70 + h**3/21 - 3*h. Factor m(c).
-2*c*(c - 1)*(c + 1)/7
Factor -4*m**3 + 8*m**2 - 20/3*m + 2/3*m**4 + 2.
2*(m - 3)*(m - 1)**3/3
Let i(k) be the first derivative of k**6/60 - k**5/10 + 9*k**4/40 - 7*k**3/30 + k**2/10 - 9. Suppose i(z) = 0. What is z?
0, 1, 2
Let s(b) be the first derivative of 1/2*b**5 + 4 - 1/8*b**4 + 0*b**2 + 0*b**3 + 0*b - 1/3*b**6. Factor s(t).
-t**3*(t - 1)*(4*t - 1)/2
Factor -2/3*s**2 + 4/3 + 2/3*s.
-2*(s - 2)*(s + 1)/3
Factor -3/5*k**3 + 6/5*k**2 + 3/5*k - 6/5.
-3*(k - 2)*(k - 1)*(k + 1)/5
Let t(s) be the second derivative of 9*s + 24*s**2 + 0 - 4*s**3 + 1/4*s**4. Factor t(c).
3*(c - 4)**2
Let s be 1/(3 - (-10)/(-4)). Suppose -5*o + 0*o**4 - 12*o**2 + o - s*o**4 - 8*o**3 - 2 - 4*o = 0. Calculate o.
-1
Let s(p) be the third derivative of p**5/16 - 5*p**4/48 + 11*p**2. Factor s(v).
5*v*(3*v - 2)/4
Let i(d) be the second derivative of -d**5/45 - d**4/12 - d**3/9 + 5*d**2/2 - 2*d. Let o(v) be the first derivative of i(v). Factor o(k).
-2*(k + 1)*(2*k + 1)/3
Let q = 368 + -364. Factor 1/3*d**3 - d**2 + 1/3*d**q - 2/3 - 5/3*d.
(d - 2)*(d + 1)**3/3
Let a be (-40)/64*1/5. Let q = a + 3/8. Find o, given that 1/2*o + q*o**2 + 1/4 = 0.
-1
Let j(a) = -5*a**2 + 7*a - 3. Let g(m) = 16*m**2 - 22*m + 10. Let r = 3 - 1. Let o = r + -12. Let q(v) = o*j(v) - 3*g(v). Factor q(u).
2*u*(u - 2)
Let s(w) = -9 + w - 6*w - 3*w - w**2. Let p be s(-6). Factor 0*d - d - 2*d**2 + 2 + 3*d - 2*d**p.
-2*(d - 1)*(d + 1)**2
Let m be (-6)/8 - (-10)/(-8). Let z be (-8)/m + 2 + 0. Solve -4*f**3 + z*f + 15*f**4 + 23*f**5 - 23*f**3 - 15*f**2 - 2*f**5 = 0 for f.
-1, 0, 2/7, 1
Let c(z) = 6*z - 1. Let x be c(1). Let n(y) be the second derivative of 1/9*y**3 + 0 + 2/9*y**4 + 1/63*y**7 - 2*y + 0*y**2 + 1/5*y**x + 4/45*y**6. Factor n(r).
2*r*(r + 1)**4/3
Suppose 0 = -q + 10*q - 18. Factor -2/5*l - 8/15*l**q + 2/15.
-2*(l + 1)*(4*l - 1)/15
Let j be 12/(-18) - 52/3. Let n be 2/14*j/(-9). Solve 2/7 + n*t**2 - 4/7*