. Let k(b) = b. Let l(v) = -2*v**2 + 2*v - 2. Let g(j) = m*k(j) - l(j). Factor g(q).
2*(q - 1)**2
Let q(g) = -3*g**2 - 11*g + 3. Let u = 35 - 57. Let p(z) = z**2 + 3*z - 1. Let k(t) = u*p(t) - 6*q(t). Factor k(n).
-4*(n - 1)*(n + 1)
Let j be 6/16 + (-341)/2728. Factor -5/4*z**3 - 3/2*z**2 - j*z**4 + 0 + 0*z.
-z**2*(z + 2)*(z + 3)/4
Let n(k) be the first derivative of -k**4/5 + 2*k**3/5 - k**2/5 - 77. Let n(r) = 0. Calculate r.
0, 1/2, 1
Let u(r) be the first derivative of -3*r**4/4 + r**3/3 + 3*r**2/2 - r + 232. Factor u(m).
-(m - 1)*(m + 1)*(3*m - 1)
Suppose -1 - 1 = -h. Let m be 2/(8/6)*h. Suppose 3*t**2 + 30*t**m + 57*t**4 + 6*t**2 + 18*t**4 - 6*t**2 = 0. What is t?
-1/5, 0
Let u(o) be the second derivative of -o**6/50 + 3*o**5/50 + o**4/20 - o**3/5 + 63*o. What is p in u(p) = 0?
-1, 0, 1, 2
Let f(p) be the third derivative of -p**6/150 - p**5/30 + 7*p**4/15 + p**3 - 99*p**2 + p. Solve f(d) = 0.
-5, -1/2, 3
Suppose 0*w + 12 = w + 5*v, -12 = -4*w - 2*v. Factor 2*h + 3 - h**2 + 2*h**2 - 5*h**2 + 3*h**w.
-(h - 3)*(h + 1)
Let x(z) be the third derivative of -z**6/30 + 7*z**5/15 - 4*z**4/3 - 32*z**3/3 - 26*z**2. Let x(u) = 0. What is u?
-1, 4
Let q(g) be the third derivative of -32/27*g**3 - 5/27*g**5 - 1/90*g**6 - 28/27*g**4 + 0*g + 0 + 17*g**2. Find o, given that q(o) = 0.
-4, -1/3
Suppose -2/7*c**3 + 2*c + 12/7*c**2 + 0 = 0. Calculate c.
-1, 0, 7
Suppose 2*o + 4*b = -12, o + o - 23 = 3*b. Suppose 4*f = -5*c + 2*c + 21, -6 = 2*c - o*f. Factor 0*g**2 + 0*g + 0 - 2/3*g**4 + 2/3*g**c.
-2*g**3*(g - 1)/3
Let z(i) be the second derivative of -9*i**5/140 - 13*i**4/21 - 11*i**3/14 + 5*i**2/7 + i + 61. Determine r so that z(r) = 0.
-5, -1, 2/9
Let f(y) = -3*y**5 + 7*y**4 - 21*y**3 + 19*y**2 - 6*y. Let v(m) = -16*m**5 + 34*m**4 - 105*m**3 + 95*m**2 - 30*m. Let s(w) = -33*f(w) + 6*v(w). Factor s(j).
3*j*(j - 6)*(j - 1)**3
Let b be (-12033)/42*(-1)/3. Let j = 96 - b. Factor 1/2*g + j*g**2 + 0.
g*(g + 1)/2
Let c be (-6)/(-15) - ((-6)/10 + -1). Factor -13*a + 0*a**4 - 5*a**4 - 12*a**c + 4*a**3 - 7*a + 9*a**4 - 8.
4*(a - 2)*(a + 1)**3
Suppose 0 = 3*n - 15*n - 48. Let t be (-1 - (-2 - -3) - 4)/n. Determine h so that -21/4*h + t + 9/4*h**2 = 0.
1/3, 2
Let c = -14815 + 162971/11. Suppose -116/11*a**3 - c*a - 46/11*a**4 - 6/11*a**5 + 18/11 - 100/11*a**2 = 0. Calculate a.
-3, -1, 1/3
Let l(v) be the second derivative of 24*v**2 + 7/10*v**6 + 33/5*v**5 + 24*v**4 + 40*v**3 + 0 - 11*v. Factor l(y).
3*(y + 2)**3*(7*y + 2)
Factor -104*h - 3*h**3 - 32 + 727*h**2 - 33*h**3 - 555*h**2.
-4*(h - 4)*(h - 1)*(9*h + 2)
Let g be (-54)/(-18) + (-1 - -1). Suppose 0 = -g*k + 9 + 15. Let -2 - 15*j**5 - 8*j**4 + 5*j + 50*j**3 - k + 60*j**2 - 2*j**4 = 0. What is j?
-1, 1/3, 2
Let w be 6/33 - (-4)/88*29. Find u, given that w + 0*u - 3/8*u**2 = 0.
-2, 2
Let h = -241 - -1695/7. Let a = 955/6 + -6661/42. Factor -h*k + 4/7 + a*k**2.
4*(k - 1)**2/7
Suppose 0 = 9*y - 8*y - 4. Find q, given that -24*q**y - 13*q**2 + 33*q**2 - 14*q**2 + 15*q**5 + 3*q**3 = 0.
-2/5, 0, 1
Let a(o) be the second derivative of -23*o - 2/3*o**2 - 4/27*o**4 - 14/27*o**3 + 0. Factor a(z).
-4*(z + 1)*(4*z + 3)/9
Determine k so that -336/5*k + 311/5*k**3 + 5*k**5 - 33*k**4 - 31/5*k**2 + 196/5 = 0.
-1, 1, 14/5
Suppose 0 + 4/5*s + 2/5*s**3 - 6/5*s**2 = 0. Calculate s.
0, 1, 2
Suppose 5*w - 31 = -4*c - 2, -3*w = -c - 31. Let -67*p**2 + 2 - 18*p - 2*p**3 - 10*p**3 - w*p**5 + 39*p**5 - 46*p**4 + 111*p**2 = 0. Calculate p.
-1, 1/5, 1/3, 1
Let x be 10 - (-2 - -20 - 11). Find u, given that -6/11*u + 0*u**2 + 2/11*u**x - 4/11 = 0.
-1, 2
Let c be -30*((-2)/(-4))/(-1). Suppose 4*u + c = 9*u. Factor -t**2 - 4*t + 8*t**2 - 5*t**2 + 2*t**u.
2*t*(t - 1)*(t + 2)
Let b(o) = o**2 + o + 1. Let n(l) = 16*l**2 + 2. Let u(j) = j - 1. Let g be u(3). Let z(x) = g*n(x) - 12*b(x). Factor z(p).
4*(p - 1)*(5*p + 2)
Let a(m) = m**2 - 6*m + 6. Let y(g) be the first derivative of g**2/2 - g + 6. Let p = 34 - 33. Let f(s) = p*a(s) + 6*y(s). Find d such that f(d) = 0.
0
Find x, given that 12/7 - 6/7*x**2 - 6/7*x = 0.
-2, 1
Determine n, given that -6/17*n**5 + 0 + 4*n**4 + 20/17*n**2 - 82/17*n**3 + 0*n = 0.
0, 1/3, 1, 10
Factor 383*y - y**3 + 155*y**2 - 621 + 0*y**3 + 4*y - 206*y**2 - 2*y**3.
-3*(y - 3)**2*(y + 23)
Let p = 1/46 + 10/69. Let h(k) be the second derivative of -p*k**4 + 0*k**2 - k**3 + 0 - 2*k. Let h(t) = 0. What is t?
-3, 0
Let z(w) be the first derivative of -4/3*w**3 + w**4 + 3 + 0*w**2 - 2/3*w**6 + 0*w + 4/5*w**5. Factor z(u).
-4*u**2*(u - 1)**2*(u + 1)
Let j = -29092 - -29097. Find q such that 7/4 - 3/4*q**2 - j*q = 0.
-7, 1/3
Let r(n) be the third derivative of -n**6/60 - n**5/10 + 3*n**4/4 - 5*n**3/3 - 5*n**2 + 8. Factor r(s).
-2*(s - 1)**2*(s + 5)
Let m(t) = 21*t**3 - 11*t**2 - t + 3. Suppose -2*r - 24 = 6*r. Let j(z) = 20*z**3 - 12*z**2 - 2*z + 2. Let q(y) = r*j(y) + 2*m(y). Factor q(l).
-2*l*(l - 1)*(9*l + 2)
Let v(b) = -b - 1. Let o be v(1). Let w be 6/(o/12*-9). Solve -w*p + 2 - 2 + 5*p**2 - 7*p**2 = 0 for p.
-2, 0
Factor 14*r + 1/2*r**2 + 98.
(r + 14)**2/2
Let y(z) = 54*z - 157. Let o be y(3). Factor -2/5*h**4 + 0*h + 2/5*h**2 + 2/5*h**o + 0 - 2/5*h**3.
2*h**2*(h - 1)**2*(h + 1)/5
Let l(p) be the second derivative of p**4/6 - 3*p**3/2 - 7*p**2/2 - 2*p. Let g be l(7). Factor g*r + 2 - 14*r + 2*r**2 - 18*r.
2*(r - 1)**2
Suppose -4*o = 4*n - 24, -2*n + 2*o + 27 = 7*o. Let b = -4 - -6. Find p, given that -10*p**3 - 5*p + 12*p**2 + 3*p**4 - n + b - p = 0.
1/3, 1
Let g(c) be the second derivative of -2*c**6/105 + 6*c**5/7 - 64*c**4/7 - 1024*c**3/21 + 161*c + 3. Solve g(w) = 0.
-2, 0, 16
Let s(y) be the second derivative of y**6/420 + y**5/105 - y**4/84 - 2*y**3/21 - 9*y**2/2 - 8*y. Let l(z) be the first derivative of s(z). Factor l(d).
2*(d - 1)*(d + 1)*(d + 2)/7
Suppose 4*z = -4*j - 12, 4*j - 7*j = 9. Let b(t) be the first derivative of 3 + z*t**3 + 0*t - 1/4*t**4 + 0*t**2. Factor b(o).
-o**3
Let p(u) be the first derivative of -2/3*u + 1/12*u**4 + 2/9*u**3 - 1/6*u**2 - 9. Suppose p(h) = 0. What is h?
-2, -1, 1
Let z(x) = -x**3 - 5*x**2 + 12*x - 4. Let q be z(2). Let w be (q/(-33))/(48/18 + -2). Factor -6/11 + 2/11*p**2 - w*p.
2*(p - 3)*(p + 1)/11
Let u(k) be the first derivative of -49*k**6/6 - 154*k**5/5 + 17*k**4 + 584*k**3/3 + 256*k**2 + 128*k + 69. Suppose u(z) = 0. Calculate z.
-2, -4/7, 2
Suppose 27*f = 7*f. Let y(x) be the first derivative of 2 + f*x**2 + 2/3*x**3 + 1/2*x**4 + 0*x. Factor y(c).
2*c**2*(c + 1)
Suppose 5 = 3*c - 10. Suppose 14*d**2 - 7*d**5 + 3 - c - 6*d + 9*d - 12*d**4 + 4*d**3 = 0. Calculate d.
-1, 2/7, 1
Let a(c) = -c**3 + 41*c**2 + 576*c + 46. Let d be a(-11). Suppose 2*f**d + 0 - 3*f - 1/3*f**3 = 0. Calculate f.
0, 3
Let p be (16/(-8))/((-112)/32). Factor 2/7 - p*y + 2/7*y**2.
2*(y - 1)**2/7
Let j = -53 - -84. Let l = j + -29. Factor -149*z - 7*z**l + 161*z + 2 + 2.
-(z - 2)*(7*z + 2)
Let x = -269 - -4843/18. Let a(z) be the second derivative of 0 + 0*z**2 - x*z**3 + 1/72*z**4 + z - 1/180*z**6 + 1/60*z**5. Factor a(n).
-n*(n - 2)*(n - 1)*(n + 1)/6
Let c be -4 + 13/4 - (-30)/8. Suppose c*u - 15 = 3*b, -6*b + 3 = -7*b. Factor 2*m**u - 1/2*m**3 - 2*m + 0.
-m*(m - 2)**2/2
Let y = -2398 + 2398. Let h(z) be the second derivative of -1/3*z**3 + 2*z - 3/4*z**2 - 1/24*z**4 + y. Solve h(u) = 0.
-3, -1
Let x(i) be the first derivative of 1/3*i**4 + 4/9*i**3 + 0*i + 28 - 4/3*i**2. Factor x(g).
4*g*(g - 1)*(g + 2)/3
Factor 263*j - 97 - 56*j**2 - 123*j + 4*j**3 + 9.
4*(j - 11)*(j - 2)*(j - 1)
Let w(h) be the second derivative of h**4/30 - 21*h**3/5 + 8*h + 37. Factor w(p).
2*p*(p - 63)/5
Let w(b) be the second derivative of -b**5/30 + b**4/18 + 7*b**3/3 - 15*b**2 + 2*b + 224. Determine x, given that w(x) = 0.
-5, 3
Suppose 4*s = 0, p + 3*s + 7 + 18 = 0. Let o be ((-6)/p)/((-6)/(-10)). Factor -o*c**2 - 2/5*c**3 + 0*c + 0.
-2*c**2*(c + 1)/5
Let u(a) be the second derivative of a**7/231 - 9*a**5/110 - 2*a**4/33 + 4*a**3/11 + 70*a + 2. Find r such that u(r) = 0.
-2, 0, 1, 3
Let y(z) be the second derivative of -z**5/240 - z**4/24 - z**3/6 - 4*z**2 - 10*z. Let a(o) be the first derivative of y(o). Factor a(j).
-(j + 2)**2/4
Let n(x) = -15. Let p(o) = o - 45. Let b(v) = 8*n(v) - 3*p(v). Let d be b(5). Factor -a**2 + 0*a**3 + 0*a**3 + d*a**2 + a**3.
a**2*(a - 1)
Let s(u) = -2*u**2 + 46*u - 44. Let m be s(22). Let b(a) 