1. Let y be 42/28*(1 - p). Factor y*m**2 - 4 - 5*m**2 - 2*m**2 - 4 - 12*m.
-4*(m + 1)*(m + 2)
Let u(b) = -20*b**3 + 168*b**2 - 148*b - 304. Let f(y) = 2*y**3 - 2*y**2 + y + 1. Let v(a) = 8*f(a) + u(a). Find m, given that v(m) = 0.
-1, 2, 37
Determine o so that 122*o - 2*o**2 - 702 - 1681 + 58*o - 1667 = 0.
45
Let v(x) = -x**3 - 8*x**2 - 7*x + 4. Let a be v(-7). Suppose -a*g = -3*g - 2. Factor -8/3*r**4 - 4/3*r - 2/3 + 2*r**g + 8/3*r**3.
-2*(r - 1)**2*(2*r + 1)**2/3
Suppose 0 + 3/7*w**2 - 3/7*w = 0. What is w?
0, 1
Let -21/4*p**2 + 21/4 + 1/4*p**3 - 1/4*p = 0. What is p?
-1, 1, 21
Let c(a) be the first derivative of a**4/28 + 4*a**3/21 + a**2/14 - 6*a/7 - 71. Factor c(i).
(i - 1)*(i + 2)*(i + 3)/7
Let t(m) be the first derivative of m**4/28 - 11*m**3/21 - 316. Solve t(l) = 0.
0, 11
Let q(m) be the second derivative of 3*m**5/40 + 9*m**4/8 + 7*m**3/2 - 3*m + 3. Solve q(u) = 0.
-7, -2, 0
Let m be (75/(-125))/((-156)/40). Solve m*r**4 - 2/13*r**2 + 2/13*r**5 + 0 + 0*r - 2/13*r**3 = 0.
-1, 0, 1
Let c(u) be the first derivative of u**3 + 105*u**2 + 3675*u - 185. Solve c(h) = 0 for h.
-35
Let x(w) be the first derivative of -6 - 4*w + 4/3*w**3 + 0*w**2. Factor x(m).
4*(m - 1)*(m + 1)
Let l(k) be the third derivative of -k**8/560 - k**7/20 - 49*k**6/120 - 14*k**3/3 - 23*k**2. Let x(v) be the first derivative of l(v). Factor x(f).
-3*f**2*(f + 7)**2
Let j be (32/10)/(2/5). Factor 15 - 11 - 12*o + j + 3*o**2 + 0.
3*(o - 2)**2
Factor 12*b**2 + 18*b - 347*b**3 + 176*b**3 + 173*b**3.
2*b*(b + 3)**2
Suppose -48*c = -50*c. Determine z so that 5/4*z**3 + 0*z**4 + 0*z**2 - 5/4*z**5 + c + 0*z = 0.
-1, 0, 1
Let z = 1942 + -9709/5. Solve 0*i**2 + 3/5*i**3 + 0 + z*i**4 + 0*i = 0.
-3, 0
Let s(b) = -2*b**2 - 6*b + 4. Let p(g) = 1. Let v(j) = 4*p(j) - s(j). Solve v(o) = 0.
-3, 0
Suppose 3*y - 57 = -42. Let r(x) be the second derivative of -1/6*x**3 + 0*x**2 - 1/15*x**6 - x + 0*x**y + 0 + 1/6*x**4 + 1/42*x**7. Factor r(u).
u*(u - 1)**3*(u + 1)
Let m(d) be the first derivative of d**6/8 + 3*d**5/20 - 15*d**4/16 - d**3/4 + 3*d**2 - 3*d + 61. Factor m(o).
3*(o - 1)**3*(o + 2)**2/4
Let z = 1448/3 + -209966/435. Let f = 276/1015 - z. Determine b so that 2/7 + 2/7*b**3 - f*b**2 - 2/7*b = 0.
-1, 1
Let a(s) be the third derivative of s**10/529200 + s**9/35280 + s**8/7840 - 19*s**5/60 - 11*s**2. Let v(h) be the third derivative of a(h). Factor v(p).
2*p**2*(p + 3)**2/7
Let g be 18/(-48) - (-54)/16. Suppose 6*a - g = 15. Factor 0*x - 2/3*x**a - 1/2*x**2 - 1/6*x**4 + 0.
-x**2*(x + 1)*(x + 3)/6
Determine p, given that 4*p**4 - 800*p + 43*p**3 + 137*p**2 + 2*p**4 + 29*p**3 - 2*p**4 + 103*p**2 = 0.
-10, 0, 2
Find a such that -15*a**2 - 41 + 19*a + 4 - 3*a**3 - 11 + 47*a = 0.
-8, 1, 2
Solve -a**5 + 234*a**2 + 86/3*a**4 - 184/3 - 268/3*a - 421/3*a**3 = 0.
-1/3, 2, 23
Let l(y) = -y**3 + 10*y**2 - y + 18. Let c be l(10). Let k be (-2)/c + (-143)/(-156). Factor -77/6*x**3 + 16/3*x**2 + 0 + 49/6*x**4 - k*x.
x*(x - 1)*(7*x - 2)**2/6
Let u(o) be the second derivative of -o**5/25 + 94*o**4/15 - 74*o**3/3 + 184*o**2/5 + 347*o. Factor u(m).
-4*(m - 92)*(m - 1)**2/5
Let x = 6 + -6. Let l = x - -291. Factor 10*p**4 - l*p**3 + 297*p**3 - 4*p**2 + 3*p - 3*p.
2*p**2*(p + 1)*(5*p - 2)
Suppose -19*i - 40 = -24*i. Let t(y) = y**3 - 10*y**2 + 17*y - 6. Let c be t(i). Factor 2/7*z**4 + 0*z**c - 2/7 - 4/7*z + 4/7*z**3.
2*(z - 1)*(z + 1)**3/7
Let -14/3*b**4 + 4/3*b**3 + 14/3*b**2 + 0 - 4/3*b = 0. What is b?
-1, 0, 2/7, 1
Factor 312*n**2 + 274*n**3 - 368*n**2 - 270*n**3 + 196*n.
4*n*(n - 7)**2
Let i(l) be the third derivative of -l**7/350 - 3*l**6/100 + l**5/100 + 3*l**4/20 - 2*l**2 - 23. Factor i(g).
-3*g*(g - 1)*(g + 1)*(g + 6)/5
Let 2/19*x**3 - 8/19*x**2 + 8/19*x + 0 = 0. What is x?
0, 2
Let b = 3/103 + 288/721. Suppose 9/7*u**2 - b - 12/7*u + 30/7*u**3 - 24/7*u**4 = 0. What is u?
-1/2, -1/4, 1
Factor -9/2*n**4 + 2*n - 25/2*n**3 + 0 - 6*n**2.
-n*(n + 1)*(n + 2)*(9*n - 2)/2
Factor -12150 + 537/2*a**2 + 11880*a + 3/2*a**3.
3*(a - 1)*(a + 90)**2/2
Let b(g) be the first derivative of -3/100*g**5 + 0*g**2 + 0*g**3 + 1/20*g**4 + 9 + 8*g. Let c(w) be the first derivative of b(w). Factor c(y).
-3*y**2*(y - 1)/5
Let i(t) be the second derivative of -t**7/2520 - t**6/540 + t**5/360 + t**4/36 + 7*t**3/6 - 6*t. Let h(q) be the second derivative of i(q). Factor h(b).
-(b - 1)*(b + 1)*(b + 2)/3
Let l be -13 + 13 + 22/99. Solve 2/9*b**2 - l*b + 0 = 0.
0, 1
Let z(r) = r**3 - r**2 + r + 1. Let c(g) = 3*g**3 + 5*g**2 - 23*g + 31. Suppose 5*q = 4*p + 4, 0 = -q - 5*p + 14 + 10. Let y(u) = q*z(u) - c(u). Factor y(x).
(x - 3)**3
Let l be 108/48 + 1/(-4). Let j(n) be the second derivative of 1/12*n**4 - 1/10*n**5 + 1/16*n**l - 7*n + 7/48*n**3 + 0. Factor j(x).
-(x - 1)*(4*x + 1)**2/8
Let z = 8101/2 - 4049. Factor 3/2*x**5 - z*x**3 - 3/2*x**2 + 0 + 3/2*x**4 + 0*x.
3*x**2*(x - 1)*(x + 1)**2/2
Let i(b) be the first derivative of 0*b**2 - 18 - 1/3*b + 1/9*b**3. Factor i(j).
(j - 1)*(j + 1)/3
Factor 4/7*y**2 - 12/7*y - 16.
4*(y - 7)*(y + 4)/7
Let c(p) be the second derivative of -p**8/10920 + p**7/1365 - p**6/468 + p**5/390 + p**3/3 - 7*p. Let g(x) be the second derivative of c(x). Factor g(y).
-2*y*(y - 2)*(y - 1)**2/13
Let w(s) be the second derivative of s**5/4 + 5*s**4/3 - 35*s**3/2 + 66*s. Let w(c) = 0. What is c?
-7, 0, 3
Let b(d) be the second derivative of -5/12*d**4 - 12*d - 1/20*d**5 + 0*d**2 + 0*d**3 + 0. Factor b(f).
-f**2*(f + 5)
Let z(k) be the second derivative of 1/4*k**4 + 1/3*k**3 + 1/60*k**6 + 1/4*k**2 + 0 + 4*k + 1/10*k**5. Factor z(d).
(d + 1)**4/2
Factor -5 + 29*m**2 + 10*m - 31*m**2 - 4 - 3.
-2*(m - 3)*(m - 2)
Suppose -w = 3*w. Let m be (w - 2)/(2/(-6)). Solve m*f**3 - 10*f**3 + 2*f**3 - 2*f**3 = 0 for f.
0
Let t = -5/129 - -16/43. Factor 1/3*m**3 - t*m + 0*m**2 + 0.
m*(m - 1)*(m + 1)/3
Find r, given that 1/5*r**2 - 4*r + 20 = 0.
10
Let h(v) be the third derivative of v**8/168 + v**7/35 + 2*v**2 - 116*v. Let h(z) = 0. What is z?
-3, 0
Let f = 41 - 37. Factor -38 - 15*r**5 + 38 + f*r**3 - 5*r**2 - 35*r**4 - 29*r**3.
-5*r**2*(r + 1)**2*(3*r + 1)
Let p(z) = 3*z - 6. Let k be p(3). Let r(f) = 7 + 2 + k*f**2 + 14*f - 5. Let g(c) = 5*c**2 + 29*c + 8. Let o(b) = -2*g(b) + 5*r(b). Solve o(m) = 0 for m.
-2, -2/5
Let d(x) be the second derivative of -x**4/4 + 13*x**3/2 - 18*x**2 - 798*x. Factor d(j).
-3*(j - 12)*(j - 1)
Let t(r) = -2*r**4 - 4*r**3 + 16*r**2 + 12*r + 10. Let b(v) = v**3 - v**2 + v - 1. Let c(a) = 4*b(a) + t(a). Factor c(h).
-2*(h - 3)*(h + 1)**3
Let p be (2 - (-8)/(-5)) + (611/(-130) - -5). Find d, given that -7/10*d**3 + p*d - 1/5 + 1/5*d**2 = 0.
-1, 2/7, 1
Let s(x) be the third derivative of x**5/60 + 13*x**4/12 + 374*x**2. Factor s(j).
j*(j + 26)
Let g(m) = -8*m**2 - 29*m + 3. Let f(l) be the first derivative of -2*l**3/3 - 7*l**2/2 + l + 3. Let w(c) = -18*f(c) + 4*g(c). Suppose w(y) = 0. What is y?
-3, 1/2
Let k(c) be the second derivative of 10/9*c**3 + 25/3*c**2 - 12*c + 1/18*c**4 + 0. Factor k(f).
2*(f + 5)**2/3
Solve -70*l**3 + 10*l**5 + 128*l**3 - 12*l**5 + 4*l**4 + 84*l**2 = 0 for l.
-3, -2, 0, 7
Let i(w) be the third derivative of -w**8/20160 + w**6/720 - w**5/180 + 23*w**4/24 + 4*w**2. Let k(q) be the second derivative of i(q). Factor k(n).
-(n - 1)**2*(n + 2)/3
Suppose -7 = -2*t + 1, 16 = -2*q + 5*t. Let 0*o**2 - q*o**2 - o - 3*o**2 - 9*o = 0. Calculate o.
-2, 0
Suppose 2*o - 2*n = -4 - 0, -n - 2 = -3*o. Solve 4 + 1 + p**o - 3*p - 7 + p**2 = 0.
-1/2, 2
Suppose t + 3*t = -0*t. Suppose t = -5*w + 19*w - 28. Factor 4/7 - 6/7*a + 0*a**w + 2/7*a**3.
2*(a - 1)**2*(a + 2)/7
Let m(a) be the third derivative of -a**5/12 + 5*a**4/24 + 10*a**3 + a**2 - 207. Factor m(i).
-5*(i - 4)*(i + 3)
Let p(b) be the third derivative of b**8/588 - b**7/105 + b**5/21 - b**4/42 - b**3/7 + 101*b**2. Determine q so that p(q) = 0.
-1, -1/2, 1, 3
Let 13*u**3 + 6*u**4 + 23*u**3 + 27*u**3 + 75*u**2 + 14*u**3 - 14*u**3 - 54*u = 0. What is u?
-9, -2, 0, 1/2
Let t(f) be the first derivative of -5/11*f**4 + 2/11*f + 6 + 8/11*f**3 + 6/55*f**5 - 6/11*f**2. Factor t(l).
2*(l - 1)**3*(3*l - 1)/11
Let b(m) be the third derivative of 0*m + 0*m**3 + 1/1512*m**8 - 38*m**2 - 1/135*m**5 + 0*m**6 - 1/108*m**4 + 0 + 2/945*m**7. Factor b(t).
2*t*(t - 1)*(t + 1)**3/9
Let u(g) = -g**2 + 29*g + 28. Let j(h) = 30*h + 27. Let a(p) = -2*