 + 2/3*d.
(d - 2)**2*(d + 1)**2/6
Let z be 60/45 + 314/(-6). Let c = 55 + z. Let -7*p**c + 0 - p**3 + 9*p + 0 - 8*p**3 + 5*p**2 + 2 = 0. Calculate p.
-1, -2/7, 1
Suppose r - 5*r - 8 = 2*k, 5*k - 5*r = 10. Let s(x) = -2707*x - 2707. Let i be s(-1). Solve i + 4/3*o**5 + 0*o**2 - 4*o**4 + 8/3*o**3 + k*o = 0 for o.
0, 1, 2
Let h(l) = -6*l**2 + 78*l + 4971. Let p be h(36). Factor 20/23*f**2 + 0 + 2/23*f**p - 22/23*f.
2*f*(f - 1)*(f + 11)/23
Let z(m) = -2*m**2 - 94*m + 108. Let p(b) = 2*b. Let j(a) = 6*p(a) - z(a). Factor j(k).
2*(k - 1)*(k + 54)
Suppose 320*x = 313*x + 105. Suppose 41 = x*c - 34. Let -9/2*p - c + 1/2*p**2 = 0. Calculate p.
-1, 10
Let g(t) = 3*t**5 - 46*t**4 + 42*t**3 + 21*t**2 - 20*t. Let k(r) = r**5 - 3*r**3 - r**2 + 3*r. Let h(s) = -g(s) - 5*k(s). Let h(z) = 0. What is z?
-1/2, 0, 1/4, 1, 5
Determine k, given that -6966*k + 2580343 + 3*k**2 + 996*k + 319727 + 70005 = 0.
995
Factor 53871*t**2 + 800*t - 26775*t**2 + 2*t**3 - 26890*t**2 + 792.
2*(t + 2)**2*(t + 99)
Let k(n) be the first derivative of -7*n**4/12 - 103*n**3/6 + 15*n**2 + 185*n + 33. Let q(x) be the first derivative of k(x). Determine s, given that q(s) = 0.
-15, 2/7
Let m(w) be the first derivative of 3*w**4/8 + 17*w**3/2 + 225*w**2/4 + 297*w/2 - 394. Factor m(h).
3*(h + 3)**2*(h + 11)/2
Let u(i) be the second derivative of i**4/12 - 22*i**3/3 + 125*i**2/2 - 2*i + 6. Let z be u(41). Solve 6/17 + 2/17*a**z - 8/17*a = 0 for a.
1, 3
Let d(v) = 2116*v**3 + 2854*v**2 + 800*v + 52. Let t(h) = -h**2 + 6. Let c(j) = d(j) + 2*t(j). Suppose c(l) = 0. What is l?
-1, -4/23
Suppose 3163*k - 131811 = 76947. Determine z, given that -k*z - 18 - 121/2*z**2 = 0.
-6/11
Factor 28/3 + x - 1/3*x**2.
-(x - 7)*(x + 4)/3
Let m(h) be the third derivative of -h**6/360 + 97*h**5/90 - 191*h**4/24 + 2135*h**2. Suppose m(u) = 0. Calculate u.
0, 3, 191
Let a(h) = -9*h**2 - 1686*h - 1651. Let k(g) = 4*g**2 + 842*g + 826. Let x(z) = -6*a(z) - 13*k(z). Factor x(n).
2*(n - 416)*(n + 1)
Suppose 0 = -4*t - v + 18, 2 = -10*v + 9*v. Let a(m) be the first derivative of 0*m - 3/2*m**4 + 3*m**3 + 0*m**2 + 1/5*m**t - 4. Suppose a(c) = 0. Calculate c.
0, 3
Let z(i) = 45*i + 76. Let j(v) = -9*v - 15. Let m(x) = 11*j(x) + 2*z(x). Let u be m(-2). Determine b, given that 22*b - 2*b**2 - 22 - u*b + 7*b = 0.
1, 11
Let c(k) = -k**2 - 14*k - 31. Let o be c(-11). Solve 38*l - 9*l**4 + 10*l + 13*l**4 + 12*l**3 - 64*l**o = 0 for l.
-6, 0, 1, 2
Let b(a) be the first derivative of -42/5*a**5 + 16*a**3 + 3/2*a**4 + 5/2*a**6 - 21/2*a**2 - 6*a + 124. Find s, given that b(s) = 0.
-1, -1/5, 1, 2
Find d such that -3*d**4 - 119520*d - 8425*d**2 - 9281*d**2 + 480*d**3 + 1570318 - 1756321 = 0.
-3, 83
Let 6*a**5 + 114*a**2 + 81/2*a**4 + 27/2 + 63*a + 99*a**3 = 0. Calculate a.
-3, -1, -3/4
Let n = 73 - 71. Factor -31*x + 16*x**4 + 52*x**n + 24*x - 12*x**4 - 24*x**3 + 16 - 41*x.
4*(x - 2)**2*(x - 1)**2
Let x(s) be the first derivative of -s**5/30 + 41*s**4/24 + 85*s**3/18 + 43*s**2/12 + 847. Solve x(t) = 0.
-1, 0, 43
Suppose 27*m - 140 = 13*m. Factor 1615*f**5 - 30*f**4 + 40 - m*f**2 - 22*f + 82*f - 1620*f**5 - 55*f**3.
-5*(f - 1)*(f + 1)*(f + 2)**3
Suppose -13/2*b + 87/4 + 1/4*b**4 - 22*b**2 + 13/2*b**3 = 0. Calculate b.
-29, -1, 1, 3
Let k(r) be the first derivative of -1/4*r**4 - 204 + 53/2*r**2 - 27*r - 25/3*r**3. Find p, given that k(p) = 0.
-27, 1
Find d, given that 2/5*d**3 - 41/5*d**2 + 25 - 46*d = 0.
-5, 1/2, 25
Let d(x) = x**3 + 386*x**2 + 4494*x + 2248. Let v be d(-374). What is u in 44/9*u**2 - 10/9*u**v + 2/3*u**3 - 8/3*u - 16/9 = 0?
-2, -2/5, 1, 2
Find x, given that 52*x - 50324*x**3 - 256 - 388*x**2 - 4*x**4 + 50396*x**3 + 524*x = 0.
1, 8
Let b = 27941/15 - 5588/3. Let t(l) be the second derivative of 0 + b*l**4 + 0*l**3 - 1/50*l**6 + 0*l**2 + 0*l**5 + 1/210*l**7 + 16*l. Factor t(g).
g**2*(g - 2)**2*(g + 1)/5
Let p be (-100)/(-15) - (-26)/(-39) - 4. Let l(d) be the second derivative of 0 + 12*d + 2*d**p + 5/6*d**3 + 1/12*d**4. Factor l(y).
(y + 1)*(y + 4)
Let u(l) be the second derivative of 2*l**6/15 + 11*l**5/15 - 2*l**4/3 - 88*l**3/9 - 16*l**2 + 1419*l - 3. Find n, given that u(n) = 0.
-3, -2, -2/3, 2
Suppose 996 = -4*b - 1720. Let g = b + 2038/3. Factor 2/3*j**2 - 2/3 + g*j**3 - 1/3*j.
(j - 1)*(j + 1)*(j + 2)/3
Let y(i) be the first derivative of 5/6*i**2 - 2/3*i + 7/9*i**3 + 2. Factor y(o).
(o + 1)*(7*o - 2)/3
Let -2/17*b**2 - 390/17 - 88/17*b = 0. Calculate b.
-39, -5
Let h = 67609/5421520 - -2/67769. Let x(z) be the third derivative of 1/3*z**3 - 1/16*z**4 + 1/420*z**7 - 1/24*z**5 + 0*z + h*z**6 + 8*z**2 + 0. Factor x(k).
(k - 1)**2*(k + 1)*(k + 4)/2
Let m(x) be the first derivative of -1/8*x**2 - 1/32*x**4 + 0*x + 81 - 1/8*x**3. Suppose m(j) = 0. What is j?
-2, -1, 0
Suppose -3*u = -4*v + 48, 4*v + 7*u - 48 = 4*u. Let o be ((-4)/v)/(6/(-120)). Find j, given that 10/3*j**3 + o*j - 46/3*j**2 + 16/3 = 0.
-2/5, 1, 4
Let g(a) be the third derivative of -a**7/350 + 11*a**6/50 - 17*a**5/20 + 21*a**4/20 + a**2 - 1069*a. Factor g(v).
-3*v*(v - 42)*(v - 1)**2/5
Let s = 339 + -92. What is d in -151*d + s*d + 39*d**2 + 2*d**3 + 60 + d**3 = 0?
-10, -2, -1
Suppose 0 = -k + r - 42 + 128, 3*k - 4*r - 257 = 0. Factor -128 - 4*q**3 - 15*q + 105*q - 131*q - k*q - 40*q**2.
-4*(q + 2)*(q + 4)**2
Solve -14*u + 45/2*u**2 + 105/2*u**3 + 0 + 3/2*u**5 + 35/2*u**4 = 0 for u.
-7, -4, -1, 0, 1/3
Let a(g) = 3*g**3 - 39*g**2 - g + 15. Let y be a(13). Suppose q = y - 0. Suppose 2/3 + 4/3*u + 2/3*u**q = 0. Calculate u.
-1
Let z(x) be the first derivative of 825/2*x**2 - 49 - 40*x**3 - 1210*x + 5/4*x**4. What is n in z(n) = 0?
2, 11
Let w(a) be the second derivative of 0 - 1/5*a**5 + 23*a + 8*a**2 - 16/3*a**3 + 5/3*a**4. Find r, given that w(r) = 0.
1, 2
Suppose 18 = 4*j + 4*y + y, 24 = 2*j - 5*y. Suppose -5*h = -j*h. Determine r so that 10*r**3 + h - 17*r - 5*r**5 + 0 + 12*r = 0.
-1, 0, 1
Let p be (-27 - -48*(-341)/(-558))*(29/21 + 1). Factor 2/3*s**2 + 4/3 - p*s + 8/9*s**3.
2*(s - 2)*(s + 3)*(4*s - 1)/9
Let w(g) be the second derivative of -g**7/63 - 13*g**6/90 + 17*g**5/20 + 17*g**4/18 - 86*g**3/9 + 12*g**2 - 21*g + 31. Determine m so that w(m) = 0.
-9, -2, 1/2, 2
Let u(b) = 8*b**2 - 2*b - 2. Let m be u(-1). Let n(v) be the first derivative of 4*v - 5*v**3 + m*v + 8*v**3 + 12 - 4*v**3. Determine c so that n(c) = 0.
-2, 2
Let m(l) be the third derivative of -7*l**7/39 + 133*l**6/130 - 6*l**5/13 - 254*l**4/39 + 96*l**3/13 - 5619*l**2 + l. Determine t, given that m(t) = 0.
-36/35, 2/7, 2
Let x(k) be the first derivative of 302 + 9/2*k**4 - 2*k**3 + 3*k**5 + 1/2*k**6 - 21/2*k**2 - 9*k. Find y, given that x(y) = 0.
-3, -1, 1
Let l(q) be the second derivative of q**6/120 - 3*q**5/40 - q**4/2 + 277*q**3/6 + 280*q. Let x(b) be the second derivative of l(b). Factor x(t).
3*(t - 4)*(t + 1)
Let c(i) be the third derivative of i**7/70 + i**6/20 - i**5/4 - 3*i**4/4 + 1473*i**2. Let c(g) = 0. Calculate g.
-3, -1, 0, 2
Let y(n) be the first derivative of 12*n**5/5 + 105*n**4/8 + 18*n**3 + 27*n**2/4 - 1805. Find f, given that y(f) = 0.
-3, -1, -3/8, 0
Let n(w) be the second derivative of w**6/6 - 9*w**5/4 + 65*w**4/6 - 20*w**3 - 4*w + 1. Factor n(v).
5*v*(v - 4)*(v - 3)*(v - 2)
Let h(j) be the second derivative of -12*j**3 - 1/21*j**7 - 10*j**4 - 2/3*j**6 - 89*j + 0*j**2 - 37/10*j**5 + 0. Factor h(p).
-2*p*(p + 2)**2*(p + 3)**2
Let w(s) = s**2 - 20*s + 95. Let o be w(13). Suppose -7*t + 12 = -o*t + 3*p, 3*t - p = 4. Factor 1/2*q**t + q**3 - 1/2*q**4 + 0 - q.
-q*(q - 2)*(q - 1)*(q + 1)/2
Let p(m) be the second derivative of m**5/25 + 63*m**4/5 - 254*m**3/5 + 382*m**2/5 - 33*m + 15. Find q, given that p(q) = 0.
-191, 1
Let g(d) be the third derivative of d**9/45360 + d**8/20160 - d**7/945 - d**6/180 + 33*d**4/4 - 90*d**2. Let p(h) be the second derivative of g(h). Factor p(z).
z*(z - 3)*(z + 2)**2/3
Suppose 26*c - 377 = -299. Let n be c/((-42)/(-4)) + 5000/2100. Determine t, given that 1/3*t - 1/3*t**3 - n*t**2 + 8/3 = 0.
-8, -1, 1
Let k(n) = n**4 - n**3 - n**2 - 7*n. Let g(v) = -24*v**4 + 1672*v**3 - 171372*v**2 + 169884*v. Let r(a) = -g(a) - 20*k(a). Factor r(f).
4*f*(f - 206)**2*(f - 1)
Let i(w) = -w**3 - 2*w. Let m(p) = -14642*p**3 + 726*p**2 - 14*p + 206. Let u(a) = i(a) - m(a). Let x(o) be the first derivative of u(o). Factor x(q).
3*(121*q - 2)**2
Su