Let f = -16511/24 + 688. Let h(o) be the third derivative of -f*o**5 + 0 - 3*o**2 - 7/48*o**4 + 0*o - 1/6*o**3. Factor h(m).
-(m + 1)*(5*m + 2)/2
Suppose -4*p + 68 = -2*a - 200, 0 = -4*p - 4*a + 268. Suppose -j + p = -11. Find g, given that 95*g - 36*g**2 - 7*g**2 + j*g**2 - 30 = 0.
-3, 2/7
Let y = -402/7 + 60. Let u be ((-54)/(-8))/(2 - (-4 - 162/(-48))). Determine l so that u*l - 6/7 - y*l**2 + 6/7*l**3 = 0.
1
Let a(h) be the second derivative of -h**4/24 - 17*h**3/3 + 1723*h. Factor a(r).
-r*(r + 68)/2
Let x(q) be the second derivative of -q**5/10 + 13*q**4/3 + 61*q**3 + 288*q**2 - 7*q - 33. Factor x(v).
-2*(v - 32)*(v + 3)**2
Let -2/9*w + 794/9*w**4 + 2/3*w**5 - 716/3*w**3 - 30 + 180*w**2 = 0. What is w?
-135, -1/3, 1
Let c(m) be the second derivative of -m**5/5 - 4*m**4 + 10*m**3 + 52*m**2 - 2*m - 1141. Factor c(l).
-4*(l - 2)*(l + 1)*(l + 13)
Let s(y) be the second derivative of -y**4/8 - 23*y**3/2 - 387*y**2/4 - 2*y - 525. Solve s(m) = 0.
-43, -3
Let b be (4 - 11) + (-70)/(-7). Factor 30 - 17 + 9 - 18*i - 1 - b*i**2.
-3*(i - 1)*(i + 7)
Let b(i) be the third derivative of -i**6/150 + 29*i**5/150 - 3*i**4/2 + 321*i**2. Find n, given that b(n) = 0.
0, 9/2, 10
Let i = 230630 + -230628. Find r such that -129/2*r**i + 207/2*r - 27/2 + 21/2*r**3 = 0.
1/7, 3
Let l(d) = d**3 - d**2 - d - 18. Let t be l(0). Let j be 2 - (-1)/(t/(-12)). Factor 0 - 2/3*z**2 - j*z.
-2*z*(z + 4)/3
Let o(p) = -2*p**3 - 24*p**2 + 80*p - 54. Let b = -122 + 112. Let g(w) = -4*w**3 - 49*w**2 + 160*w - 107. Let l(i) = b*o(i) + 4*g(i). Let l(a) = 0. Calculate a.
-14, 1, 2
Let f(n) = 141*n**2 - 210*n - 211. Let w(t) = -35*t**2 - t - 1. Let u(h) = -f(h) - 4*w(h). Suppose u(v) = 0. What is v?
-1, 215
Let y(r) be the third derivative of -r**5/30 - 14*r**4/3 + 124*r**3 + 452*r**2. Factor y(d).
-2*(d - 6)*(d + 62)
Let y(b) = b**3 + 3*b**2 - 2*b + 4. Let z be y(-3). Let h = z - 8. Factor -12*m**2 + 2*m**3 + 0*m**2 - 17*m**3 + h*m**2 + 5*m**5.
5*m**2*(m - 2)*(m + 1)**2
Suppose 27 = 5*u + 7. Suppose 0 = 16*a + a - 408. Factor -a*f - f**u - 9*f**3 - 24*f**2 - 24 - 6*f**2 - 20*f.
-(f + 2)**3*(f + 3)
Let l = 33 + 31. Suppose -197*j - 11*j = -9*j - 1592. Let 1/3*d**3 + l*d - 512/3 - j*d**2 = 0. What is d?
8
Solve -979*p**2 - 282 - 384 - 707*p**2 - 7*p**3 - 17*p**3 - 2337*p + 9*p**3 = 0 for p.
-111, -1, -2/5
Let f(m) be the first derivative of m**4/26 - 22*m**3/39 - 2*m**2 + 1327. Factor f(s).
2*s*(s - 13)*(s + 2)/13
Let o(s) be the third derivative of s**5/12 + 55*s**4/2 - 670*s**3/3 + 3729*s**2. Factor o(m).
5*(m - 2)*(m + 134)
Let i(m) be the second derivative of -m**5/4 - 17*m**4/6 + 7*m**3/6 - 1930*m. Factor i(o).
-o*(o + 7)*(5*o - 1)
Let o(a) be the first derivative of -57 + 0*a + 0*a**2 + 1/7*a**3 + 0*a**4 - 3/35*a**5. Factor o(r).
-3*r**2*(r - 1)*(r + 1)/7
Let r(q) be the third derivative of -q**5/15 - 7*q**4/2 + 468*q**3 - q**2 + q - 89. Solve r(h) = 0 for h.
-39, 18
Suppose 7*s - 3*s - 13 = -i, -3*i = -3*s + 6. Solve -n**2 - n - s*n**2 - 9 - 5 - 10 - 19*n = 0 for n.
-3, -2
Suppose -4*h = 5*z - 61, -2*h + 141 = -5*z + 178. Suppose -6/5 + 12/5*a**h + 78/5*a**2 - 1/5*a + 17*a**3 = 0. Calculate a.
-6, -1, -1/3, 1/4
Let h(k) be the third derivative of 1/660*k**6 + 0 + 7/330*k**5 + 0*k + 3/11*k**3 + 5/44*k**4 + 39*k**2. Let h(m) = 0. Calculate m.
-3, -1
Let g(d) be the first derivative of -89 + 3*d**4 + 0*d + 2/5*d**5 + 8*d**3 + 8*d**2. Determine x so that g(x) = 0.
-2, 0
Let z(o) = -o**2 + 12*o + 66. Let t be z(16). Find p, given that 22*p**4 - 5*p + 14*p**4 - p**2 + 5*p**3 + 6*p**t - 41*p**4 = 0.
-1, 0, 1
Let x(y) be the second derivative of -3/20*y**5 - 5 + 0*y**2 - 1/10*y**6 + 2*y + 1/2*y**3 + 1/4*y**4. Factor x(s).
-3*s*(s - 1)*(s + 1)**2
Let o(s) = 5*s**2 - s + 8. Let m(g) = 25*g**2 + 286*g - 263. Let t(a) = m(a) - 4*o(a). Solve t(l) = 0.
-59, 1
Let n(r) be the first derivative of 1/60*r**5 - 37 + 3/16*r**4 + 0*r + 3/4*r**3 - 19/2*r**2. Let j(o) be the second derivative of n(o). Factor j(x).
(x + 3)*(2*x + 3)/2
Let z = 5/2948 - -497927/168036. Let g(u) be the third derivative of 42*u**2 + 0 + 1/570*u**5 + 0*u + z*u**3 - 13/114*u**4. Factor g(h).
2*(h - 13)**2/19
Suppose 31/11*f**4 - 1/11*f**5 + 60/11 - 27/11*f**3 - 91/11*f**2 + 28/11*f = 0. Calculate f.
-1, 1, 2, 30
Factor 572 - 5*b**2 - 112*b + 19*b**2 - 8*b**2 - 272 - 2*b**2.
4*(b - 25)*(b - 3)
Let w(o) = o**4 - 144*o**3 + 143*o**2 + 6*o + 4. Let d(p) = p**3 - p**2 - 3*p - 2. Let q(z) = -2*d(z) - w(z). Let q(k) = 0. What is k?
0, 1, 141
Let i = -101/110 + 95/22. Let x(c) be the first derivative of 12/5*c + i*c**2 - 12 - 7/10*c**4 - 32/15*c**3. Factor x(a).
-2*(a - 1)*(a + 3)*(7*a + 2)/5
Let a(d) be the second derivative of -36 - 3/80*d**5 + 0*d**3 + 2*d + 0*d**2 - 1/80*d**6 + 3/32*d**4. Find x, given that a(x) = 0.
-3, 0, 1
What is f in 0 + 8*f + 60/7*f**4 - 4/7*f**5 - 52/7*f**3 - 60/7*f**2 = 0?
-1, 0, 1, 14
Let b(h) be the first derivative of 3/2*h**2 - 11/4*h - 1/12*h**3 - 106. Let b(c) = 0. Calculate c.
1, 11
Let k be 5/(120/59) - 1449/1288. Suppose 2/3*o**2 - k*o - 2 = 0. What is o?
-1, 3
Suppose -40*h = -162*h. Factor 1/3*l**2 + 0*l - 1/6 + h*l**3 - 1/6*l**4.
-(l - 1)**2*(l + 1)**2/6
Let y(k) be the first derivative of -392*k**6/15 + 2408*k**5/25 - 2521*k**4/20 + 191*k**3/3 - 59*k**2/10 + k/5 - 3832. Find v such that y(v) = 0.
1/28, 1
Let d = -925780 + 925860. Determine x so that -295*x**3 - 260/3*x**4 - 845/3*x**2 - d*x - 20/3 = 0.
-2, -1, -1/4, -2/13
Let i be (-615)/21 + 20 + 13. Determine r so that 4 - 2/7*r**2 + i*r = 0.
-1, 14
Factor -132/17*x - 496/17 - 2/17*x**2.
-2*(x + 4)*(x + 62)/17
Suppose 0 = t - 6*i + 3*i - 19, -t - 5 = 3*i. Suppose 4537 = t*f + 4509. Find g, given that -32/7*g - 8/7*g**f + 26/7*g**3 - 6/7*g**2 + 8/7 = 0.
-1, 1/4, 2
Let y = 229 - 225. Determine j, given that -24*j - 35 + 3*j**5 + 47 + 21*j**3 - 5*j**y - 10*j**4 + 3*j**2 = 0.
-1, 1, 2
Suppose 7*i - 80 = 60. Factor -55*b + 29*b + 2*b**2 - i + 4*b**2.
2*(b - 5)*(3*b + 2)
Let k be 1 + 2 + -3 + 0 + -8. Let p(h) = -9*h**2 + 25*h + 15. Let w(u) = -14*u**2 + 38*u + 24. Let b(q) = k*p(q) + 5*w(q). Factor b(r).
2*r*(r - 5)
Let m(f) be the second derivative of -1/15*f**5 - 27*f + 0 + 0*f**4 + 2/3*f**3 + 13*f**2. Let x(l) be the first derivative of m(l). Let x(s) = 0. What is s?
-1, 1
Let h be (-15 - -17)*90 - (-8)/(-2). Let s be (h/(-110))/(4/(-5)). Let 0*b**s + 0 - 8/9*b**3 + 8/9*b**4 + 0*b - 2/9*b**5 = 0. Calculate b.
0, 2
Suppose 8 - 2 = 3*a. Factor -8*i - 46*i**2 - 19*i**2 - 49*i**2 + 22*i**a.
-4*i*(23*i + 2)
Let v be 80/100 + ((-14)/5 - -3) + 3. Let k(s) be the first derivative of -30 + 5/4*s**v + 0*s**3 - 10*s - 15/2*s**2. Determine g so that k(g) = 0.
-1, 2
Let v(j) be the third derivative of -3/40*j**6 + 244*j**2 + 0*j + 1/4*j**5 + 1/4*j**4 + 0 + 0*j**3. Factor v(f).
-3*f*(f - 2)*(3*f + 1)
Let j(k) be the second derivative of -k**4/18 + 113*k**3/9 + 2*k + 324. Factor j(g).
-2*g*(g - 113)/3
Let g(w) = -3*w**3 - 15*w**2 - 12*w - 15. Let p(x) = x**2 + x + 1. Let o(m) = -g(m) - 15*p(m). Factor o(s).
3*s*(s - 1)*(s + 1)
Let j(g) be the second derivative of -g**5/12 - 5*g**4/12 - 87*g**2/2 - 145*g. Let b(i) be the first derivative of j(i). Factor b(k).
-5*k*(k + 2)
Let s(u) be the first derivative of -2/7*u**5 - 2/3*u**3 + 9/14*u**4 + 23 + 2/7*u**2 + 1/21*u**6 + 0*u. Determine l so that s(l) = 0.
0, 1, 2
Let l = -141364 + 1135325/8. Let w = 552 - l. Suppose -3/4 - 3/2*m**2 - 15/8*m - w*m**3 = 0. Calculate m.
-2, -1
Find w such that -5/6*w**2 - 1090445/6 - 2335/3*w = 0.
-467
Let l(h) = -4*h**4 + 56*h**3 - 192*h**2 + 176*h - 60. Let z(j) = -4*j**4 + 60*j**3 - 192*j**2 + 178*j - 60. Let k(v) = 3*l(v) - 4*z(v). What is q in k(q) = 0?
1, 15
Factor 5/2*a**2 - 3/2*a**3 - 1/6*a**4 + 5 + 53/6*a.
-(a - 3)*(a + 1)**2*(a + 10)/6
Let b(w) be the first derivative of 2*w**3/3 - 189*w**2 - 1152*w + 879. Factor b(g).
2*(g - 192)*(g + 3)
Find f, given that 51/7 - 52/7*f + 1/7*f**2 = 0.
1, 51
Let o = 1093577 - 1093574. Factor n**2 + 0 + 8/3*n**o + 0*n.
n**2*(8*n + 3)/3
Factor 4*i + 2/9*i**3 - 2*i**2 + 0.
2*i*(i - 6)*(i - 3)/9
Let a be (-137946)/(-3324) - 39*1. Suppose -a + 11/2*r - 1/2*r**5 + 7/2*r**4 - 5*r**3 - r**2 = 0. What is r?
-1, 1, 5
Let r(k) be the first derivative of -k**5/15 - 103*k**4/6 - 1540*k**3 - 142100*k**2/3 + 1372000*k/3 - 684. Factor r(z).
-(z 