/210 - 71*f**6/60 + 4897*f**5/60 + 426*f**4 + 864*f**3 + 10*f**2 - 8. Factor k(h).
(h - 72)**2*(h + 1)**2
Suppose 176*m = 174 + 354. Factor -d**m - 6/5*d + 17/5*d**2 + 0.
-d*(d - 3)*(5*d - 2)/5
Suppose 4 = g + 2*g + 5*a, -13 = -4*g + a. Suppose -3*d + g*k = -9, 7*d - 2*d = k + 11. Factor 25 - s**3 - 5*s**d - 3*s + 20 - 45 + s**4.
s*(s - 3)*(s + 1)**2
Let k be (-56)/(-70) + (-1 - 1586/(-10)). Let w = k - 158. Determine x so that 4/5*x**2 - 2/5 + w*x = 0.
-1, 1/2
Let j be 413/42 + 2/12. Factor -d**2 + 3 + j*d**2 - 2 + 2 - 12*d.
3*(d - 1)*(3*d - 1)
Let -7 - 304*y**3 + 324*y**3 + 2 - 45*y**2 + 30*y = 0. What is y?
1/4, 1
Let d(f) be the first derivative of -5*f**4/18 + 4*f**3/27 + 5*f**2/9 - 4*f/9 - 106. Find w such that d(w) = 0.
-1, 2/5, 1
Let r(v) be the first derivative of -1/2*v**2 - 6 - 1/24*v**4 - v + 1/4*v**3. Let i(m) be the first derivative of r(m). Factor i(c).
-(c - 2)*(c - 1)/2
Let y(h) be the third derivative of 0*h - 4*h**2 - 1/6*h**4 + 0*h**3 + 1/60*h**5 + 0. Determine c so that y(c) = 0.
0, 4
Let 4/9*q**2 + 0 - 2/3*q + 2/9*q**3 = 0. Calculate q.
-3, 0, 1
Let w(k) be the first derivative of -k - 14 - 11/10*k**2 - 1/20*k**4 - 7/15*k**3. What is r in w(r) = 0?
-5, -1
Let a(n) = -n**3 - 12*n**2 + 3*n - 28. Let y be a(-12). Let w = 64 + y. Factor 4/3*k**3 + w*k**2 + 0 - 4/3*k.
4*k*(k - 1)*(k + 1)/3
Suppose 0 = -94*o + 100*o. Let j = 125 - 873/7. Solve -j*n**5 - 12/7*n**3 - 2/7*n + o - 8/7*n**2 - 8/7*n**4 = 0.
-1, 0
Let r(g) be the first derivative of -g**5 - 845*g**4/2 - 47035*g**3 + 143650*g**2 - 144500*g + 734. Find y such that r(y) = 0.
-170, 1
Factor -d**2 + 5*d**2 - 2*d**3 - 10*d**2 - 4*d**2 + 10*d**4 + 2*d**5.
2*d**2*(d - 1)*(d + 1)*(d + 5)
Let d(j) = -2*j - 2. Let r be d(-2). Suppose 4*s = -6*v + 2*v, -5*s = 4*v + 3. Factor 3*x**2 + r*x**2 - 7*x**2 + 2*x**v + 4*x**2.
2*x**2*(x + 1)
Let f(a) be the second derivative of 0 + 39/20*a**5 + 7*a + 3/5*a**6 + 0*a**2 + 3*a**4 + 1/14*a**7 + 2*a**3. Determine g so that f(g) = 0.
-2, -1, 0
Suppose -14*j + 5 + 79 = 0. Solve -2*i**3 + i - 12*i**2 - 16*i - j + i**3 - 2*i**3 = 0.
-2, -1
Let l(v) = v**3 + 3*v**2 + 5*v + 9. Let k be l(5). Let o be 0 + (-9)/(k/(-28)). Suppose -o*i + 12/13*i**2 + 2/13 = 0. Calculate i.
1/6, 1
Let v(f) be the second derivative of -1/10*f**5 + 0*f**3 + 1 + 0*f**2 + 1/24*f**6 - 1/12*f**4 - 38*f. Find z such that v(z) = 0.
-2/5, 0, 2
Let p(o) be the second derivative of 1/36*o**4 + 7/18*o**3 + 0 + 2*o + 5/3*o**2. Factor p(d).
(d + 2)*(d + 5)/3
Let a(n) be the third derivative of n**5/30 + 3*n**4/2 + 17*n**3/3 - 27*n**2. Suppose a(f) = 0. What is f?
-17, -1
Factor 1/10 - 1/2*r**2 - 1/10*r**3 - 2/5*r**5 + 4/5*r**4 + 1/10*r.
-(r - 1)**3*(2*r + 1)**2/10
Let k(d) = -d**2 + 6*d + 55. Let n be k(11). Let h(i) be the third derivative of -7*i**2 + 0*i**4 + 1/60*i**5 + 0*i + n + 0*i**3. Let h(t) = 0. Calculate t.
0
Let r(i) be the second derivative of i**4/12 + 5*i**3/2 + 22*i**2 + 225*i. Factor r(c).
(c + 4)*(c + 11)
Let m = 359/84 - 74/21. Factor -m*x + 1/2 + 1/4*x**2.
(x - 2)*(x - 1)/4
Let c(g) be the third derivative of -1/60*g**4 + 18*g**2 + 0 + 0*g - 1/600*g**6 + 1/100*g**5 + 0*g**3. Factor c(w).
-w*(w - 2)*(w - 1)/5
Suppose 12 = -3*g + 36. Find x such that -g - 2*x**2 + 19*x + 32*x - 43*x = 0.
2
Suppose -2*u + 21 = 49. Let c = u - -17. Let 6*d**2 + d + 2*d + 2 - 2 + c*d**3 = 0. What is d?
-1, 0
Let t(r) be the first derivative of -4 + 0*r - 1/2340*r**6 + 1/390*r**5 + 0*r**4 + 0*r**2 - 10/3*r**3. Let j(a) be the third derivative of t(a). Factor j(g).
-2*g*(g - 2)/13
Let r = 43 + -47. Let g be ((-64)/16)/(r*2/10). Let 0 + 2/9*j**3 + 0*j**2 + 0*j + 2/9*j**g - 4/9*j**4 = 0. What is j?
0, 1
Let t(i) = -46*i + 692. Let f be t(15). Find c, given that 1/4*c**f - 7*c + 49 = 0.
14
Let d(j) = -j**2 + 2*j - 332 - 2*j + 331. Let c(g) = 8*g**2 - 8*g + 14. Let n(k) = -2*c(k) - 12*d(k). Factor n(i).
-4*(i - 2)**2
Let x(w) be the third derivative of w**9/3024 + w**8/1344 - w**7/504 - w**6/144 - 9*w**4/8 - 15*w**2. Let d(o) be the second derivative of x(o). Factor d(q).
5*q*(q - 1)*(q + 1)**2
Let y(v) be the first derivative of -3/10*v**2 + 0*v**3 - 1/10*v**6 + 0*v**5 + 0*v + 3/10*v**4 + 12. Factor y(z).
-3*z*(z - 1)**2*(z + 1)**2/5
Let k = -5 - -2. Let z be 3 + (1 - (3 + k)). Suppose -7*x + 12*x**3 + 8*x**4 + z*x**2 + 2*x**5 + 4*x**2 + 9*x = 0. What is x?
-1, 0
Let m(w) be the third derivative of 0*w**3 + 1/30*w**5 + 0*w - 7*w**2 - 1/180*w**6 - 1/105*w**7 + 0 - 1/504*w**8 + 1/18*w**4. Determine j so that m(j) = 0.
-2, -1, 0, 1
Let b(o) be the first derivative of -o**6/6 + 2*o**5 - 3*o**4 - 24*o**3 + 210. Find m, given that b(m) = 0.
-2, 0, 6
Let k(m) = -m**5 + m**4 + m**3 + m**2 + m - 1. Let b(d) = -48*d**5 + 30*d**4 + 20*d**3 + 4*d**2 + 3*d - 3. Let r(x) = -b(x) + 3*k(x). Solve r(u) = 0 for u.
-1/3, -1/15, 0, 1
Factor 6*v**2 - 25*v - v**2 - 34 + 4.
5*(v - 6)*(v + 1)
Suppose 3*b + 2 = 4*h, -b = -4*h + 1 + 13. Let k be 0/(4/b + (-3)/(-9)). Factor 3/4*c**2 + 0*c + k.
3*c**2/4
Let p(n) be the second derivative of 0 - 1/30*n**6 - 10*n - 1/10*n**5 + 0*n**4 + 1/2*n**2 + 1/3*n**3. What is m in p(m) = 0?
-1, 1
Let n = 28/73 + -50/511. Let l(f) be the second derivative of -8/21*f**3 + 0 - 4/35*f**5 - 6*f + n*f**2 + 2/105*f**6 + 2/7*f**4. Suppose l(y) = 0. Calculate y.
1
Suppose -3*m = -3*q - q - 7, 3*q + 5*m - 31 = 0. Let 0 + 5*t + 3 + q*t**2 - 5 - 4*t**2 = 0. What is t?
1/2, 2
Solve -4/7*u**3 + 16 + 12/7*u**2 + 96/7*u = 0 for u.
-2, 7
Let i(j) be the first derivative of 2*j**3/63 + j**2/21 - 20*j/7 - 16. Suppose i(r) = 0. What is r?
-6, 5
Let k(g) = -4*g**3 + 119*g**2 - 306*g. Let c(v) = -4*v**3 + 118*v**2 - 308*v. Let q(n) = -3*c(n) + 2*k(n). Factor q(m).
4*m*(m - 26)*(m - 3)
Factor -768/5 - 3/5*n**2 - 96/5*n.
-3*(n + 16)**2/5
Let y(v) be the third derivative of -v**5/12 + 20*v**4/3 - 155*v**3/6 + 2*v**2 + 15. Factor y(l).
-5*(l - 31)*(l - 1)
Let r(y) = 4*y + 13. Let l be r(-4). Let g(s) = -s**2 - s. Let j(o) = 9*o - 15. Let x(b) = l*g(b) + j(b). Factor x(p).
3*(p - 1)*(p + 5)
Let -13/2*n + 1/2*n**2 - 7 = 0. Calculate n.
-1, 14
Let m(o) be the third derivative of -o**5/90 - o**4/3 - 80*o**2. Factor m(w).
-2*w*(w + 12)/3
Let n(a) be the second derivative of -a + 1/30*a**4 + 0*a**3 + 0*a**2 + 0 - 2/75*a**6 + 1/50*a**5. Factor n(z).
-2*z**2*(z - 1)*(2*z + 1)/5
Let o = 2/23657 + 2104733/8753090. Let i = -3/74 + o. Let -2/5 + 1/5*g**2 - i*g = 0. Calculate g.
-1, 2
Suppose 0 = m + 130 - 132. Let t = 8 + -8. Factor 0 + 0*u**4 + 1/2*u**3 - 1/4*u - 1/4*u**5 + t*u**m.
-u*(u - 1)**2*(u + 1)**2/4
Determine m so that 0 + 1/3*m**2 + 7/3*m - 7/3*m**3 - 1/3*m**4 = 0.
-7, -1, 0, 1
Factor -19*w**2 - 18*w**2 + 6*w**4 - 97*w**4 + 4*w + 3*w**4 + 105*w**3 + 16*w**5.
w*(w - 4)*(w - 1)*(4*w - 1)**2
Suppose -j + 3*g = 4*g + 3, 2*j + 3 = -g. Suppose 0*h = 5*h - 4*w - 11, -4*h + 4*w + 8 = j. Factor -9*m**2 + 6*m - 6 - 6*m**h + 6.
-3*m*(m + 2)*(2*m - 1)
Let i(n) be the second derivative of -n**6/1080 + n**5/120 + n**3/2 - 3*n. Let y(a) be the second derivative of i(a). Determine s, given that y(s) = 0.
0, 3
Factor 9/7*a**2 + 12/7 + 20/7*a + 1/7*a**3.
(a + 1)*(a + 2)*(a + 6)/7
Let l = -6/31 - 19/62. Let t = l - -3/4. Factor 1/4*d**3 - 3/4*d**2 - t + 3/4*d.
(d - 1)**3/4
Suppose 4*u - 5*c - 153 = 0, 6*u = u + 3*c + 175. Let s = u + -29. Factor o**2 - 5*o**4 + o**2 + s*o**2.
-5*o**2*(o - 1)*(o + 1)
Let z be 2/(-11) - (-2866)/(-132)*-4. Let w = z - 86. Determine a so that 2/3*a - w*a**3 + 4/3 - 4/3*a**2 = 0.
-2, -1, 1
Let w(a) be the second derivative of a**4/18 + 7*a**3/9 - 6*a**2 + 4*a. Factor w(h).
2*(h - 2)*(h + 9)/3
Let s(p) be the third derivative of -p**9/30240 + p**8/2880 - p**7/1680 - 7*p**5/60 - 24*p**2. Let z(j) be the third derivative of s(j). Factor z(b).
-b*(b - 3)*(2*b - 1)
Factor 0*c**4 - 14*c**3 + 2*c**4 - 233*c**2 + 62*c - 2*c**4 - 40 - 2*c**4 + 227*c**2.
-2*(c - 1)**2*(c + 4)*(c + 5)
Let n be (-6)/(-33) + 31/11. Suppose 2*i - n*i + 4*h = -19, -20 = 5*h. Find c such that -7*c**2 - i + 3 + 3*c**2 = 0.
0
Let u(z) be the first derivative of -z**5/80 + z**3/8 - 11*z**2/2 + 15. Let n(o) be the second derivative of u(o). Determine h, given that n(h) = 0.
-1, 1
Let a(u) be the second derivative of -u**8/420 + u**7/105 - u**5/15 + u**4/6 - 3*u**3 - 35*u. Let w(p) be the second derivative of a(p). Factor w(o).
-4*