1, 1
Let l(h) be the third derivative of -h**6/960 + h**5/240 - h**4/192 + h**2 + 39. Factor l(y).
-y*(y - 1)**2/8
Let d = 136 + -133. Let s(p) be the third derivative of 0*p + 0 - 1/180*p**5 + 1/36*p**4 + d*p**2 + 0*p**3. Factor s(z).
-z*(z - 2)/3
Suppose 19*l - 8 = 17*l. Let 16*w**5 - 7*w**4 - 18*w**l - 15*w**4 + 12*w**4 - 8*w**3 = 0. Calculate w.
-1/4, 0, 2
Find i such that -84/11*i**2 + 1176/11*i + 2/11*i**3 - 5488/11 = 0.
14
Solve 25536*c**2 - 25532*c**2 - 183*c + 40804 - 625*c = 0.
101
Let f be (-12)/9*(-774)/((-18)/(-3)). Let g = f - 167. What is o in 3/7*o**2 + 0*o + 0 - 3/7*o**3 - 3/7*o**4 + 3/7*o**g = 0?
-1, 0, 1
Let w = 523/2765 - -6/553. Factor -1/5 + 2/5*d**3 - w*d - 1/5*d**4 + 2/5*d**2 - 1/5*d**5.
-(d - 1)**2*(d + 1)**3/5
Solve 1/5*c**3 + 11/5*c + 1 + 7/5*c**2 = 0.
-5, -1
Let k(a) be the second derivative of a**5/110 - 8*a**4/33 - 35*a**3/33 - 18*a**2/11 + a + 2. Factor k(s).
2*(s - 18)*(s + 1)**2/11
Let f(q) = -9*q + 8. Let l be f(0). Let r be (5*(-3)/(-75))/(l/20). Factor -1/2*j**3 + j**2 - r*j + 0.
-j*(j - 1)**2/2
Let b(i) = i - 10. Let j be b(12). Suppose 0 = -l + 3*z + 3, 0 = -2*l + 5*l + 5*z + 5. Find o, given that 2/13 + l*o - 2/13*o**j = 0.
-1, 1
Suppose 2705*k = 2698*k. Let a(i) be the first derivative of 0*i**5 + 1/8*i**6 + 0*i + k*i**2 + 11 - 3/16*i**4 + 0*i**3. Solve a(n) = 0.
-1, 0, 1
Suppose -7 = 4*h + 5*k, 4 = h - 2*k - 4. What is l in -6*l**5 + 16*l**4 + 17*l**3 + 2*l - h*l - 31*l**3 + 4*l**2 = 0?
0, 2/3, 1
Let l(x) be the second derivative of x**5/80 - 17*x**4/12 + 289*x**3/6 + 4*x - 12. Factor l(t).
t*(t - 34)**2/4
Let b = -253289/81 - -6255/2. Let l = b + 2/81. Factor 1/4 + l*c - 1/2*c**3 - 1/4*c**4 + 0*c**2.
-(c - 1)*(c + 1)**3/4
Let g(u) = -5*u**2 - 48*u + 12. Let k be g(-10). Let h be 150/240*k/(-10). Determine y so that h*y + 0*y**2 - 1/6*y**3 - 1/3 = 0.
-2, 1
Let f be (-3 - -17 - 8400/588)/(12/(-70)). Suppose 1/3 - 2*i + f*i**2 = 0. Calculate i.
1/5, 1
Let m be (-18)/12 + (-13)/(-2) + -2. Factor 0*p**4 + 2*p**3 - 5*p**4 - 12*p**m.
-5*p**3*(p + 2)
Let b be (-7)/(35/(-15)) + 7. Suppose b*z - 20*z = 0. Let 0 + 2/3*o**4 + 4/3*o + z*o**3 - 2*o**2 = 0. Calculate o.
-2, 0, 1
Let l(c) = -c + 12. Let r be l(7). Let g(m) be the first derivative of 1/2*m**2 - 2/3*m + 1/15*m**r - 1/4*m**4 + 1/9*m**3 - 6. Let g(q) = 0. What is q?
-1, 1, 2
Let p(k) be the second derivative of -k + 0 + 0*k**3 + 7/2*k**2 + 1/4*k**4. Let g(r) = -r**2 - 3. Let j(b) = -15*g(b) - 6*p(b). Factor j(i).
-3*(i - 1)*(i + 1)
Let u(v) = -v + 10. Let r be u(7). Factor 5*w - w**r - 2*w**3 + 2*w**3 - 3 - w**2.
-(w - 1)**2*(w + 3)
Let t(s) be the first derivative of -s**5/90 + s**4/27 - 15*s + 13. Let d(v) be the first derivative of t(v). Factor d(g).
-2*g**2*(g - 2)/9
Solve -2*u**5 - 15*u**3 + 17*u**3 + 10*u**5 - 200*u**2 + 402*u**4 - 4*u**5 + 196*u**3 = 0.
-100, -1, 0, 1/2
Let g(m) be the third derivative of m**7/140 + 3*m**6/80 - 9*m**5/40 + 5*m**4/16 + 114*m**2. Let g(d) = 0. What is d?
-5, 0, 1
Let m(u) be the third derivative of -1/4*u**5 - 1/40*u**6 + 2*u**2 + 2 + 0*u + 0*u**4 + 0*u**3. Factor m(a).
-3*a**2*(a + 5)
Solve 4*n**3 + 6*n**2 + 6*n**2 - 15*n - 4*n**2 + 3*n = 0 for n.
-3, 0, 1
Let l(h) be the third derivative of -75*h**5/4 + 175*h**4/2 - 490*h**3/3 - 2*h**2 + 13. Factor l(j).
-5*(15*j - 14)**2
Let l = 11789/30 - 393. Let v = l - -13/30. Factor 2/5*z + v*z**2 + 0.
2*z*(z + 1)/5
Factor 2*l**4 + 3*l**5 + 67597*l**3 - 67596*l**3 - 2*l**5.
l**3*(l + 1)**2
Let o = 810 + -4859/6. Let n(f) be the third derivative of -1/60*f**6 - 1/10*f**5 + 0*f - o*f**4 + 0 + 0*f**3 - 11*f**2. Factor n(l).
-2*l*(l + 1)*(l + 2)
Let f(x) be the first derivative of -x**6/6 + x + 7. Let n(c) = -149*c**5 - 63*c**4 + 219*c**3 + 51*c**2 - 72*c + 14. Let k(q) = 2*f(q) - n(q). Solve k(h) = 0.
-1, 2/7, 1
Let y(d) = 3*d**2 - d + 1. Let x(g) = -2*g**2 - 90*g + 86. Let h(u) = x(u) + 2*y(u). Factor h(c).
4*(c - 22)*(c - 1)
Let j(b) = -b**3 - 2*b**2 + 30*b + 39. Let o be j(-6). Suppose -6*s - 48/5 + 69/5*s**2 + 9/5*s**o = 0. What is s?
-8, -2/3, 1
Let s = -13/10 - -3/2. Let p(l) be the second derivative of -s*l**2 + 0 + 0*l**3 + 1/30*l**4 + 8*l. Suppose p(n) = 0. Calculate n.
-1, 1
Find a such that -5*a**2 - 12*a + 33*a + 9*a + 20*a = 0.
0, 10
Let b be 32/(-48)*(-3 - 0). Let t(i) = i**2 - 12*i - 11. Let r be t(13). Find y such that -8*y + 14*y**b + 4 - y**2 - 5*y**r - 4*y**2 = 0.
1
Determine h so that -1/2 + 11/4*h**2 + 9/4*h = 0.
-1, 2/11
Let b be (-2 - -1)/((-8)/24). Suppose 14 - b = 2*a - 5*l, -3*a + 3*l + 12 = 0. Determine s, given that 3*s**4 - 8*s**2 + 10*s**3 - 2*s**a + 2*s**4 - 7*s**4 = 0.
0, 2
Let q(g) be the second derivative of -g**6/90 - 3*g**5/5 - 9*g**4 + 662*g. Factor q(s).
-s**2*(s + 18)**2/3
Suppose 4*j - 2 = 4*p + 14, -16 = -4*j. Let g(q) be the second derivative of p - 9*q - 4/3*q**4 - 2/3*q**3 + 0*q**2. Suppose g(i) = 0. Calculate i.
-1/4, 0
Let l = 2/21375 - -64117/85500. Factor 15/2*a**2 + l*a**3 + 75/4*a + 0.
3*a*(a + 5)**2/4
Let t(b) be the third derivative of b**5/15 - b**4/3 - 32*b**3 + 886*b**2. Factor t(v).
4*(v - 8)*(v + 6)
Let z = -222 + 225. Let o be (-66)/24 - (-9)/3. Let 0*h + 1/2*h**z + 0 + 1/4*h**2 + o*h**4 = 0. What is h?
-1, 0
Let y(f) be the first derivative of f**6/2340 - f**5/390 - 2*f**3/3 + 3. Let p(o) be the third derivative of y(o). Determine g so that p(g) = 0.
0, 2
Suppose -s + 92 = 4*g, -g = -3*g + 4*s + 46. Let p(w) = w - 20. Let f be p(g). Factor 10/7*a**2 + 4/7*a**f + 8/7*a + 2/7.
2*(a + 1)**2*(2*a + 1)/7
Factor -1/2*y**4 + 1/4*y + 0 + 1/2*y**2 - 1/4*y**3.
-y*(y - 1)*(y + 1)*(2*y + 1)/4
Let r be (-2 + (-65)/(-25))*1. Solve -r*o**2 + 0 + 0*o = 0 for o.
0
Let j(u) be the first derivative of -u**6/21 - 2*u**5/35 + u**4/14 + 2*u**3/21 + 98. Factor j(p).
-2*p**2*(p - 1)*(p + 1)**2/7
Let b(f) = 1 - 2*f - 7 - 4 + 4*f. Let k be b(7). Factor -k*u**2 + 0*u**2 + 5*u**2 + 4 - 4*u.
(u - 2)**2
Factor -1/8*x**3 + 0 + 4*x + 31/8*x**2.
-x*(x - 32)*(x + 1)/8
Let a = 21 - 16. Suppose -48 = -a*r - 28. Find m, given that -12*m - 12/7 - 30*m**3 - 75/7*m**r - 207/7*m**2 = 0.
-1, -2/5
Let o(y) be the second derivative of 0 + 0*y**2 + 0*y**4 - 1/240*y**6 - 1/160*y**5 - 16*y + 0*y**3. Solve o(w) = 0.
-1, 0
Suppose p = -18 + 21. Factor 5*l**5 - 87*l**4 + 6*l**5 + 78*l**4 + l**5 - 3*l**p.
3*l**3*(l - 1)*(4*l + 1)
Determine b so that 20 - 1174*b + 23049*b**2 + 59319/2*b**4 - 305721/2*b**3 = 0.
2/39, 5
Let m(x) be the first derivative of -x**8/168 + x**7/175 + x**6/150 - x**2 - 11. Let d(o) be the second derivative of m(o). Suppose d(c) = 0. Calculate c.
-2/5, 0, 1
Let c be 3/1*((-6)/3)/2. Let f be (-4)/(-2) + (c - -1 - -3). Solve 7/3*q - 1/3*q**4 - f*q**2 + 5/3*q**3 - 2/3 = 0.
1, 2
Let s(p) be the second derivative of 0 + 1/12*p**5 + 25/6*p**2 - 6*p - 5/2*p**3 + 5/12*p**4. Factor s(f).
5*(f - 1)**2*(f + 5)/3
Let 3/5*r**2 + 0 - 153/5*r = 0. What is r?
0, 51
Suppose 0 = -13*t + 15*t - 8. Let c be (4/14)/(t/28). Factor -y**c + 0 - 1/3*y**3 - 2/3*y.
-y*(y + 1)*(y + 2)/3
Factor 20/7 + 2/7*a**2 - 2*a.
2*(a - 5)*(a - 2)/7
Let v(l) = l**4 + l**3. Let n be 750/36 - (-2)/12. Let k(b) = 8*b**4 + 5*b**3 + 2*b - 1. Let p(f) = n*v(f) - 3*k(f). Determine c, given that p(c) = 0.
-1, 1
Let j(k) be the first derivative of 0*k - 3*k**4 + 7/6*k**6 - 28 + 0*k**2 - 9/5*k**5 + 4/3*k**3. Solve j(w) = 0.
-1, 0, 2/7, 2
Let l(q) be the second derivative of q**7/63 - 7*q**6/45 - 11*q**5/30 + 23*q**4/18 + 10*q**3/9 - 16*q**2/3 + 2*q - 80. Solve l(b) = 0.
-2, -1, 1, 8
Let o(r) = -r + 4. Let d be o(4). Let a(f) = f**2 + 2. Let v be a(d). Factor 3*c**3 + 0*c**3 + 7*c - c - 6*c**2 - c**3 - v.
2*(c - 1)**3
Suppose 2/5*y**2 + 0 - 12/5*y = 0. Calculate y.
0, 6
Suppose -g = 4*g - 4*f + 5, g + 3*f = 18. Suppose -4*z**2 + 3*z - 4*z**3 - g*z = 0. What is z?
-1, 0
Let m be 20/(-12) - 28/(-6). Let b(w) be the first derivative of 1/4*w**2 - 2 - 1/3*w**m + 1/8*w**4 + 0*w. Let b(p) = 0. Calculate p.
0, 1
Let o be 0/(17 + (11 - 24)). Let t(m) be the second derivative of 1/6*m**3 + 6*m - 5/4*m**2 + o - 1/120*m**4. Factor t(h).
-(h - 5)**2/10
Factor 16/9 - 1/9*u**2 - 5/3*u.
-(u - 1)*(u + 16)/9
Let g(i) be the third derivative of -i**6/540 - 49*i**5/270 - 46*i**4/27 - 20*i**3/3 + i**2 + 239. Solve g(y) = 0 for y.
-45, -2
Let t(d) be the third derivative of 1/147*d**7 + 1/168*d**8 - 1/210*d**6 + 0*d