5
Let r(x) be the second derivative of 5/8*x**3 + 1/8*x**4 - 1/80*x**5 + x**2 + 0 - 17*x. Solve r(l) = 0.
-1, 8
Determine o, given that -6*o**4 + 3*o**2 + 4*o**4 + 7*o**4 - 8*o**2 = 0.
-1, 0, 1
Let c(h) be the first derivative of h**3 - 3*h - 30. Factor c(z).
3*(z - 1)*(z + 1)
Let o(u) = -u**3 - 4*u**2 + 6*u + 7. Let k be o(-5). Let y be (3 - k)/1 - -3. Factor -39*j**4 + j**2 + 2 + y*j**3 - j**2 + 37*j**4 - 4*j.
-2*(j - 1)**3*(j + 1)
Let t(f) = 3*f**2 - 42*f + 143. Let s(d) = -3*d**2 + 42*d - 142. Let z(r) = 4*s(r) + 5*t(r). Find j, given that z(j) = 0.
7
Let j(k) = k**2 + 328*k + 5447. Let b(x) = -25*x**2 - 8855*x - 147070. Let l(r) = 2*b(r) + 55*j(r). Factor l(s).
5*(s + 33)**2
Solve 14800/3*v**3 - 5000*v**2 + 0*v + 2/9*v**5 + 598/9*v**4 + 0 = 0.
-150, 0, 1
Let x be 4/26 - 1/(364/(-35)). Determine v so that 1/2 - 1/4*v**2 - x*v = 0.
-2, 1
Let c(i) be the first derivative of -8/27*i**3 + 8/45*i**5 - 1/9*i**4 - 1/9*i**2 + 8 + 0*i + 1/9*i**6. Let c(x) = 0. What is x?
-1, -1/3, 0, 1
Let s(d) = -2*d**2 - 70*d - 192. Let n be s(-32). Factor -4/21*y**2 - 2/21*y - 2/21*y**3 + n.
-2*y*(y + 1)**2/21
Determine u, given that 17/7*u**2 - 10*u + 8/7 = 0.
2/17, 4
Let p be 1 + -1 - (0 + -1)*12. Let m be 5*2/p*(-2)/(-10). Determine q so that 0*q**4 + 0*q - 1/3*q**2 + m*q**5 - 1/2*q**3 + 0 = 0.
-1, 0, 2
Suppose 10*q**4 + 51*q - 15*q**4 + 7*q**4 + 13*q + 20*q**3 + 64*q**2 = 0. Calculate q.
-4, -2, 0
Let h be 10/4 + (-155)/682*11. Factor h - 15/2*c + 3/2*c**2.
3*c*(c - 5)/2
Factor -4/11*g**3 - 134/11*g**2 + 0*g + 0.
-2*g**2*(2*g + 67)/11
Factor -4 - 19 - 5*n**2 + 40*n + 3 + 3 - 18.
-5*(n - 7)*(n - 1)
Determine d so that -58*d + 5*d**2 + 61*d - 242*d + 7*d + 11520 - 248*d = 0.
48
Let o(l) be the first derivative of -l**6/30 + 3*l**5/5 - 5*l**4/2 - 50*l**3/3 + 5*l**2/2 - 20. Let g(z) be the second derivative of o(z). Factor g(f).
-4*(f - 5)**2*(f + 1)
Let g(x) be the third derivative of -x**5/80 + 83*x**4/96 - 9*x**3/4 - 220*x**2. Factor g(i).
-(i - 27)*(3*i - 2)/4
Let x(w) = -54*w - 2. Let t(c) = -c**2 - 109*c - 5. Let b(n) = 2*t(n) - 5*x(n). Factor b(f).
-2*f*(f - 26)
Let k = 5807 - 11559/2. Factor 5/4*j**2 - k*j + 605/4.
5*(j - 11)**2/4
Solve -4/3 + 2/9*f + 2/9*f**2 = 0 for f.
-3, 2
Let j = 4190/3147 - -2/1049. Let r(w) be the second derivative of 2*w**2 + 0 + j*w**3 + 1/3*w**4 + 4*w. Factor r(c).
4*(c + 1)**2
Let b(w) be the second derivative of -49/60*w**5 + 36*w + 0 + 0*w**2 - 2/9*w**3 - 7/9*w**4. Factor b(z).
-z*(7*z + 2)**2/3
Suppose 0 = -5*g - 3*j - 9, -6*g + 3*j + 9 = -10*g. Let w(d) be the third derivative of -7/30*d**6 + 0*d + d**4 + 0 + g*d**3 - 19/15*d**5 - d**2. Factor w(l).
-4*l*(l + 3)*(7*l - 2)
Let q be (32/12 - 3)*1944/(-135). Suppose -64/5*b - 134/5*b**2 + 24/5 + q*b**3 = 0. What is b?
-2/3, 1/4, 6
Let q be 2/(-4)*26/1482*0. Determine g so that 12/5*g**2 - 4/5*g**5 + 4*g**4 + 0*g - 28/5*g**3 + q = 0.
0, 1, 3
Let d(b) = b - 2. Let q be d(3). Suppose -6*k + 11 = -k - 4*h, 3*k + 3*h = 12. Factor -4*j**4 - 5*j**4 + 5*j**4 + 8*j**2 - q - k.
-4*(j - 1)**2*(j + 1)**2
Let r(m) be the first derivative of m**7/4200 + m**6/900 - m**5/600 - m**4/60 + m**3/3 - 3. Let a(b) be the third derivative of r(b). Find w such that a(w) = 0.
-2, -1, 1
Let b = 32 + -4. Factor -b + 16*k + 4*k**3 - 27 + 16*k**2 + 55.
4*k*(k + 2)**2
Factor -16/5 + 2/5*k**2 - 4/5*k.
2*(k - 4)*(k + 2)/5
Let j(x) = x + 15. Let t be j(-13). Let b = t - -5. Find l such that -5*l + 2*l**3 + b*l - 4*l**3 = 0.
-1, 0, 1
Factor -122*g - 84 + 937*g**2 - 1930*g**2 + 957*g**2 + 2*g**3.
2*(g - 21)*(g + 1)*(g + 2)
Let f(q) = -7*q**2 - 762*q + 736. Let y(r) = -3*r**2 - 380*r + 368. Let b(k) = 10*f(k) - 22*y(k). Suppose b(p) = 0. Calculate p.
1, 184
Suppose 9*r + 38 = 28*r. Let g(l) be the second derivative of 4*l**r + 22/3*l**3 + 2/7*l**7 + 8*l**4 + 28/15*l**6 + 3*l + 26/5*l**5 + 0. Factor g(k).
4*(k + 1)**4*(3*k + 2)
Let j = 23521/60 + -392. Let d(n) be the third derivative of -1/360*n**6 + 0 + 0*n + 0*n**3 - 1/36*n**4 - j*n**5 - 9*n**2. Factor d(i).
-i*(i + 1)*(i + 2)/3
Let 13*m**3 - 33*m**4 + 6*m**3 + 28*m**4 - 2*m**3 - 2*m**3 = 0. Calculate m.
0, 3
Let k(z) = z**3 - 5*z**2 + z + 17. Let f be k(4). Let d(n) = -n**3 + 4*n**2 + 6*n - 3. Let o be d(f). Factor 5/3*m - 25/6 - 1/6*m**o.
-(m - 5)**2/6
Let s(d) be the second derivative of 0 - 4/9*d**3 + 1/9*d**4 + 0*d**2 + 1/15*d**5 - 5*d. Factor s(z).
4*z*(z - 1)*(z + 2)/3
Let r(d) be the third derivative of 2*d**7/105 + 11*d**6/30 + 43*d**5/15 + 23*d**4/2 + 24*d**3 + 21*d**2 + 5. Factor r(t).
4*(t + 1)*(t + 3)**2*(t + 4)
Let q(z) be the first derivative of z**5/20 - 7*z**4/8 + 3*z**3 - 17*z**2/4 + 11*z/4 + 321. Determine w, given that q(w) = 0.
1, 11
Let a(t) be the first derivative of 2/15*t**2 + 0*t - 2/45*t**3 + 19. Factor a(u).
-2*u*(u - 2)/15
Let g be 3 - (-19 + (-2 - -9)). Let k(m) = -11*m + 1. Let b be k(-2). Factor 4*a**2 - 13*a + b*a - g + a**2.
5*(a - 1)*(a + 3)
Let v = -7 + 20. Factor -37*k**3 + v*k**3 - k**4 - 98*k + 3*k**4 + 50 + 92*k**2 - 22*k.
2*(k - 5)**2*(k - 1)**2
Let p(n) be the second derivative of -n**9/756 + 2*n**7/105 + 5*n**3/2 - 17*n. Let f(x) be the second derivative of p(x). Suppose f(q) = 0. What is q?
-2, 0, 2
Suppose v + 20 = 4*b, -4 - 16 = 2*v - 4*b. Let g be 910/245 + (-3 - v). Factor g*h**2 + 4/7 + 8/7*h + 1/7*h**3.
(h + 1)*(h + 2)**2/7
Let w(j) = 5*j**3 - 4*j**2 - 29*j + 43. Let h(o) = -14*o**3 + 10*o**2 + 88*o - 128. Let t(k) = -3*h(k) - 8*w(k). Find s, given that t(s) = 0.
-5, 2
Let p(c) be the second derivative of -3*c**5/20 - 4*c**4 - 42*c**3 - 216*c**2 - 2*c + 86. Find s such that p(s) = 0.
-6, -4
Factor -2/13*w**2 + 12/13*w - 16/13.
-2*(w - 4)*(w - 2)/13
Let r be -2*(2/4 + 0). Let g(x) = -3*x**2 - 6*x - 9. Let d(c) = 67*c + 73*c + 64*c + 1 - 205*c. Let w(f) = r*g(f) - 3*d(f). Solve w(l) = 0.
-2, -1
Let a(u) be the second derivative of 0 - 5/33*u**6 + 4/33*u**3 - 4*u + 0*u**2 + 8/33*u**4 + 1/22*u**5. Factor a(b).
-2*b*(b - 1)*(5*b + 2)**2/11
Let p(y) = -4*y**2 + 11*y. Let v(z) = 2*z - 3*z**2 + 2*z**2 + 4*z - 3*z. Let m(j) = 4*p(j) - 18*v(j). Factor m(i).
2*i*(i - 5)
Suppose -38*a**2 + 12*a - 42*a**2 - a**3 + 65*a**2 + 4*a**3 = 0. Calculate a.
0, 1, 4
Let k(v) be the third derivative of -2*v**7/105 - v**6/15 + v**5/15 + v**4/3 + 89*v**2. Solve k(q) = 0 for q.
-2, -1, 0, 1
Let x be 3/(-27) - (6/(-27))/2. Let m(c) be the second derivative of -2/15*c**3 + x*c**2 - 5*c + 1/30*c**4 + 0. Solve m(q) = 0 for q.
0, 2
Let t(s) be the first derivative of -7*s**5 + 65*s**4/2 + 215*s**3/3 + 25*s**2 - 99. Factor t(q).
-5*q*(q - 5)*(q + 1)*(7*q + 2)
Let r(l) be the third derivative of -1/480*l**6 - 1/8*l**4 + 0*l + 1/3*l**3 + 1/40*l**5 + 0 - 2*l**2. Let r(i) = 0. Calculate i.
2
Suppose -11 = -l + 1 - 10. Factor 0*n - 4/5*n**l + 4/5.
-4*(n - 1)*(n + 1)/5
Factor 56*l + 82/3*l**2 + 8/3.
2*(l + 2)*(41*l + 2)/3
What is s in 12/5*s + 0 + 24/5*s**3 - 4/5*s**5 + 0*s**4 + 32/5*s**2 = 0?
-1, 0, 3
Suppose -2*u - 4 = 20. Let o be ((-10)/(-1))/(u + 14). Factor -2*d - 2*d**4 - o*d**2 - 4*d**3 + 2*d + 3*d**2.
-2*d**2*(d + 1)**2
Let b(l) be the third derivative of l**7/840 - l**6/120 - 3*l**4/8 - 7*l**2. Let a(k) be the second derivative of b(k). Factor a(y).
3*y*(y - 2)
Let y be (3/9)/((-17)/(-102)). Factor -3/5*k**y - 6/5*k - 3/5.
-3*(k + 1)**2/5
Let u be 2/9 - 364/(-63). Find w such that -9*w**3 - w**5 + 7*w**4 + 5*w**4 - u*w**4 = 0.
0, 3
Let i(c) be the third derivative of c**7/315 - 7*c**6/90 + 13*c**5/30 + 7*c**4/18 - 40*c**3/9 + 652*c**2. Suppose i(d) = 0. What is d?
-1, 1, 4, 10
Let j(k) be the first derivative of -k**3/6 + 91*k**2/4 + 46*k + 133. Factor j(g).
-(g - 92)*(g + 1)/2
Let z(u) = 3*u + 23. Let i be z(-7). Suppose -2*l + 4 = -i*o, 3*o = 3 - 0. Determine n so that -2*n**l + 13/3*n**2 + 1/3*n**4 - 4*n + 4/3 = 0.
1, 2
Find a, given that 26912/13 - 464/13*a + 2/13*a**2 = 0.
116
Suppose -62*w - 144 = -150*w + 40*w. Factor 8/9 + 4/9*x**2 - 14/9*x + 2/9*x**w.
2*(x - 1)**2*(x + 4)/9
Let c(r) = r**3 + 5*r**2 + r - 10. Let y be c(-4). Let f(t) = -16*t + 14. Let j(n) = -n**3 - n + 1. Let x(a) = y*j(a) - f(a). Factor x(g).
-2*(g - 2)*(g - 1)*(g + 3)
Let p be (-588)/(-168)*(-8)/(-7). Factor -18/13*o + 10/13*o**3 - 2/13*o**p + 0 - 6/13*o**2.
-2*o*(o - 3)**2*(o + 1)/13
Suppose -6*p + i = -2*p - 331, 2*i - 10 = 0. Factor 17*x**3 + p*x**2 + 4*