he first derivative of 9*a**3 + 9*a**2 - 25 - 3 + 15*a - 8*a**3. Factor c(x).
3*(x + 1)*(x + 5)
Let 9/4*y - 2 - 1/4*y**2 = 0. Calculate y.
1, 8
What is j in 276*j + 120 - 2394/5*j**2 - 21/5*j**4 + 87*j**3 = 0?
-2/7, 1, 10
Suppose 354 = 47*g + 71*g. Solve 4/7*s**g + 4/7*s**2 - 4/7 - 4/7*s = 0 for s.
-1, 1
Let r(i) be the third derivative of -13*i**2 + 1/8*i**4 - 1/70*i**7 + 3/40*i**6 + 0 - 3/20*i**5 + 0*i + 0*i**3. Factor r(c).
-3*c*(c - 1)**3
Suppose -3*q - 10 = -2*y - 27, 0 = 3*q + 2*y - 1. Factor l**4 + 0*l**3 + 3*l**3 - l**2 - 7*l**q + 5*l**2.
l**2*(l - 2)**2
Let l = -267 - -281. Suppose 0 = -l*k + 16*k. Factor 6/7*b + k - 3/7*b**2.
-3*b*(b - 2)/7
Let j be 10/20 + (-18)/(-28) + -1. Let c(l) be the first derivative of 0*l**2 + 6 - j*l**4 - 2/35*l**5 - 2/21*l**3 + 0*l. Solve c(r) = 0.
-1, 0
Factor -5/4*f**2 + 0 - 1/4*f**3 - 3/2*f.
-f*(f + 2)*(f + 3)/4
Let q(a) be the third derivative of -a**8/336 + a**7/105 + 3*a**6/40 - 11*a**5/30 - a**4/6 + 4*a**3 + 429*a**2. Determine n, given that q(n) = 0.
-3, -1, 2
Let f = -7598 + 7600. Factor -5 + 0*j + 5/4*j**f.
5*(j - 2)*(j + 2)/4
Let g be ((-21)/(-245))/3 - 1/(-5). Let s = g + 6/35. Factor -4/5*x**3 + 0*x + 0 + 0*x**2 + s*x**4.
2*x**3*(x - 2)/5
Factor 3/4*u**2 + 21/4 + 6*u.
3*(u + 1)*(u + 7)/4
Let m be (12/(-15))/(30/(-75)). Factor 4/5*v**3 + 8/5*v**m + 4/5*v + 0.
4*v*(v + 1)**2/5
Let o = -8 + 10. Let a(b) = 5*b**2 + 10*b + 9. Let v(r) = 81*r**2 + 159*r + 144. Let k(t) = o*v(t) - 33*a(t). Let k(n) = 0. What is n?
-3, -1
Let m = 485 + -483. Find d such that 8/5 - 16/5*d - 2*d**m = 0.
-2, 2/5
Let x = 1550/3 + -516. What is s in 2/3 - x*s**2 + 0*s = 0?
-1, 1
Suppose -10*s - 105 = -105. Let j(t) be the second derivative of -1/27*t**3 + 10*t + s + 1/54*t**4 + 0*t**2. Factor j(i).
2*i*(i - 1)/9
Let p(c) be the first derivative of -27*c**5/20 - 3*c**4/4 + 4*c**3 + 6*c**2 + c - 4. Let y(s) be the first derivative of p(s). Factor y(j).
-3*(j - 1)*(3*j + 2)**2
Suppose 4231*g = 4224*g. Factor -50/9*b**4 + g - 20/3*b**3 - 2*b**2 + 0*b.
-2*b**2*(5*b + 3)**2/9
Let x(n) be the first derivative of n**4/90 - n**3/15 + 2*n**2/15 - n - 13. Let u(g) be the first derivative of x(g). Factor u(l).
2*(l - 2)*(l - 1)/15
What is l in 27/2*l**2 + 0 - 1/2*l**3 - 13*l = 0?
0, 1, 26
Let -4*u - 29*u**2 - 4 + 79*u**2 - 51*u**2 = 0. What is u?
-2
Factor -12365 - 5883*i - i**2 + 3529 + 5695*i.
-(i + 94)**2
Let f(t) be the first derivative of 3 - 4*t - 1/9*t**4 + 0*t**2 + 0*t**3 + 1/15*t**5. Let s(h) be the first derivative of f(h). Let s(c) = 0. Calculate c.
0, 1
Let m(l) = 2*l**3 + 6*l**2 - 30*l + 41. Let n be m(-6). Solve 9/4*w**4 - 3/2*w + 0 - 9/4*w**2 + 3/4*w**n + 3/4*w**3 = 0.
-2, -1, 0, 1
Suppose 2*j = -l + 9, -2*j = 5*l - 6*l - 3. Let r(s) be the first derivative of -1/16*s**4 + 1 + 0*s**2 + 0*s - 1/12*s**j. Solve r(c) = 0.
-1, 0
Factor 31/9*y - 32/9 + 1/9*y**2.
(y - 1)*(y + 32)/9
Let p be -3 - (-3 - (-80)/(-28)). Suppose -5*q + 2*m = -12, -4*q + 3*m + 15 = 4. Solve -2/7 - 50/7*b**q + p*b = 0 for b.
1/5
Let m = -14 + 26. Suppose 0 = 14*o - m*o. What is k in -2/11*k**4 + 0 + 0*k**2 + 4/11*k**3 + o*k = 0?
0, 2
Let j(u) be the first derivative of 9/14*u**2 - 2 - 12/7*u + 1/7*u**3. Suppose j(p) = 0. Calculate p.
-4, 1
Suppose 0 = 4*w + 255 + 21. Let x = 485/7 + w. Factor 0 + 2/7*g - x*g**2.
-2*g*(g - 1)/7
Let x(d) be the first derivative of -3*d**5/5 + 15*d**4/4 + 78*d**3 + 108*d**2 + 98. Factor x(f).
-3*f*(f - 12)*(f + 1)*(f + 6)
Let o(l) be the second derivative of -l**6/30 - 13*l**5/5 - 25*l**4/2 - 74*l**3/3 - 49*l**2/2 + 269*l. Factor o(u).
-(u + 1)**3*(u + 49)
Let f(b) = b**4 - b**3 + b**2 + b - 1. Let x(r) = 6*r**4 + 4*r**3 + 10*r**2 - 4*r - 12. Let z(s) = 4*f(s) - x(s). Factor z(n).
-2*(n - 1)*(n + 1)*(n + 2)**2
Let u(x) = 2*x - 3. Let q be u(2). Let c be 0*q*(-4)/12. Factor 0*l**3 + c + 0*l - 1/3*l**2 + 1/3*l**4.
l**2*(l - 1)*(l + 1)/3
Let j be (-5)/(10/3)*-4. Suppose 3*a**5 - j*a**2 + a**3 + a**5 - a**5 - 10*a**3 = 0. Calculate a.
-1, 0, 2
Let x(v) be the third derivative of -v**6/600 + 67*v**5/100 - 4489*v**4/40 + 300763*v**3/30 - 208*v**2 + v. Suppose x(j) = 0. What is j?
67
Factor -2/5*q**4 + 6/5*q**2 + 0 + 0*q**3 - 4/5*q.
-2*q*(q - 1)**2*(q + 2)/5
Factor 111*x - 1 + 1 - 307*x - 966*x**2 - 2*x**4 - 686*x - 86*x**3.
-2*x*(x + 1)*(x + 21)**2
Suppose 0 = 14*x + 3894 - 3950. What is o in -15*o**3 - 9/2*o**x + 0 + 0*o + 12*o**2 = 0?
-4, 0, 2/3
Let b(p) = -p**2 - 12*p - 15. Let u be b(-10). Suppose -u*v + 9 = -1. Let -17*l**v + 77*l + l**2 - 73*l = 0. Calculate l.
0, 1/4
Suppose 3*q = d + 3, d - 4*d = -2*q + 2. Let s(x) be the first derivative of 0*x**2 + 2 - 1/20*x**4 + d*x - 1/15*x**3. Let s(y) = 0. Calculate y.
-1, 0
What is j in -838*j**4 + 798*j**4 + 28*j**3 + 212*j - 197*j**2 + 533*j**2 - 56 = 0?
-2, -1, 1/5, 7/2
Suppose 8*t - 2*t = -36. Let q(f) = -5*f**2 + 6*f + 14. Let u(i) = -i + 1. Let y(b) = t*u(b) - q(b). Factor y(o).
5*(o - 2)*(o + 2)
Factor 18/7*q + 26/7*q**3 - 4/7 + 48/7*q**2.
2*(q + 1)**2*(13*q - 2)/7
Let o = 486/11 + -482/11. Let 6/11*y + o + 2/11*y**2 = 0. Calculate y.
-2, -1
Let p(a) be the second derivative of a**5/360 + a**4/72 - a**3/12 - 6*a**2 - 23*a. Let k(t) be the first derivative of p(t). Suppose k(x) = 0. Calculate x.
-3, 1
Let o(v) be the second derivative of v**5/105 + 2*v**4/21 - 10*v**3/21 + 2*v**2 - 3*v. Let n(c) be the first derivative of o(c). Find a, given that n(a) = 0.
-5, 1
Let g(h) be the second derivative of 0 + 13/3*h**3 - 9*h + 2/3*h**4 + 3*h**2. Factor g(r).
2*(r + 3)*(4*r + 1)
Let r = 2301/20 + -574/5. Let w(y) be the second derivative of 0*y**2 - 1/30*y**6 + 3*y - r*y**4 - 1/6*y**3 + 0 - 3/20*y**5. Factor w(d).
-d*(d + 1)**3
Factor -1/2*b**4 + 0*b**2 - 1/2*b**3 + 0 + 0*b.
-b**3*(b + 1)/2
Determine y, given that 4/5*y + 2/5*y**4 - 2/5*y**2 + 2/5*y**5 - 6/5*y**3 + 0 = 0.
-2, -1, 0, 1
Let -6 - 5/4*h + 1/4*h**2 = 0. What is h?
-3, 8
Let l(x) = x**2 - 7*x + 9. Let c be l(6). Factor -3*u - u + 6*u**2 - 18*u**c - 3*u**5 + u + 12*u**4 + 6*u**2.
-3*u*(u - 1)**4
Let i(r) = -36*r - 140. Let q be i(-4). Determine w, given that -14/3*w**5 + 0 - 26/3*w**3 + q*w**2 - 52/3*w**4 + 0*w = 0.
-3, -1, 0, 2/7
Let i(w) = 2*w**3 - 114*w**2 + 2156*w - 13723. Let z(m) = m**3 - 57*m**2 + 1079*m - 6861. Let o(k) = 2*i(k) - 5*z(k). Let o(u) = 0. What is u?
19
Suppose 249*t = 246*t + 12, 27 = 3*f + 3*t. Solve -27/5*g**f - 144/5*g - 72/5*g**2 - 48/5 + 9*g**4 + 96/5*g**3 = 0.
-1, -2/3, 2
Let x(n) = 21*n + 445. Let v be x(-21). Factor -1/3 - 13/3*y**2 - v*y**3 - 4/3*y**4 - 2*y.
-(y + 1)**2*(2*y + 1)**2/3
Suppose -5*x = p - 6*p - 5, -4*p + 17 = 3*x. Suppose -4*b = 4*n - 32, b - x*b = 4*n - 32. Factor 5*u**2 + 5 - n - 2*u**2.
3*(u - 1)*(u + 1)
Suppose 0 - 1/3*t**4 + 13/3*t**3 + 0*t**2 + 0*t = 0. What is t?
0, 13
Let h be -4 - -6 - (3/(-1) - -2). Let d(x) be the third derivative of 0*x**h + 0*x - 8*x**2 + 0*x**4 + 1/210*x**7 - 1/120*x**6 + 0*x**5 + 0. Factor d(p).
p**3*(p - 1)
Let s be (-14)/(-22)*(-27 + 38). Let a(l) be the third derivative of 3*l**2 + 3/80*l**6 + 0*l + 0*l**4 + 0 + 9/80*l**5 + 1/280*l**s + 0*l**3. Factor a(r).
3*r**2*(r + 3)**2/4
Let y(c) be the second derivative of 3*c**5/10 + c**4/3 + c**3/9 - 76*c. Factor y(d).
2*d*(3*d + 1)**2/3
Determine a, given that 7*a**3 - 5*a**3 - 5*a**3 - 21*a**2 - 18*a = 0.
-6, -1, 0
Let i(s) be the third derivative of -s**9/2880 + 23*s**8/6720 - s**7/84 + s**6/60 - 43*s**5/60 - 10*s**2. Let o(q) be the third derivative of i(q). Factor o(y).
-3*(y - 2)*(y - 1)*(7*y - 2)
Let i be (-9*14/21)/((-4)/(-106)). Let d = i + 481/3. Find h such that 1/3 - 2/3*h + d*h**4 - h**2 + 4/3*h**3 = 0.
-1, 1/2
Let q be 3/(-18) - (889/(-6) + 1). Factor -q*r**2 + 18 + 57*r + 53*r**2 + 73*r**2.
-3*(r - 3)*(7*r + 2)
Let d be -64 - -77 - 14/2. Let f(o) be the third derivative of 0*o**3 + 0*o + 1/144*o**8 - 1/90*o**d + 0*o**5 + 0 + 0*o**4 - 2/105*o**7 + 8*o**2. Factor f(l).
l**3*(l - 2)*(7*l + 2)/3
Let k(f) = f**3 - 6*f**2 + f - 1. Let l be k(6). Suppose -q = -5*c - 0*c - 23, 11 = -3*q - l*c. Suppose 5*a - 2*a**3 - q*a - 191 + 192 - a**4 = 0. What is a?
-1, 1
Suppose 234 = 10*q + 3*q. Suppose -o = 3*s - 1 - 0, -2*s = 5*o - q. Factor 1/2*f**3 + 1/6*f**5 + 1/6*f**2 + 1/2*f**o + 0 + 0*f.
f**2*(f + 1)**3/6
Let o(b) = 11*b**3 + 208*b**2 + 2704*b - 7. Let m(d) = 5*d**3 + 104*d**2 + 1352*d - 