a) = 0 for a.
2
Let b(m) be the second derivative of 2*m**7/105 - 58*m**6/75 + 39*m**5/5 + 15*m**4 - 109*m - 1. Factor b(l).
4*l**2*(l - 15)**2*(l + 1)/5
Let a(v) = -4*v**2 - 4*v. Let t(o) = -3*o**2 - 6*o - 3. Let m(z) = 4*a(z) - 5*t(z). Let m(p) = 0. What is p?
-1, 15
Factor 0 - 10*m**3 + 0*m - 5/2*m**4 - 15/2*m**2.
-5*m**2*(m + 1)*(m + 3)/2
Let m(a) be the third derivative of a**6/40 - 3*a**5/10 + 132*a**2 - a. Factor m(o).
3*o**2*(o - 6)
Suppose 2*n + 2*n - 2*b = -10, -n + 3*b + 5 = 0. Let c(v) = -3*v - 10. Let s be c(n). Factor 0*f**s + 0*f - f**2 - f + 0*f.
-f*(f + 1)
Factor 22*a**2 + a**3 - 36*a + 18*a**4 - 34*a**2 + 26*a**3 + 3*a**5.
3*a*(a - 1)*(a + 2)**2*(a + 3)
Let h(n) be the first derivative of -5*n**4/9 + 14*n**3/27 + n**2/3 + 121. Suppose h(g) = 0. Calculate g.
-3/10, 0, 1
Let v(o) = -2*o**5 + 7*o**4 + 5*o**3 - o**2 + 3*o + 3. Let c(i) = -i**5 + i**4 + 2*i**3 + i**2 + i + 1. Let l(k) = -6*c(k) + 2*v(k). Solve l(j) = 0.
-4, -1, 0, 1
Let x = -13941/10 - -2801/2. Solve 12/5*g**2 - 12/5 - x*g = 0 for g.
-1/3, 3
Factor 0 + 2 - 2 + 2026*u**3 - 2028*u**3 + 18*u**2.
-2*u**2*(u - 9)
Let m be ((-8)/3)/(-1*(-2)/(-3)). Factor q - q + 2*q**5 - 2*q - m*q**4 + 4*q**2.
2*q*(q - 1)**3*(q + 1)
Let x(i) = -10*i**4 - 90*i**3 - 301*i**2 - 368*i - 180. Let m(v) = -2*v**4 - 18*v**3 - 60*v**2 - 74*v - 36. Let a(j) = -11*m(j) + 2*x(j). Factor a(o).
2*(o + 1)*(o + 2)*(o + 3)**2
Let g be ((-99)/(-27) + -1)/(5/(75/70)). Factor 8/7*y**3 - 10/7*y**2 + g*y - 2/7*y**4 + 0.
-2*y*(y - 2)*(y - 1)**2/7
Let w be ((-2)/4)/(1/(-4)). Let -4 - 9*j - 9*j**w + 0*j - 3 + 4 - 3*j**3 = 0. What is j?
-1
Suppose -2*g - 5 = 37. Let n be (g/(-126))/(-1*(-2)/18). Factor 0*u**3 - n*u**4 + 0 + 0*u + 3/2*u**5 + 0*u**2.
3*u**4*(u - 1)/2
Suppose 2*v + 2 + 0 = 0. Let b be 2*10/(-4)*v. Let 13*y**4 - y + 8*y**2 + 4*y**b - 21*y**4 - 3*y = 0. What is y?
-1, 0, 1
Let q(v) be the first derivative of -v**3/15 + 11*v**2/10 - 18*v/5 + 43. Find m such that q(m) = 0.
2, 9
Let p = 2665/126 + -293/14. Factor 0*q + 8/9 - p*q**2.
-2*(q - 2)*(q + 2)/9
Let b(p) = -p**3 - 2*p**2 + 12*p - 7. Let x be b(-5). Find g, given that 9/2*g + 7*g**3 + 1/2*g**5 - 3*g**4 - 1 - x*g**2 = 0.
1, 2
Let z(c) be the second derivative of 19*c - 1/50*c**5 - 2/5*c**2 + 1/15*c**3 + 1/15*c**4 + 0. Suppose z(j) = 0. Calculate j.
-1, 1, 2
Let h be (8/(-24))/(1/(-6)). Factor -1 - 5 + 3 + 5*g**h + 6 + g**3 + 7*g.
(g + 1)**2*(g + 3)
Let x = 2127 - 2126. Suppose 1/2*n**2 - 1/2*n - x = 0. Calculate n.
-1, 2
Let a(p) be the third derivative of -p**8/840 + p**7/1260 + 2*p**6/45 - p**5/15 + 2*p**4/3 + 24*p**2. Let c(g) be the second derivative of a(g). Factor c(t).
-2*(t - 2)*(t + 2)*(4*t - 1)
Let h be (4 + (6 - 4))*18/72. Let o(d) be the second derivative of h*d**2 + 0 - 1/4*d**4 + 0*d**3 - 8*d. Find k, given that o(k) = 0.
-1, 1
Let p(u) = 5*u**3 + 4*u**2 + u - 6. Let x(s) = -27*s**3 - 20*s**2 - 5*s + 30. Let i(a) = 22*p(a) + 4*x(a). Factor i(r).
2*(r - 1)*(r + 2)*(r + 3)
Solve -10*l + 5/6*l**2 + 0 = 0 for l.
0, 12
Find j, given that -1152/7 - 2/7*j**2 - 96/7*j = 0.
-24
Factor -4*w**2 - 7935 - 8249 - 19916 - 1096*w + 336*w.
-4*(w + 95)**2
Let p = -52 + 95. Let m = 45 - p. Factor 2/7*w**m - 6/7*w + 4/7.
2*(w - 2)*(w - 1)/7
Let w = -4673 + 4677. Factor -8/15*d + 0 + 2/15*d**w + 6/5*d**2 - 4/5*d**3.
2*d*(d - 4)*(d - 1)**2/15
Let m be ((-36)/20)/(9/(-15)). Let j(n) be the first derivative of 3/2*n**2 - 6*n - 4 + 28*n**m. Factor j(z).
3*(4*z - 1)*(7*z + 2)
Let v = -98/13 - -86/13. Let u = 37/26 + v. Factor 1/4 + 1/2*z**3 - 1/4*z**5 - u*z**2 - 1/4*z + 1/4*z**4.
-(z - 1)**3*(z + 1)**2/4
Let w(v) be the third derivative of v**7/1890 - v**6/540 - 66*v**2. Factor w(y).
y**3*(y - 2)/9
Let n = 135241/120 + -1127. Let k(l) be the third derivative of 0 + 0*l**4 + n*l**5 + 0*l**3 - 1/420*l**7 - 1/240*l**6 + 1/672*l**8 - l**2 + 0*l. Factor k(w).
w**2*(w - 1)**2*(w + 1)/2
Let c(f) be the first derivative of -f**8/1680 - f**7/280 - f**6/180 - 9*f**3 + 30. Let t(d) be the third derivative of c(d). Determine x, given that t(x) = 0.
-2, -1, 0
Let h = 59 - 67. Let j be 10 + h - 6/8. Let 3/4*a**3 - 1/4*a**5 + 0 + 1/4*a**4 + 1/2*a - j*a**2 = 0. Calculate a.
-2, 0, 1
Suppose -4*z = -3*i - 5, -4*z + 31 - 14 = 9*i. Factor 0 + 3/5*m + 3/5*m**z.
3*m*(m + 1)/5
Let o(i) be the second derivative of i**4/12 + 20*i**3/3 - 41*i**2/2 + 643*i. Factor o(z).
(z - 1)*(z + 41)
Let u(z) be the first derivative of 39 + 15*z**4 - 10 - z**3 + 17*z**5 - 77*z**5. Find c, given that u(c) = 0.
0, 1/10
Let t be ((-6)/(-4) + 1)*-2. Let y(b) = b**3 + 4*b**2 - 6*b. Let k be y(t). Factor k*n - n**4 - n**3 + n**2 - 4*n + 0*n**4 + 0*n**3.
-n*(n - 1)*(n + 1)**2
Let a(j) be the second derivative of 1/42*j**3 + 0*j**2 + 0 + 1/140*j**5 - 1/42*j**4 - 8*j. Determine y so that a(y) = 0.
0, 1
Let r = 24667 - 24663. Determine j so that -r*j**4 + 10/9*j**5 + 52/9*j**2 - 16/9 + 14/9*j**3 - 8/3*j = 0.
-1, -2/5, 1, 2
Let d(f) be the third derivative of f**8/504 + 2*f**7/315 - f**5/45 - f**4/36 - 9*f**2 + 2*f. Find i such that d(i) = 0.
-1, 0, 1
Let b(h) be the first derivative of -h**5/120 + 7*h**4/72 - 11*h**3/36 + 5*h**2/12 + 16*h + 6. Let r(j) be the first derivative of b(j). Factor r(y).
-(y - 5)*(y - 1)**2/6
Suppose v + 2 = 2*p, -2*p + 5*p = 4*v - 2. Let r(k) be the second derivative of -1/4*k**4 + 0 - 1/3*k**3 - 1/60*k**6 - 1/4*k**v - 4*k - 1/10*k**5. Factor r(x).
-(x + 1)**4/2
Let l(m) = -5*m**3 - 3*m**2 + 2*m. Suppose -1 - 9 = 2*d. Let g = d + 11. Let w(n) = -15*n**3 - 9*n**2 + 6*n. Let x(h) = g*w(h) - 21*l(h). Factor x(c).
3*c*(c + 1)*(5*c - 2)
Find w such that 0*w**2 + 0 + 0*w - 22/25*w**3 + 2/25*w**5 - 4/5*w**4 = 0.
-1, 0, 11
Let j(s) be the second derivative of -s**6/45 - s**5/10 + s**4/18 + s**3/3 - 24*s. Solve j(l) = 0 for l.
-3, -1, 0, 1
Let -4/11*b**3 - 40/11 + 34/11*b + 10/11*b**2 = 0. What is b?
-5/2, 1, 4
Let x(t) be the first derivative of -17 - 2*t**2 + 2/3*t + 2*t**3 - 2/3*t**4. Factor x(y).
-2*(y - 1)**2*(4*y - 1)/3
Let y(k) be the second derivative of -k**4 + 21*k**3/2 - 30*k**2 - 15*k + 3. Suppose y(a) = 0. What is a?
5/4, 4
Factor -241 - 13*j**2 - 111*j + 18*j**2 + j**2 + 31 - 9*j**2.
-3*(j + 2)*(j + 35)
Suppose 0 = 4*a - 12, 107*a = -4*b + 105*a + 14. Suppose 1/6*t**b + 1/6 + 1/3*t = 0. Calculate t.
-1
Let t = 886/45 + -170/9. Let f(g) be the second derivative of -4/15*g**3 + t*g**2 + 0 + 1/30*g**4 + 5*g. Solve f(z) = 0 for z.
2
Let x(n) be the third derivative of n**5/12 - 275*n**4/8 - 415*n**3/3 + 3*n**2 - 165. Solve x(c) = 0 for c.
-1, 166
Let s(h) be the second derivative of -h**6/60 + 3*h**5/20 - h**4/24 - 2*h**3 - 4*h**2 + 175*h. Suppose s(n) = 0. Calculate n.
-1, 4
Suppose -24*c + 22*c - 13 = -5*s, -21 = -s + 5*c. Find y such that 3*y + 7/4*y**2 - s = 0.
-2, 2/7
Let t be 1*1*(-4 - (4 - 5)). Let d(q) = 2 + q**3 + q**2 - q - 10*q - 3*q**3. Let x(f) = f**3 + 6*f - 1. Let l(y) = t*d(y) - 5*x(y). Factor l(a).
(a - 1)**3
Let -21/8*k**4 - 39/8*k**3 + 0 + 3/8*k - 15/8*k**2 = 0. Calculate k.
-1, 0, 1/7
Let o(x) be the third derivative of -x**8/896 + x**7/280 + 3*x**6/320 - x**5/20 + x**4/16 - 300*x**2 - 1. Suppose o(z) = 0. What is z?
-2, 0, 1, 2
Let o be 2/6 + -1*3/(-45). Determine f so that 8/5*f + 0 + 0*f**2 - o*f**3 = 0.
-2, 0, 2
Let x be (-2)/(-3) + (-12 - 880/(-72)). Factor -8/9*z - 2/9*z**2 - x.
-2*(z + 2)**2/9
Suppose 224 = 23*p + 89*p. Let z(q) be the second derivative of q - 1/4*q**4 + 1/20*q**5 + 0 + 1/30*q**6 + q**p - 1/6*q**3. Factor z(m).
(m - 1)**2*(m + 1)*(m + 2)
Let h(c) be the first derivative of -c**4/10 - 4*c**3/15 + 4*c**2 - 48*c/5 - 111. Factor h(z).
-2*(z - 2)**2*(z + 6)/5
Let r(j) be the second derivative of -j**6/30 - 3*j**5/4 - 56*j - 1. Solve r(y) = 0.
-15, 0
Find l, given that -2/17*l**2 - 22/17*l - 36/17 = 0.
-9, -2
Let v be (2 - -7)*(-2)/(-1). Suppose 4*f**3 + 16*f**2 + 8 + v*f + 2*f + 0 + 0*f**2 = 0. What is f?
-2, -1
Suppose k + 18 = 3*k. Suppose b + b - k = -3*u, u + 11 = 4*b. Solve -2*f**2 - 4*f + 4*f + f**b = 0 for f.
0, 2
Let x(d) = -7*d**4 + 37*d**3 - 8*d**2 + 3*d - 5. Let o(a) = 2*a**4 + a**3 + a**2 + a - 1. Let f(g) = 10*o(g) - 2*x(g). Factor f(i).
2*i*(i - 1)**2*(17*i + 2)
Suppose 5*g + 30 = 3*n, 4*n + 5*g - 32 = -62. Factor n - 3/5*j**4 + 2/5*j**2 - j**3 + 0*j.
-j**2*(j + 2)*(3*j - 1)/5
Let q(v) = -45*v**2 + 110*v - 345. Let s(c) = 