5
Factor -19*a + 25*a + 4*a - 63 - a**2 - 3*a**3 + 41*a + 16*a**2.
-3*(a - 7)*(a - 1)*(a + 3)
Let b(l) = -4*l**3 - 26*l**2 - 98*l - 128. Let p(q) = -5*q**3 - 27*q**2 - 99*q - 128. Let f(s) = -3*b(s) + 2*p(s). Find y, given that f(y) = 0.
-4
Solve -2 - 200/3*y - 5000/9*y**2 = 0.
-3/50
Let p(a) be the second derivative of -a**7/210 + a**6/30 + a**5/60 - a**4/6 + 7*a**2 - 3*a. Let h(i) be the first derivative of p(i). Solve h(c) = 0.
-1, 0, 1, 4
Let b(i) be the second derivative of i**8/4200 + i**7/2100 - i**6/200 + i**5/150 - 11*i**4/6 - 3*i. Let v(a) be the third derivative of b(a). Solve v(f) = 0.
-2, 1/4, 1
Suppose -1/4*f**3 + 11/2 + 31/4*f + 2*f**2 = 0. What is f?
-2, -1, 11
Find j, given that -40 - 455/3*j**2 - 10/3*j**4 + 155/3*j**3 + 430/3*j = 0.
1/2, 1, 2, 12
Solve -9/2*d - 33/8*d**4 - 5/2 - 31/8*d**3 + 7/8*d**5 + 113/8*d**2 = 0 for d.
-2, -2/7, 1, 5
Let t(x) be the first derivative of -5*x**3/18 + 10*x**2/3 + 15*x/2 + 32. Factor t(n).
-5*(n - 9)*(n + 1)/6
Let 249*p**2 + 10*p**3 - 2*p**4 + 238*p**2 - 499*p**2 = 0. Calculate p.
0, 2, 3
Let p(c) be the first derivative of 22 - 13*c**2 - 1/3*c**3 - 169*c. Factor p(s).
-(s + 13)**2
Suppose 0 = 3*f + 2*f - 15. Suppose 3*u - r = 4, -5*u + 4 = -f*u - r. Suppose 0 - b**3 + 0*b**4 + 1/2*b + 1/2*b**5 + u*b**2 = 0. Calculate b.
-1, 0, 1
Determine f so that -9*f + 9*f - 19*f**4 + 15*f**4 + 24*f**2 + 6*f**3 - 2*f**3 - 16*f - 32 = 0.
-2, -1, 2
Let i be 0/(5/(-15)*-9 - (3 + 3)). Factor i - 1/4*p**2 - 1/4*p.
-p*(p + 1)/4
Let c(p) be the first derivative of -2*p**2 - 12*p + 6*p**4 + 2*p**4 + 21 + 2*p**3 + 2*p**3 - 7*p**4. Factor c(y).
4*(y - 1)*(y + 1)*(y + 3)
Let a(y) be the second derivative of -y**7/112 + 11*y**6/20 - 363*y**5/40 - 184*y. Find p, given that a(p) = 0.
0, 22
Solve 43/5*r**2 + 0 - 1/5*r**4 - 12/5*r**3 - 6*r = 0.
-15, 0, 1, 2
Let -21/2*v**2 + 21/2*v**4 + 0 - 39/4*v + 3/4*v**5 + 9*v**3 = 0. What is v?
-13, -1, 0, 1
Let q(d) = -86*d**2 + 90*d - 2. Let m(r) = r**3 - 260*r**2 + 273*r - 7. Let t(l) = -2*m(l) + 7*q(l). Factor t(o).
-2*o*(o - 1)*(o + 42)
Let a(q) be the first derivative of -q**4/32 + 29*q**3/24 + 61*q**2/16 + 31*q/8 - 566. Suppose a(l) = 0. Calculate l.
-1, 31
Let k(i) be the first derivative of -5*i**6/6 + 7*i**5 - 25*i**4/2 + 56. Determine p, given that k(p) = 0.
0, 2, 5
Let m(w) be the second derivative of -2*w**3/3 - w**2 - 3*w. Let o be m(-1). Solve -o*h + 8 + 161*h**3 - 11*h**3 - 3*h - 11*h - 70*h**2 = 0 for h.
-1/3, 2/5
Factor 8*c**3 + 2*c**2 - 171458*c + 6*c**4 + 171458*c.
2*c**2*(c + 1)*(3*c + 1)
Let v be (-33)/22*(-8)/15. Determine s, given that 2/5*s**4 + 0 - 8/5*s**3 - v*s + 2*s**2 = 0.
0, 1, 2
Let h be 5/(-20)*0/11. Let r(x) be the third derivative of 0 + 1/60*x**5 + 0*x**4 + 5*x**2 + 0*x + 1/120*x**6 + h*x**3. Solve r(t) = 0 for t.
-1, 0
Let m be 185/850 + 14/(-119). Factor 0*t**2 + 0*t - 4/5*t**4 + m*t**5 + 0 + 8/5*t**3.
t**3*(t - 4)**2/10
Suppose 0 = 3*b - 2*b. Find r such that 129*r**4 + b*r - 131*r**4 + 2*r**2 - 2*r + 2*r**3 = 0.
-1, 0, 1
Let h = 65 + -60. Factor -12*s + 1 - h - s**3 + 0*s**3 - 3*s**3 - 12*s**2.
-4*(s + 1)**3
Let b(f) = -35*f**4 + 30*f**3 + 40*f**2 - 60*f - 65. Let k(n) = -n**4 - n - 1. Let w(q) = b(q) - 30*k(q). Suppose w(x) = 0. Calculate x.
-1, 1, 7
Suppose -16 = r - 3*r. Suppose 2*m = 6*m - r. Solve -4*w**2 + 20*w**3 - 9*w**m + w**2 - 16 - 48*w = 0.
-1, -2/5, 2
Let i(g) be the second derivative of -g**6/50 - 3*g**5/50 + 13*g**4/20 - g**3 - 62*g + 2. Factor i(o).
-3*o*(o - 2)*(o - 1)*(o + 5)/5
Factor -80*z**3 - 7*z**2 - 105*z + 13*z**4 - 165*z**2 - 9*z**4 + 17*z.
4*z*(z - 22)*(z + 1)**2
Let b(x) be the first derivative of 2 + 1/3*x - 1/9*x**3 + 0*x**2. Factor b(h).
-(h - 1)*(h + 1)/3
Let i be (2/(-4))/1 - 18/12. Let t be i/11 - 8/(-44). Factor -1/7*z**2 + t - 2/7*z.
-z*(z + 2)/7
Let c be 4/(-7)*(2990/(-234) + 12). Suppose 3*s - 5 = -g + 5, 20 = 2*s + 4*g. Let -2/9*n**3 + c*n**s - 2/9*n + 0 = 0. What is n?
0, 1
Let u(j) be the second derivative of -10*j + 0*j**2 + 0 - 1/24*j**4 + 1/12*j**3. Factor u(p).
-p*(p - 1)/2
Factor -136*f + 38*f**3 - 13*f**3 + 52*f**2 - 37*f**3 - 264*f**2.
-4*f*(f + 17)*(3*f + 2)
Let o(t) = 5*t**4 + 9*t**3 - 4*t**2 + 4. Let p(h) = -h**3 + h**2 - 1. Suppose 3*n = 4*x + 28, -6*n = -n - 2*x - 28. Let v(w) = n*p(w) + o(w). Factor v(s).
5*s**3*(s + 1)
Let d = 9 - 7. Suppose d*s - 16 = -2. Factor -s*m + 7*m - 2*m**3.
-2*m**3
Let s(r) = -r**3 + 10*r**2 - 13*r + 5. Let y be s(9). Let z = -29 - y. Find i, given that -172*i - 4*i**3 + 0*i**5 + 175*i + z + 0 + i**5 - 2*i**2 = 0.
-1, 1, 2
Suppose -a = -2*a + 3, -2*o = -a - 15. Let f be 4/15 + o/((-90)/(-4)). Determine v, given that 6*v**2 + 8/3*v**4 - 2/3 - f*v - 22/3*v**3 = 0.
-1/4, 1
Let b(j) = j**2 + 4*j - 3. Let o be b(5). Let v be 20/11 + (o/(-11) - -4). Suppose x**3 + 3/7*x**4 + 0 + 0*x**v - 4/7*x = 0. Calculate x.
-2, -1, 0, 2/3
Let n(y) be the second derivative of -y**7/10 - 13*y**6/20 - y**5 + y**4 + 5*y**2/2 - 16*y. Let m(s) be the first derivative of n(s). Find v such that m(v) = 0.
-2, 0, 2/7
Let r(a) be the first derivative of -a**5/20 + 3*a**4/4 - 11*a**3/12 - 24. Factor r(q).
-q**2*(q - 11)*(q - 1)/4
Let p(h) be the second derivative of h**4/120 - 13*h**3/3 + 845*h**2 - 362*h. Factor p(x).
(x - 130)**2/10
Let m = 1861/6 + -929/3. Factor -3/2 - a + m*a**2.
(a - 3)*(a + 1)/2
Let u be (-105)/30 - (-325)/90. Let b(j) be the second derivative of -1/9*j**3 + 0*j**2 + 0 - u*j**4 + 2*j. Factor b(c).
-2*c*(2*c + 1)/3
Let c(k) be the first derivative of -4/25*k**5 + 11 + 1/15*k**6 + 0*k + 1/10*k**4 + 0*k**2 + 0*k**3. Determine d, given that c(d) = 0.
0, 1
Let r = -16 + 19. Suppose r*m**2 - 9*m**3 + 9*m + 18*m**4 - 14*m**4 + 3 - 10*m**4 = 0. Calculate m.
-1, -1/2, 1
Let c(g) = -g**2. Let t be 3 + -1 + 13 + -11. Let d(v) = 8*v**2 - 20*v + 16. Let k(f) = t*c(f) + d(f). Suppose k(u) = 0. Calculate u.
1, 4
Let t(n) be the third derivative of 0*n**6 + 0*n**3 - 18*n**2 + 0 + 0*n + 1/315*n**7 - 1/30*n**5 + 1/18*n**4. Suppose t(o) = 0. What is o?
-2, 0, 1
Let o(v) be the first derivative of v**4/32 + 3*v**3/8 - 17*v**2/8 + 3*v + 36. Solve o(r) = 0 for r.
-12, 1, 2
Let x(w) = w**2 + 11*w - 3. Let d be x(-6). Let o = 33 + d. Determine j, given that 0*j + o*j**4 + 1/5*j**3 - 1/5*j**5 + 0 + 0*j**2 = 0.
-1, 0, 1
Let g(m) be the third derivative of -29*m**6/240 + 59*m**5/60 - 31*m**4/12 + 2*m**3/3 + 524*m**2. Determine o, given that g(o) = 0.
2/29, 2
Let b(a) = -3*a**2 - 3. Let r(q) = q**5 - q**3 - q**2 - 1. Let y(l) = 3*l - 4. Let n be y(1). Let j(k) = n*b(k) + 3*r(k). Factor j(p).
3*p**3*(p - 1)*(p + 1)
Let n(m) = 15*m**5 - 45*m**4 + 85*m**3 - 70*m**2 + 25*m. Let r(u) = 7*u**5 - 23*u**4 + 43*u**3 - 35*u**2 + 12*u. Let x(k) = -2*n(k) + 5*r(k). Factor x(b).
5*b*(b - 2)*(b - 1)**3
Let v(d) = -4*d**4 - 5*d**2 + 3*d. Let n(u) = -u**4 - u**3 - u**2 + u. Suppose 11*q - 16*q - 10 = 0. Let l(j) = q*v(j) + 6*n(j). Solve l(o) = 0 for o.
0, 1, 2
What is c in 324*c**4 - 504*c**3 - 23017*c - 248*c**2 + 22985*c - 24*c**2 = 0?
-2/9, 0, 2
Let s be 38 + -35 - (-142)/(-48). Let f(o) be the first derivative of s*o**4 + 1/3*o + 2/9*o**3 - 2 + 5/12*o**2. Determine m so that f(m) = 0.
-2, -1
Let p = 17 + -17. Let x(y) = -y + 21. Let g be x(p). Factor g*f**5 + 81*f**3 + f + 5*f + 39*f**2 + 38*f**4 + 31*f**4.
3*f*(f + 1)**3*(7*f + 2)
Let y(i) be the third derivative of 1/84*i**4 + 1/210*i**5 + 0*i - 7*i**2 - 1/735*i**7 + 0*i**3 + 0 - 1/420*i**6. Factor y(x).
-2*x*(x - 1)*(x + 1)**2/7
Let t = -42689 - -2988303/70. Let k = t + -9/14. Determine q so that -2/5*q + k*q**3 + 4/5 - 4/5*q**2 = 0.
-1, 1, 2
Let w = 11 + -10. Suppose -w + 16 = 3*n. Factor 3*y**2 - 11*y**2 + 6*y**3 + n*y**2.
3*y**2*(2*y - 1)
Let a = -1548 - -1550. Suppose 0 + 2/7*h**a + 2/7*h = 0. What is h?
-1, 0
Let -426/5*r**2 - 42 - 4/5*r**3 - 632/5*r = 0. What is r?
-105, -1, -1/2
Let f(w) be the third derivative of -w**6/240 + w**5/5 - 55*w**4/16 + 121*w**3/6 - 31*w**2 - 6. Factor f(v).
-(v - 11)**2*(v - 2)/2
Let c(d) = -2*d**2 - 59*d + 93. Let s be c(-31). Let n(x) be the first derivative of 1/14*x**4 - 4/7*x**2 + 0*x**3 + 1 + s*x. Factor n(g).
2*g*(g - 2)*(g + 2)/7
Let p(l) be the third derivative of -1/3*l**3 - 3/8*l**5 + 0 - 42*l**2 + 7/12*l**4 + 0*l. Solve p(d) = 0 for d.
2/9, 2/5
Let d = -15337 - -15340. Suppose 2*z**4 + 10/7*z**5 - 16/7*z*