761. Let g(o) = o**4 + o**3 - 3*o**2 - 1. Let b(x) = g(x) - t(x). Factor b(a).
-5*(a - 19)*(a + 2)**3
Determine z, given that -4/5*z - 32/5*z**2 + 4/5*z**3 + 6 + 2/5*z**4 = 0.
-5, -1, 1, 3
Let c(n) be the first derivative of 9*n**4/28 + 115*n**3/21 + 41*n**2/7 - 24*n/7 + 276. Determine m, given that c(m) = 0.
-12, -1, 2/9
Let j(x) = -2*x**2 - 3 + 4*x**2 - 4*x**2 - x**2 + 3*x**3 + 6*x**4. Let s(f) = 5*f**4 + 2*f**3 - 3*f**2 - 2. Let w(l) = -2*j(l) + 3*s(l). Factor w(m).
3*m**2*(m - 1)*(m + 1)
Factor -22/5*f - 6/5*f**2 - 12/5 + 2/5*f**4 + 6/5*f**3.
2*(f - 2)*(f + 1)**2*(f + 3)/5
Let h = 85 + -73. Factor 5*s**3 - 3*s**3 + 9*s**2 - 5*s**3 - h.
-3*(s - 2)**2*(s + 1)
Let a(c) be the first derivative of 7*c**4/4 - 4*c**3 - 25*c**2/2 - 6*c + 92. Suppose a(l) = 0. Calculate l.
-1, -2/7, 3
Let q(x) = -4*x**3 + 4*x**2 + 2*x. Let c = -7 + 9. Let v(m) = 20*m**3 - 19*m**2 - 9*m. Let j(y) = c*v(y) + 11*q(y). Determine l, given that j(l) = 0.
-1/2, 0, 2
Let i(g) be the third derivative of -g**9/60480 + g**8/6720 + g**7/2016 + 3*g**4/8 - 11*g**2. Let u(k) be the second derivative of i(k). Factor u(q).
-q**2*(q - 5)*(q + 1)/4
Let b(x) = -4*x**3 - 5*x**2 + 4*x + 2. Let h(t) = -12*t**3 - 13*t**2 + 12*t + 5. Let g(d) = 8*b(d) - 3*h(d). Let g(o) = 0. Calculate o.
-1, 1/4, 1
Let f be (-2)/18*(-13 + 7). Suppose -1/3*c**4 + 0*c**2 + 1/3 - f*c + 2/3*c**3 = 0. Calculate c.
-1, 1
Suppose -4*u + 3*c + 23 = 0, 7*u - 2*u = 5*c + 35. Let p(g) be the second derivative of -4*g + 0*g**u + 0*g**3 - 1/18*g**4 + 0 + 1/30*g**5. Factor p(f).
2*f**2*(f - 1)/3
Suppose -5*v + 14*v + v + 21*v**2 + 35*v**2 - 58*v**2 = 0. Calculate v.
0, 5
Suppose 0 = j + 5*b - 17 + 5, 0 = j - b + 6. Let m be (60/j)/(7 + -9). Factor -12/5 + 14/5*f**3 - m*f - 24/5*f**2.
2*(f - 3)*(f + 1)*(7*f + 2)/5
Factor 530 + 44*f - 312 - 264 + 2*f**2.
2*(f - 1)*(f + 23)
Let l(s) = -s**5 - 1. Let a(i) = -i + 4. Let p be a(2). Let d(h) = -7*h**5 - 20*h**4 - 20*h**3 - 2. Let t(z) = p*l(z) - d(z). Let t(u) = 0. What is u?
-2, 0
Let l(u) be the second derivative of 1/3*u**3 - 3*u - 3/4*u**2 + 0 - 1/24*u**4. Solve l(d) = 0 for d.
1, 3
Suppose -z + 33 = 5*d, -2*d - 48 = z - 4*z. Suppose -13*t + 4*t + z = 0. Solve -4/3*v + 1/3*v**t + 4/3 = 0 for v.
2
Let y(f) be the first derivative of f**5/90 + f**4/9 - 5*f**3/9 + 8*f**2 + 14. Let p(m) be the second derivative of y(m). Factor p(s).
2*(s - 1)*(s + 5)/3
Let u be 20/(-8)*8/(-10). Let o(a) = -10*a**2 - 9*a - u - 6 + 3 + 3. Let g(v) = -v**2. Let c(f) = 3*g(f) - o(f). What is x in c(x) = 0?
-1, -2/7
Let i(n) be the third derivative of n**6/90 - n**5/3 + 8*n**4/3 + 128*n**3/9 + 5*n**2 + 2. Solve i(k) = 0 for k.
-1, 8
Let p be 5 - 0 - (-9 + -11 + 19). Let q(i) be the first derivative of 1/14*i**4 - 1/21*i**p + 2/21*i**3 + 7 + 0*i**2 + 0*i - 2/35*i**5. Factor q(g).
-2*g**2*(g - 1)*(g + 1)**2/7
Let x(q) be the second derivative of q**7/1260 + q**6/540 - q**5/180 - q**4/36 - 10*q**3/3 - 24*q. Let j(s) be the second derivative of x(s). Factor j(u).
2*(u - 1)*(u + 1)**2/3
Let t(i) = -19*i**4 - 6*i**3 + 15*i**2 + 10*i. Let o(y) = -170*y**4 - 55*y**3 + 135*y**2 + 90*y. Let v(n) = 4*o(n) - 35*t(n). Determine l so that v(l) = 0.
-1, -2/3, 0, 1
Let q(r) = r**2 + r. Let n(w) = 11*w**4 + 10*w**3 - 4*w**2 + 5*w. Let s(o) = -o**4 - o**2. Let z(i) = n(i) - 4*s(i). Let g(a) = 5*q(a) - z(a). Factor g(k).
-5*k**2*(k + 1)*(3*k - 1)
Let h(s) be the first derivative of -2/3*s**3 + 0*s - 12/5*s**5 + 9/4*s**4 - 5 + 0*s**2 + 5/6*s**6. Factor h(z).
z**2*(z - 1)**2*(5*z - 2)
Let z(v) be the second derivative of -v**4/66 - 7*v**3/33 + 18*v**2/11 + 17*v - 1. Factor z(p).
-2*(p - 2)*(p + 9)/11
Let m = -7401 - -7401. Solve 35/4*a**3 + m + 0*a + 15/4*a**2 + 25/4*a**4 + 5/4*a**5 = 0 for a.
-3, -1, 0
Determine b so that 0*b + 54/11*b**3 + 0 + 2/11*b**4 + 100/11*b**2 = 0.
-25, -2, 0
Let p(b) be the second derivative of b**8/6720 + b**7/1680 - b**6/1440 - b**5/240 + 3*b**3/2 - 16*b. Let r(a) be the second derivative of p(a). Factor r(d).
d*(d - 1)*(d + 1)*(d + 2)/4
Let j = 69 + -45. Let c be ((-12)/9)/((-8)/j). Factor 0*n**4 + 7*n**2 - 5*n**2 - n**c - 1 + 0.
-(n - 1)**2*(n + 1)**2
Let j(q) = 7*q**2 - 8*q + 36. Let k be j(11). Let 4*m**3 + m**4 + 795 - k + 4*m**2 = 0. What is m?
-2, 0
Let w(s) be the first derivative of -s**5/80 - s**4/16 + s**2/2 + 2*s + 11. Let h(f) be the first derivative of w(f). Factor h(t).
-(t - 1)*(t + 2)**2/4
Let f(t) = t**2 + t. Let w(y) = 4*y**2 - 6*y. Let c(p) = -5*f(p) + w(p). Let j be c(0). Solve 2/3*b**4 + 2/3*b**3 + j*b + 0 - 4/3*b**2 = 0 for b.
-2, 0, 1
Suppose 50 = 2*n - 22. Let f = n - 31. Solve 9*i - 4 - 6*i + i**3 + 3*i**2 + f = 0.
-1
Let d(s) be the second derivative of 11*s**7/84 + 109*s**6/30 + 161*s**5/4 + 650*s**4/3 + 5875*s**3/12 - 625*s**2/2 - 79*s - 1. Factor d(m).
(m + 5)**4*(11*m - 2)/2
Suppose 8 = z + z. Suppose 9*w + 11 = 38. Factor -2*o - o**2 - 3*o**2 - 2*o**2 + 6*o**z - w*o**5 + 5*o.
-3*o*(o - 1)**3*(o + 1)
Let k(s) = -s**3 + s**2 + 4. Let g be k(-2). Factor 12*h - g*h + 0 + 0 + 4*h**2.
4*h*(h - 1)
Suppose 10*a + 13*a = 253. Let u(n) be the first derivative of -a + 2/3*n**2 + 0*n + 2/15*n**5 + 1/18*n**6 - 1/4*n**4 - 4/9*n**3. Factor u(t).
t*(t - 1)**2*(t + 2)**2/3
Let x(w) be the first derivative of -3*w**4/4 - 5*w**3 - 12*w**2 - 12*w - 101. Factor x(o).
-3*(o + 1)*(o + 2)**2
Let c(n) be the first derivative of 0*n - 30 + 3/10*n**2 + 1/20*n**4 - 4/15*n**3. Solve c(a) = 0 for a.
0, 1, 3
Let c = 24/5 - 4. Let w be (-2160)/(-630) + (-4)/(-7). What is p in 2/5*p**w + 0*p + c*p**3 + 2/5*p**2 + 0 = 0?
-1, 0
Suppose 25343*z - 164 = 25302*z. Suppose 3/8*a**2 - 1/4 - 1/8*a + 1/8*a**3 - 1/8*a**z = 0. What is a?
-1, 1, 2
Suppose 2*p**2 + 2*p**2 + 20*p - 2*p + 107336 - 107358 = 0. What is p?
-11/2, 1
Let u(n) = 13*n - 21. Let p be u(2). Let x be -2 + (-1 - 11)/(-1*p). Let 4/5*d**3 - x*d**2 + 0 + 0*d = 0. Calculate d.
0, 1/2
Suppose b + 21 = 5*o, 0*b = 5*b - 3*o + 105. Let a be (7/b)/((-2)/4). Factor a + 4/3*w**2 + 2*w.
2*(w + 1)*(2*w + 1)/3
Suppose 8*x = 3*x + 40. Suppose x*f - 3*f = u + 14, -4*f + u = -12. Solve 6*r**4 + r**2 - 3*r**f + 8*r**3 - 6*r**2 = 0.
-2, 0, 2/3
Let o(s) be the second derivative of -s**5/25 - 11*s**4/15 + 271*s + 1. Factor o(m).
-4*m**2*(m + 11)/5
Let h = 104 + -184. Let j = -394/5 - h. Factor j*p + 3/5 + 3/5*p**2.
3*(p + 1)**2/5
Let f be 243/6 + -4 + (-3)/2. Let h = 335/9 - f. What is i in -2/9*i**5 - h*i**3 - 20/9*i**2 - 2/9 - 10/9*i**4 - 10/9*i = 0?
-1
Let k = 213 - 201. Let d be k/(102/24 - 2). Suppose -d - 32/3*w - 4*w**2 + 4/3*w**4 + 8/3*w**3 = 0. Calculate w.
-2, -1, 2
Let n = -8541 - -76874/9. Factor 7/9*k + 2/9 + n*k**2.
(k + 1)*(5*k + 2)/9
Let o(d) = -d**2 + 5*d + 2. Let b be o(0). What is t in t**b + 1/5*t - 2/5 + 2/5*t**3 = 0?
-2, -1, 1/2
Let p(y) be the third derivative of y**7/2100 + y**6/300 + y**5/120 + y**4/120 + 22*y**2. Factor p(z).
z*(z + 1)**2*(z + 2)/10
Let a be (2 - 0)/((-2)/2) - -6. Let j(n) be the third derivative of 0*n + 0 + 2*n**2 - 1/180*n**5 + 0*n**3 - 1/36*n**a. Factor j(w).
-w*(w + 2)/3
Let p(q) = 4*q**3 + 12*q**2 - 8*q + 508. Let f(w) = -2*w**2 - w - 4. Let k(x) = 28*f(x) + p(x). Factor k(s).
4*(s - 11)*(s - 3)*(s + 3)
Let q(c) = 15*c**4 + 52*c**3 + 23*c**2 - 7*c - 7. Let l(i) = -5*i**4 - 17*i**3 - 8*i**2 + 2*i + 2. Let w(z) = 7*l(z) + 2*q(z). Factor w(h).
-5*h**2*(h + 1)*(h + 2)
Let f(k) = 44*k**4 + 84*k**3 + 60*k**2 - 4*k + 24. Let r(j) = 9*j**4 + 17*j**3 + 12*j**2 - j + 5. Let p(y) = 5*f(y) - 24*r(y). Let p(l) = 0. Calculate l.
-1, 0
Let a be (4/(-48))/(-1)*9/((-18)/(-8)). Determine v so that -2/3 + 2/3*v**2 + a*v**3 - 1/3*v = 0.
-2, -1, 1
Let y = 37 - -2. Suppose 15 = -5*b + t + y, t + 9 = 2*b. Factor -b*f**2 - 7*f - 4 + f - 2*f + f**2.
-4*(f + 1)**2
Let v = 107 - 99. Suppose -6*d = -2*d - v. Suppose -1/2*c**d - 1/2 - c = 0. What is c?
-1
Let 13*z - 13*z - 10*z - 3*z - 11*z + 28 - 4*z**2 = 0. Calculate z.
-7, 1
Let q(p) be the second derivative of 0*p**2 - p - 1/18*p**4 + 1/3*p**3 + 0. Factor q(l).
-2*l*(l - 3)/3
Suppose -14*r**2 - 6*r**4 - 4/7 - 110/7*r**3 - 34/7*r = 0. Calculate r.
-1, -1/3, -2/7
Suppose -s + 5*j + 14 - 1 = 0, -2*j = -s + 7. Factor -4/3*r**s + 0*r - 2/3*r**2 + 0 - 2/3*r**4.
-2*r**2*(r + 1)**2/3
Solve 0*w + 1/7*w**4 + 0*w**2 + 1/7*w**5 + 0*w**3 + 0 = 0 for w.
-1, 0
Let h be (-2)/10*6*(-15)/6. Sup