).
-4*h*(h + 2)
Let u(f) be the first derivative of -f**4 - 16*f**3/3 + 50*f**2 + 112*f - 253. Factor u(p).
-4*(p - 4)*(p + 1)*(p + 7)
Let f(y) = 2*y**2 + 26*y - 96. Let r(z) = 3*z**2 + 25*z - 107. Let k(q) = -5*f(q) + 4*r(q). Determine t so that k(t) = 0.
2, 13
Determine d, given that 5/2*d**5 + 0*d**3 - 5/2*d**4 + 0 + 0*d + 0*d**2 = 0.
0, 1
Let h(d) = d**2 - 3*d - 16. Let u(y) = -2*y**2 + 10*y + 95 + 75 - 122. Let n be 255/25 - (-2)/(-10). Let c(z) = n*h(z) + 3*u(z). Solve c(m) = 0.
-2, 2
Let m = -20 - -81/4. Let n = 166 + -331/2. Find y such that -3/4*y + n + m*y**2 = 0.
1, 2
Suppose -o + 3*d + 1 = 7, -d = -3*o + 6. Let p be 16/(-5) - (-18 + 14). Find v, given that -p*v**2 + 0 + 0*v + 8/5*v**4 + 6/5*v**5 - 2/5*v**o = 0.
-1, 0, 2/3
Let j(i) be the first derivative of i**4/14 + 40*i**3/21 + 37*i**2/7 + 36*i/7 + 422. Factor j(s).
2*(s + 1)**2*(s + 18)/7
Let w(i) be the first derivative of 6*i**5/5 - 9*i**4/4 + 3*i**2/2 + 81. Solve w(a) = 0.
-1/2, 0, 1
Let -10/3*g - 2/3*g**4 + 10/3*g**3 + 0 + 2/3*g**2 = 0. Calculate g.
-1, 0, 1, 5
Let m = 18 + -14. Suppose m*w + 4 = 2*d, d + 3*d + 4*w = 44. Determine i so that -3*i**4 + 3*i**2 - 14 + d + 6 = 0.
-1, 0, 1
Suppose -2*b - 2271 = -2275. Let y(x) be the second derivative of -4/3*x**4 + 0*x**b + 2/3*x**3 + 0 - 4*x. Let y(k) = 0. What is k?
0, 1/4
Let w(m) = -3*m + 33. Let r be w(10). Suppose o - 3*j = 17 - 2, -4*o + 15 = -r*j. Factor 0*x**2 + 0*x + o*x**3 + 0 - 1/3*x**4.
-x**4/3
Let u(p) be the first derivative of 0*p**3 + 0*p - 1/60*p**4 - 1/2*p**2 + 11 + 1/150*p**5. Let f(j) be the second derivative of u(j). Find z such that f(z) = 0.
0, 1
Suppose 24*c - 23 = 25. Suppose 4/3*b**4 + 8/3 + 1/3*b**5 + 1/3*b**3 - 10/3*b**c - 4/3*b = 0. Calculate b.
-2, 1
Let k(d) be the first derivative of 1 + 0*d + 1/8*d**2 - 1/12*d**3. Factor k(s).
-s*(s - 1)/4
Suppose 3*y = 9*y - 18. Suppose -3*m + y*w = -0*m - 24, -52 = -5*m + 2*w. Factor 4/3 + m*g + 27*g**2.
(9*g + 2)**2/3
Let x be 8/92 + (-616)/(-322). Let l = 125/264 - 7/24. Determine t, given that 0 + 0*t - l*t**x = 0.
0
Find b, given that -1/12*b**4 + 4/3*b - 7/12*b**3 + 0 - 2/3*b**2 = 0.
-4, 0, 1
Let g(v) be the third derivative of -v**7/4200 + v**6/1800 + v**5/600 - v**4/120 + v**3/3 - 9*v**2. Let a(d) be the first derivative of g(d). Factor a(n).
-(n - 1)**2*(n + 1)/5
Let h(a) be the second derivative of -7*a**8/192 - 11*a**7/72 - 2*a**6/9 - a**5/6 - a**4/2 - 10*a. Let i(t) be the third derivative of h(t). Factor i(s).
-5*(s + 1)*(7*s + 2)**2
Let z(a) be the third derivative of a**7/420 - 7*a**6/240 - a**5/15 + 377*a**2. What is u in z(u) = 0?
-1, 0, 8
Let q(r) be the first derivative of 0*r**2 - 2*r + 1/45*r**6 - 5 - 1/9*r**3 - 1/10*r**5 + 1/6*r**4. Let m(d) be the first derivative of q(d). Factor m(k).
2*k*(k - 1)**3/3
Let t = -1231/5 - -248. Suppose 5*z + 45 = 55. Solve 12/5*c**3 + 2/5*c + c**4 + 0 + t*c**z = 0.
-1, -2/5, 0
Let q(w) be the third derivative of -w**6/40 - w**5/3 - w**4 + 39*w**2. Let x(g) = -g**2. Let t(j) = -q(j) + 2*x(j). Factor t(y).
3*y*(y + 2)*(y + 4)
Factor 2/9*b**2 + 2/9*b - 8/3.
2*(b - 3)*(b + 4)/9
Suppose 15*u - 55 = 4*u. Let v(f) be the third derivative of 0*f + 0 + 0*f**3 - 2*f**2 - 1/6*f**4 - 4/15*f**u - 4/105*f**7 - 1/6*f**6. Factor v(k).
-4*k*(k + 1)**2*(2*k + 1)
Let t(k) be the third derivative of 3*k**7/70 - k**6/5 + k**5/20 + k**4 - 2*k**3 + 6*k**2. Find w, given that t(w) = 0.
-1, 2/3, 1, 2
Find n, given that 0 - 21/5*n**3 - 36/5*n + 3/5*n**4 + 48/5*n**2 = 0.
0, 2, 3
Let h(a) be the second derivative of a**3/6 - 3*a**2/2 - 5*a. Let t be h(7). Let t*z + 3*z**2 + 5*z + 1 - 3*z - 10 = 0. Calculate z.
-3, 1
Factor 6*v**2 + 18 + 74*v + 6*v**3 - 10*v**2 + 66*v**2.
2*(v + 1)*(v + 9)*(3*v + 1)
Let d(w) = 24*w**3 + 84*w**2 + 99*w + 9. Let l(x) = -11*x**3 - 40*x**2 - 49*x - 4. Let t(n) = -4*d(n) - 9*l(n). Factor t(o).
3*o*(o + 3)*(o + 5)
Let m(d) = d**3 - 7*d**2 - 47*d + 288. Let u be m(5). What is v in 1/4*v**u - v**2 + 3/4*v + 0 = 0?
0, 1, 3
Let d(u) be the first derivative of 4*u**5/5 + 4*u**4 - 36*u**3 + 76*u**2 - 64*u + 11. Factor d(i).
4*(i - 2)*(i - 1)**2*(i + 8)
Solve 3*k**3 + 1311*k - 80*k**2 + 2166 + 385*k**2 - 185*k**2 = 0.
-19, -2
Let r = -2 + 8. Suppose 0 = p - 2, -z - 3*z + 3*p = -18. Factor r*d - 10*d - 2*d**2 + z*d.
-2*d*(d - 1)
Let x(w) be the third derivative of w**5/690 - w**4/69 + 4*w**3/69 + 9*w**2 + 13*w. Factor x(q).
2*(q - 2)**2/23
Let s(w) be the second derivative of -32*w**4/3 - 112*w**3/9 - 49*w**2/9 + 24*w + 1. Determine k so that s(k) = 0.
-7/24
Let l(u) be the second derivative of u**5/50 - 39*u**4/10 + 1121*u**3/5 + 3481*u**2/5 + 39*u. Factor l(d).
2*(d - 59)**2*(d + 1)/5
Find t such that -41/5*t - 1/5*t**2 + 36 = 0.
-45, 4
What is j in 1/3*j**3 - 7*j + 11/3 + 3*j**2 = 0?
-11, 1
Find h, given that 0*h - 44*h**2 + 38*h**2 + h - 2 + 20 - 4*h = 0.
-2, 3/2
Let c(h) be the third derivative of 0*h**3 - 1/660*h**5 + 0*h - 13*h**2 + 1/2310*h**7 - 1/440*h**6 + 1/88*h**4 + 0. Factor c(t).
t*(t - 3)*(t - 1)*(t + 1)/11
Let d = -714 + 714. Let j(x) be the second derivative of 0*x**3 + 1/30*x**6 + 0 - 1/20*x**5 + d*x**4 + 1/21*x**7 - 2*x + 0*x**2. Factor j(l).
l**3*(l + 1)*(2*l - 1)
Suppose 0 = 9*b - 22 + 4. Factor -2/3*n**4 + 0 + 14/3*n**3 + 6*n - 10*n**b.
-2*n*(n - 3)**2*(n - 1)/3
Let y(d) be the second derivative of -d**6/120 - 9*d**5/80 - 7*d**4/48 + 15*d**3/8 - 7*d**2/2 + 3*d - 2. Factor y(x).
-(x - 1)**2*(x + 4)*(x + 7)/4
Let t(j) = 6*j - 64. Let d be t(10). Let x be ((-2)/d + 0)*9. Factor -1/2*v**2 - 3/2*v**4 + 5/2*v**3 + 0*v - x*v**5 + 0.
-v**2*(v + 1)*(3*v - 1)**2/2
Factor 45*y**2 - 42*y**4 - 5 + 39*y**4 + 108*y + 5 - 6*y**3.
-3*y*(y - 4)*(y + 3)**2
Factor -7 + 6*v**2 + 75*v - 8*v - 3*v**3 - 83 + 20*v.
-3*(v - 6)*(v - 1)*(v + 5)
Let z(c) = c**2 + 11*c - 9. Let i be z(-12). Find v, given that 11*v + 11*v - 2*v**i - 22*v + 4*v**2 = 0.
0, 2
Let g = -27767/24 + 1157. Let h(w) be the second derivative of 0 - 1/4*w**2 - 10*w - g*w**4 - 1/6*w**3. Factor h(p).
-(p + 1)**2/2
Factor -34*d**2 + 24*d**2 + 0 + 0 + 72*d + 14*d**2.
4*d*(d + 18)
Let k be ((-42)/18*-1)/10. Let g(c) be the third derivative of 0*c + 0 - 4*c**2 + k*c**7 + 1/3*c**4 - 13/15*c**5 + 0*c**3 + 7/12*c**6. Factor g(y).
y*(y + 2)*(7*y - 2)**2
Factor 1/4*u**2 - 1/4*u - 3.
(u - 4)*(u + 3)/4
Let f be ((-3)/(-9))/(7*(-2)/(-189)). Let w = -4 + f. Solve w*h**2 + 0 + 0*h - 1/2*h**3 = 0.
0, 1
Determine d, given that 0*d + 6/11*d**3 + 0 + 18/11*d**2 = 0.
-3, 0
Let i(s) = 6*s + 39. Suppose 20*m = -30 - 90. Let a be i(m). Suppose 0*x**a + 3/8*x**5 + 0 - 3/8*x - 3/4*x**2 + 3/4*x**4 = 0. What is x?
-1, 0, 1
Let c(k) be the third derivative of k**5/150 + k**4/30 - k**3/5 - 2*k**2 - 18. Determine q, given that c(q) = 0.
-3, 1
Suppose -o - 156 = -2*v, -8*o = -3*o - 10. Let x = v + -155/2. Find t, given that 9/4 + x*t + 1/4*t**2 = 0.
-3
What is y in -25080*y + 2*y**4 + 6938*y**2 + 14370 - 4043 - 228*y**3 + 13873 = 0?
2, 55
Let y = -10 + 13. Factor 15*z**3 - 9 - 14 - 40*z + 3 + 95*z**2 - 50*z**y.
-5*(z - 2)*(z - 1)*(7*z + 2)
Factor -8/3 + 2/3*l**2 + 2/3*l**3 - 8/3*l.
2*(l - 2)*(l + 1)*(l + 2)/3
Let a(f) be the second derivative of -f**4/4 - 5*f**3/6 + 3*f**2/2 + 27*f. Let b(x) = 2*x**2 + 2*x - 1. Let c(o) = -3*a(o) - 5*b(o). Factor c(s).
-(s - 4)*(s - 1)
Let q be (-57688)/52 - 3 - (-9)/9. Let i = -1110 - q. What is u in 54/13*u + i*u**3 + 2/13*u**4 + 0 + 54/13*u**2 = 0?
-3, 0
Suppose -u + 3*q = 4*u - 20, 0 = 5*q. Suppose -a = a - u. Factor -4*h**3 + 0*h**a - 4*h - 1 + 4*h**4 - 3*h**4 - 6*h**2 - 2*h**4.
-(h + 1)**4
Suppose 0*x - 3/4*x**4 - 3/4*x**2 - 3/2*x**3 + 0 = 0. Calculate x.
-1, 0
Let t = 23 - 4. Let l = 23 - t. Suppose 10*j**4 + 26*j**3 - 16*j**4 + 8*j - 32*j**2 + 4*j**5 + 16*j**3 - 16*j**l = 0. What is j?
0, 1/2, 1, 2
Find t, given that 116/5*t**2 + 4/5*t**4 - 36/5*t**3 - 156/5*t + 72/5 = 0.
1, 2, 3
Let l = 1356 - 1354. Determine c, given that 3/2*c**3 + 3/2*c + 3*c**l + 0 = 0.
-1, 0
Suppose 2*y - 6*y + 20 = 0, -5*f = 2*y - 35. Factor 1/2*d**2 - 1/2*d**4 - 1/2*d**3 + 0*d + 0 + 1/2*d**f.
d**2*(d - 1)**2*(d + 1)/2
Let c(k) be the first derivative of -1/360*k**5 - 5/2*k**2 + 4 - 1/720*k**6 + 0*k**4 + 0*k**3 + 0*k. Let z(f) be the second derivative of c(f). Factor z(s).
-s**2*(s + 1)/6
Let x(q) be the first derivative of -2*q**5/5 - 2*q**4 + 16*q**2 + 32*q - 14.