 (2 - 2)*(t/(-2))/(-3). Determine n so that 0 + 0*n + 0*n**4 - 1/3*n**3 + 1/3*n**5 + f*n**2 = 0.
-1, 0, 1
Let b be -21*(-4)/3 - (1 + 2). Let f = b - 25. Factor f*z - 1/4*z**2 + 1/4.
-(z - 1)*(z + 1)/4
Factor -11 - 35 + 24*t**3 - 3*t**4 - 1934*t**2 + 1865*t**2 + 6 + 84*t + 4.
-3*(t - 3)*(t - 2)**2*(t - 1)
Let n be ((-8)/3)/(-51 - -49). Let w(y) be the first derivative of -n*y**3 + 2*y**2 + 0*y - 2. Factor w(x).
-4*x*(x - 1)
Let b = 425 - 240. Let a = 188 - b. Suppose 4/5*q**2 + 0 - 14/5*q**a + 0*q + 2*q**4 = 0. What is q?
0, 2/5, 1
Suppose -3*p = -2*j + 6*j - 9, -3 = -p + j. Let g(r) = -r**3 - 15*r**2 + 16*r + 45. Let y be g(-16). Factor -z**2 + 47*z**4 + 4*z**p - y*z**4 + 3*z**2.
2*z**2*(z + 1)**2
Let y(o) be the first derivative of -o**6/75 + 2*o**5/25 - o**4/10 + o + 10. Let x(l) be the first derivative of y(l). What is j in x(j) = 0?
0, 1, 3
Factor -276 + 260 + f**2 - 15*f + 0*f**2.
(f - 16)*(f + 1)
Factor 64 - 34*u - 37*u**2 - 10*u**2 + 48*u**2.
(u - 32)*(u - 2)
Let n(a) be the second derivative of -1/6*a**4 - 33*a + 0 - 1/3*a**3 - 1/30*a**5 - 1/3*a**2. Factor n(u).
-2*(u + 1)**3/3
Let f(c) = -c**3 + c + 1. Let q(w) = -2*w**3 + 3*w**2 + 5*w + 3. Suppose 2*l = -0*l + 5*d - 55, -l + d - 20 = 0. Let x(z) = l*f(z) + 5*q(z). Factor x(n).
5*n*(n + 1)*(n + 2)
Let j(n) be the third derivative of n**8/1344 + n**7/120 - 3*n**6/160 - 7*n**5/240 + n**4/12 - 228*n**2. What is k in j(k) = 0?
-8, -1, 0, 1
Suppose -6*w - 27 = -3*w. Let c = 12 + w. Factor -7*q - 2*q + c - 3 + 6 + 3*q**3.
3*(q - 1)**2*(q + 2)
Suppose 0 = -20*m + m + 5*m + 28. What is p in -1/3*p**3 - 8/3*p - 4/3 - 5/3*p**m = 0?
-2, -1
Determine s so that 64/9 + 56/9*s - 10/9*s**2 - 2/9*s**3 = 0.
-8, -1, 4
Suppose -138*s + 69 = -207. Factor -2/5*q**s + 8/5*q - 6/5.
-2*(q - 3)*(q - 1)/5
Suppose -j - 2*l = 0, 312*j + 3*l = 310*j. Factor j*z - 2/3 + 1/2*z**2 - 1/6*z**3.
-(z - 2)**2*(z + 1)/6
Let k(r) be the second derivative of r**6/255 + 3*r**5/85 + 13*r**4/102 + 4*r**3/17 + 4*r**2/17 - 71*r + 2. Find h, given that k(h) = 0.
-2, -1
Let q(t) be the third derivative of -t**6/60 - 2*t**5/15 - 5*t**4/12 - t**3 - 6*t**2. Let l(i) = -1. Let s(b) = 4*l(b) - 2*q(b). Factor s(o).
4*(o + 1)**2*(o + 2)
Let h be (36/(-15) + 2)*(6 + 5 + -16). Factor 2/5 + 4/5*o + 2/5*o**h.
2*(o + 1)**2/5
Let d(g) be the second derivative of -g**4/4 + 4*g**3 - 45*g**2/2 - 519*g. What is j in d(j) = 0?
3, 5
Let h(k) be the third derivative of 19*k**5/12 - 65*k**4/8 + 5*k**3/3 - 39*k**2 + 3. Factor h(y).
5*(y - 2)*(19*y - 1)
Let i(h) be the third derivative of h**6/240 + h**5/20 + 3*h**4/16 + h**3/3 + 3*h**2 - 8*h. Solve i(v) = 0 for v.
-4, -1
Let w(c) = 10*c**2 + 95*c - 50. Let h be w(-10). Factor 1/2*a**5 + h*a + 0 + 0*a**3 + 0*a**2 + 2*a**4.
a**4*(a + 4)/2
Let n(q) be the third derivative of -q**7/490 - 3*q**6/70 - 3*q**5/14 - q**4/2 - 9*q**3/14 + 387*q**2. Determine s so that n(s) = 0.
-9, -1
Let g = -9 - -8. Let l be g*(-3 - (-4 + 3)). Suppose 6*u - 2*u**3 + l - 6 + 0*u**3 + 0 = 0. Calculate u.
-2, 1
Let j(z) be the third derivative of -z**6/200 - 3*z**5/50 - 3*z**4/10 - 4*z**3/5 + 106*z**2 + 2. Factor j(i).
-3*(i + 2)**3/5
Let v(u) = 5*u**3 - 7*u**2 - 18*u + 18. Let q be 2 + 6 + -4 - -21. Let s(h) = 60*h**3 - 85*h**2 - 215*h + 215. Let r(m) = q*v(m) - 2*s(m). Factor r(o).
5*(o - 2)*(o - 1)*(o + 2)
Suppose 5*h = -4*r + 38, -163*r + 162*r - 4*h + 26 = 0. Factor -84/5*y + 1/5*y**4 - 14/5*y**3 + 61/5*y**r + 36/5.
(y - 6)**2*(y - 1)**2/5
Let y(s) = 27*s**2 + 2*s - 1. Let n be y(-1). Suppose -2*u = -n + 20. Factor 0 + 8/9*z**u - 2/9*z.
2*z*(4*z - 1)/9
Factor -14452*x**5 - 9*x**3 + 10 - 11*x**3 - 10*x**2 + 14457*x**5 + 15*x.
5*(x - 2)*(x - 1)*(x + 1)**3
Let y(i) be the first derivative of i**4/12 + 8*i**3/9 + 7*i**2/6 + 591. Factor y(w).
w*(w + 1)*(w + 7)/3
Let f = 799/1197 - 1/1197. Factor -8/3 - 8/3*t - f*t**2.
-2*(t + 2)**2/3
Let t(l) be the third derivative of -1/48*l**5 + 0 - 1/480*l**6 + 3/8*l**3 - 1/32*l**4 + 5*l**2 + 0*l. Factor t(h).
-(h - 1)*(h + 3)**2/4
Suppose 0*x + 16 = 5*x + w, -3*w = -3*x + 6. Suppose 4*a - x*a - 23 = -4*z, -12 = a - 3*z. Factor -2*y**2 + 9*y - y**2 + 5*y**2 + 3 + a*y**3 + 7*y**2.
3*(y + 1)**3
Let s be (12/(-30))/((-2)/10). Let u be (6/(-10))/(s/(-10)). Factor 0*z**2 + 0 + 0*z - 2/5*z**u.
-2*z**3/5
Suppose 3*g = -2*l + 10, 5*g - 34 = 2*l - 12. Let r = 74 + -72. Factor 6*m - 3 + 2*m**2 - 6 + 5*m**r - g*m**2.
3*(m - 1)*(m + 3)
Let m(f) be the second derivative of -2*f**7/21 + 2*f**6/5 + 17*f**5/5 + 3*f**4 - 32*f**3/3 - 24*f**2 - 48*f. Suppose m(v) = 0. Calculate v.
-2, -1, 1, 6
Factor -2*s - 48*s**2 + 17*s - 41*s**2 - 27 - 23 + 94*s**2.
5*(s - 2)*(s + 5)
Let q(g) = g**3 - 9*g**2 + 12*g + 14. Let i be q(8). Let h = i - 42. Let -2/3*d + 0 + 0*d**h + 0*d**2 - 2/3*d**5 + 4/3*d**3 = 0. What is d?
-1, 0, 1
Factor -18 + 18*x - 6*x**2 + 2/3*x**3.
2*(x - 3)**3/3
Suppose 0 = -z + 56 - 48. Determine i, given that 2 + 3*i**2 + i**2 + 0*i**2 - 13*i - i**3 + z*i = 0.
1, 2
Let g(z) be the third derivative of 0*z + 0*z**3 + 45*z**2 + 1/270*z**5 + 0 - 1/108*z**4. Let g(v) = 0. What is v?
0, 1
Factor 0*z - 4/5*z**4 - 112/5*z**2 - 44/5*z**3 + 0.
-4*z**2*(z + 4)*(z + 7)/5
Let g(r) = -r**3 + 14*r**2 - 49*r - 2. Let l(s) = 3*s**3 - 42*s**2 + 147*s + 7. Let b(t) = 14*g(t) + 4*l(t). What is n in b(n) = 0?
0, 7
Let x(w) = 3*w + 2. Let l be x(1). Factor 4*m**3 + 6*m + 2*m + l*m + 4 - 17*m - 4*m**2.
4*(m - 1)**2*(m + 1)
Factor -3*l**3 - 4 + 52 - 2*l**2 + l + 11*l + l**2 - 11*l**2.
-3*(l - 2)*(l + 2)*(l + 4)
Let n(j) be the second derivative of j**7/1680 + j**6/360 + 2*j**3/3 + 12*j. Let o(i) be the second derivative of n(i). Factor o(h).
h**2*(h + 2)/2
Factor 5*s**3 - 6*s**3 + 48*s**2 - 768*s + 1922 + 2174.
-(s - 16)**3
Suppose -46 = -9*c - 10. Factor 35*l**2 - 17*l**3 - 2*l**5 + 13*l**4 + 29*l**2 + 3*l**c - 32*l - 31*l**3.
-2*l*(l - 2)**4
Let d(i) = i**3 - i**2 - 5. Let n be d(5). Factor -9*l**2 - 3*l + 2 + 4 + 98*l**4 + 3*l**3 - n*l**4.
3*(l - 1)**2*(l + 1)*(l + 2)
Let w = 291871/4670 - -2/2335. Let -25*y + w + 5/2*y**2 = 0. Calculate y.
5
Let c be (-528)/(-2619) - (-4)/(-18). Let a = c - -103/291. Factor 7/6*h**3 + a*h + 0 + 7/6*h**2 + 1/3*h**4.
h*(h + 1)*(h + 2)*(2*h + 1)/6
Let p(c) be the first derivative of -c**3/12 - 17*c**2/8 - 15*c/2 + 121. Let p(f) = 0. What is f?
-15, -2
Suppose 0 = -7*o - 6 + 41. Let l(k) be the third derivative of 0*k + 0*k**3 + 3*k**2 + 1/28*k**4 - 1/210*k**o + 0. Factor l(v).
-2*v*(v - 3)/7
Let b = -1806 + 7225/4. Solve -1/4*i**2 + 0 - b*i = 0 for i.
-1, 0
Let u(y) = -4*y - 32. Let h be u(-10). Suppose 5*m - h*t - 25 = -3*t, 3*m + 3*t = -3. Factor 0 + 1/4*l**5 + 0*l**4 + 0*l**m + 1/4*l - 1/2*l**3.
l*(l - 1)**2*(l + 1)**2/4
Let v(g) be the second derivative of g**5/90 + 13*g**4/27 - g**3 - 141*g. Factor v(y).
2*y*(y - 1)*(y + 27)/9
Let s(g) be the second derivative of -g**5/5 + 8*g**4 + 2*g**3/3 - 48*g**2 - 657*g. Determine l, given that s(l) = 0.
-1, 1, 24
Factor -4*a**3 + 25*a**2 - 23*a**2 - 112*a + 38*a**2 + 96.
-4*(a - 6)*(a - 2)**2
Factor -1/8*o**2 + 79/2*o - 6241/2.
-(o - 158)**2/8
Let r = 93 + -91. Let h(i) be the first derivative of -3/14*i**4 - 6 + 8/21*i**3 - 4/7*i + 1/7*i**r. Factor h(d).
-2*(d - 1)**2*(3*d + 2)/7
Let z(f) be the first derivative of -f**3/9 - f**2/2 - 2*f/3 + 75. Factor z(w).
-(w + 1)*(w + 2)/3
Let b be ((-18)/(-54))/(1/249). Let y = 85 - b. Factor -8/11*j + 2/11*j**y + 8/11.
2*(j - 2)**2/11
Let m(j) be the third derivative of -j**7/1890 + j**6/216 - j**5/60 + 7*j**4/216 - j**3/27 + 9*j**2 + 3*j. Determine s, given that m(s) = 0.
1, 2
Let r = -90462/11 - -8224. Suppose r*m + 0 + 2/11*m**3 + 4/11*m**2 = 0. What is m?
-1, 0
Determine f, given that 6/7 + 15/7*f - 12/7*f**4 - 3/7*f**5 - 12/7*f**3 + 6/7*f**2 = 0.
-2, -1, 1
Factor 3/5*s**2 + 12 + 63/5*s.
3*(s + 1)*(s + 20)/5
Let r(t) be the first derivative of -3*t**5/10 - 9*t**4/2 - 11*t**3 + 63*t**2 - 147*t/2 + 87. Suppose r(s) = 0. What is s?
-7, 1
Suppose -d = -3*d + 6. Factor -3*f**3 - 3*f**3 + 0*f**3 + 2*f**d - 4*f**2 + 4*f**4 + 4*f**5.
4*f**2*(f - 1)*(f + 1)**2
Let j = 7 + -3. Let p be -46*j/48 + 4. Determine a so that 1/3*a**2 - 1/6 + 1/6*a**5 - p*a**4 + 1/6*a - 1/3*a**3 = 0.
-1, 1
Solve -159*f**2 - 162*f**2 + 21*f**2 - 399*f**3 + 39*f**3 - 63*f**4 - 3*f**5 = 0.
-10, -1, 0
Let g = 530 + -526. Let m(a) be the 