(j). Factor o(y).
-3*(y - 1)*(y + 4)
Let o be 97 - 10/(-25)*(5 - 0). Factor -10*p**2 + 45*p**4 - o*p**4 - 13*p**3 - 12*p**3 + 44*p**4.
-5*p**2*(p + 2)*(2*p + 1)
Let b(d) be the third derivative of d**6/240 + d**5/40 + d**4/16 + 4*d**3 + 24*d**2. Let k(c) be the first derivative of b(c). Factor k(a).
3*(a + 1)**2/2
Let a be 4*(15/70)/3*(1 - -1). Factor -4/7*h**5 + a*h**3 + 0*h**4 + 0*h + 0 + 0*h**2.
-4*h**3*(h - 1)*(h + 1)/7
Let o(n) be the third derivative of n**7/1050 + 7*n**6/20 + 10813*n**5/300 - 371*n**4/2 + 5618*n**3/15 + 2*n**2 - 30. Factor o(c).
(c - 1)**2*(c + 106)**2/5
Let n(a) be the second derivative of -26*a - 7/6*a**3 + 0 + 1/40*a**6 - 17/80*a**5 + a**2 + 17/24*a**4. Solve n(m) = 0 for m.
2/3, 1, 2
What is y in 0*y - 58/11*y**2 - 2/11*y**4 - 60/11*y**3 + 0 = 0?
-29, -1, 0
Let d(y) be the third derivative of 5*y**7/42 - 5*y**6/24 - y**5/15 + y**4/6 + 3*y**2 - 10*y. What is h in d(h) = 0?
-2/5, 0, 2/5, 1
Let o = -4201/3 + 1401. Determine n so that 0*n - o + 2/3*n**2 = 0.
-1, 1
Let v(i) be the third derivative of i**7/26460 - i**6/2520 + i**4/2 - 22*i**2. Let k(r) be the second derivative of v(r). Factor k(m).
2*m*(m - 3)/21
Let o(h) be the first derivative of -1/8*h**4 - 1/6*h**3 - 3 - 1/20*h**5 - 1/8*h**2 - 1/120*h**6 - 4*h. Let d(a) be the first derivative of o(a). Factor d(l).
-(l + 1)**4/4
Let d(k) = k**2 - 8*k - 4. Let l be 6/(-9)*(0 + (-12)/2). Let o(n) = n**2 - 7*n - 3. Let c(p) = l*o(p) - 3*d(p). Factor c(u).
u*(u - 4)
Let l(q) = -q**3 - q**2 + q - 1. Let p(z) = -z**4 - 7*z**3 - 7*z**2 + 7*z - 7. Suppose 15 = -2*s - 3*s. Let j(m) = s*p(m) + 21*l(m). Factor j(x).
3*x**4
Let m(o) be the third derivative of -7*o**2 + 0*o - 1/105*o**5 - 1/420*o**6 + 1/12*o**4 - 4/21*o**3 + 0. Factor m(y).
-2*(y - 1)**2*(y + 4)/7
Let p(g) be the third derivative of -g**5/40 + g**4 + 20*g**3 - 28*g**2 + 2*g. Find f such that p(f) = 0.
-4, 20
Let w(i) be the second derivative of i**6/72 + i**5/24 - 5*i**4/4 + i**3/3 + 12*i. Let r(z) be the second derivative of w(z). Factor r(v).
5*(v - 2)*(v + 3)
Factor -1/2*m**2 + 3 + 23/4*m.
-(m - 12)*(2*m + 1)/4
Let u(s) be the second derivative of s**4/3 + 232*s**3/3 + 6728*s**2 + 3*s + 18. Factor u(f).
4*(f + 58)**2
Let z = -473 + 475. Let w(o) be the second derivative of 0*o**z + 7/18*o**4 + 0 - 8*o + 2/9*o**3. Factor w(q).
2*q*(7*q + 2)/3
Let z(r) be the first derivative of -2*r**5/15 - 2*r**4/3 + 2*r**3/9 + 16*r**2/3 + 8*r + 14. Determine g so that z(g) = 0.
-3, -2, -1, 2
Let d(q) = -6*q**2 - 30*q - 51. Let a(x) = 3*x**2 + 16*x + 25. Let v(i) = -9*a(i) - 4*d(i). Factor v(p).
-3*(p + 1)*(p + 7)
Let m(l) be the third derivative of 3*l**8/5320 - l**7/665 + l**6/855 + 7*l**3/2 + 6*l**2. Let p(j) be the first derivative of m(j). Solve p(u) = 0.
0, 2/3
Suppose 17 = 31*r - 14. Factor 1/4*l**3 + 9/4*l - 3/2*l**2 - r.
(l - 4)*(l - 1)**2/4
Let x be (1*-1)/((-9)/162). Let p = -16 + x. Suppose -3*l**p - l - 2*l**3 - 3*l**3 - 3*l + 11*l**2 + l**4 = 0. Calculate l.
0, 1, 2
Suppose -54 = 95*w - 122*w. Let j(v) be the first derivative of 4/3*v - 1/6*v**4 + 1/3*v**w - 2/3*v**3 - 12 + 2/15*v**5. Determine s so that j(s) = 0.
-1, 1, 2
Let x = 1470 + -1466. What is i in 0*i**3 + 8/5 + 2/15*i**x - 6/5*i**2 - 8/15*i = 0?
-2, 1, 3
Let n(p) be the second derivative of 0 + 6*p**3 + 11*p - 27/8*p**4 - 3*p**2. Solve n(k) = 0.
2/9, 2/3
Let i(f) be the first derivative of -f**4/2 - 14*f**3/3 + 73*f**2 - 130*f - 389. Factor i(y).
-2*(y - 5)*(y - 1)*(y + 13)
Let q be (-4)/((-84)/(-687)) + 8/(-28). Let d(n) = 16*n**2 + 11*n - 9. Let u(i) = -3*i**2 - 2*i + 2. Let p(o) = q*u(o) - 6*d(o). Let p(k) = 0. Calculate k.
-2, 2
Let z be (-12)/(-9)*1/6. Suppose -2*i = 187 - 191. Let -4/3*b - i - z*b**2 = 0. What is b?
-3
Let b(z) be the third derivative of -5*z**8/336 + z**7/42 + 5*z**6/24 - z**5/12 - 5*z**4/3 - 10*z**3/3 - 70*z**2. Let b(v) = 0. What is v?
-1, 2
Factor 4/9*t**3 - 2/9*t**2 + 0*t + 0.
2*t**2*(2*t - 1)/9
Let b(c) = c**2 + 4*c - 1. Let l be b(-2). Let p(v) = -9*v**3 + 3*v**2 - 6. Let x(o) = 8*o**3 - 4*o**2 + o + 5. Let i(z) = l*p(z) - 6*x(z). Factor i(q).
-3*q*(q - 2)*(q - 1)
Solve 8/3*q**4 + 0 - 70/9*q**3 - 2/9*q**5 + 8*q - 8/3*q**2 = 0 for q.
-1, 0, 1, 6
Let w be (-2)/11 + 1742/143. Suppose 2*j + s = -0*s + 4, 0 = -2*j - 3*s + w. Determine g so that 4/5*g**4 + j - 4/5*g - 4/5*g**2 + 4/5*g**3 = 0.
-1, 0, 1
Let z(h) be the third derivative of -h**9/2016 - h**8/640 - h**7/840 - 19*h**4/24 + 12*h**2. Let f(j) be the second derivative of z(j). Factor f(d).
-3*d**2*(d + 1)*(5*d + 2)/2
Let m(y) be the second derivative of y**6/180 - 8*y**5/15 + 181*y**4/12 - 496*y**3/9 + 961*y**2/12 + 335*y. Solve m(j) = 0.
1, 31
Let b(d) = 15*d - 330. Let v be b(22). Let n(x) be the first derivative of 4/15*x**5 - 11 - 1/9*x**6 - 1/6*x**4 + 0*x**2 + v*x + 0*x**3. What is k in n(k) = 0?
0, 1
Let z(x) = -82*x**2 + 38*x + 19. Let s(v) = -29*v**2 + 13*v + 6. Let l(p) = 17*s(p) - 6*z(p). Factor l(i).
-(i + 3)*(i + 4)
Factor 15*x + 14*x**2 + 17 + 9*x - 21*x + 47*x + 7.
2*(x + 3)*(7*x + 4)
Factor -6*x - 7*x - 2*x**2 + 41*x.
-2*x*(x - 14)
Let k(t) be the second derivative of 1/30*t**4 + 0 - 4/15*t**3 + t + 0*t**2. What is n in k(n) = 0?
0, 4
Let o(g) be the third derivative of -1/45*g**5 + 0*g**3 + 2 + 0*g - 2*g**2 + 4/9*g**4. Factor o(q).
-4*q*(q - 8)/3
Let h be (54/(-90))/((-72)/20). Factor h - 7/2*t**2 - 2/3*t.
-(3*t + 1)*(7*t - 1)/6
Let d be ((-6)/12)/(8/(-1628)). Let n = 102 - d. Let 1/2*x - n - 1/4*x**2 = 0. What is x?
1
Factor -3/2*r**2 + 3/4 + 21/8*r.
-3*(r - 2)*(4*r + 1)/8
Let r(p) = -5*p**3 - 2*p**2 + 3*p + 6. Let q(b) = 3*b**3 + 3*b**2 - 3*b - 7. Let a(k) = -3*q(k) - 2*r(k). Find u such that a(u) = 0.
-1, 3
Let q be (-16)/(-4)*1 + 0. Suppose 3*z = q*h + 28, -z + h - 2 = -10. Factor 15*c**4 + 2*c**3 - 14*c**2 - 7*c**z - 6*c**2 - 8*c + 16 + 2*c**5.
2*(c - 1)**2*(c + 2)**3
Solve 0*z**2 - 9*z**2 + 629*z + 4*z**2 + 286*z = 0.
0, 183
Let y(c) = 4*c**4 - 16*c**3 - 53*c**2 + 3*c + 9. Let o(z) = -z**4 + 4*z**3 + 13*z**2 - 2. Let d(m) = -18*o(m) - 4*y(m). Factor d(v).
2*v*(v - 6)*(v + 1)**2
Let z be (936/208)/(147/54 - (-4)/(-18)). Find p, given that 0 - 3/5*p**3 - z*p + 12/5*p**2 = 0.
0, 1, 3
Suppose d = 6*d. Let 11*y**3 - 6*y**3 + 50*y**2 + d*y**3 - 50 - 5*y = 0. Calculate y.
-10, -1, 1
What is f in -2/7*f**3 + 2/7*f + 0 + 0*f**2 = 0?
-1, 0, 1
Suppose 90 = 4*b - 3*c, 5*b - 4*b - 2*c - 20 = 0. Factor 27 + 4*h**3 + b*h**2 + 33*h - 24 + 13 + 3*h.
4*(h + 1)**2*(h + 4)
Factor -3/5 - 1/5*m**4 + 2/5*m**3 - 2/5*m + 4/5*m**2.
-(m - 3)*(m - 1)*(m + 1)**2/5
Suppose 22 = -3*x - 5. Let k = -6 - x. What is g in -k*g**3 + 2*g**5 - 17*g**5 - 37*g**2 + 31*g**2 + 24*g**4 = 0?
-2/5, 0, 1
Let w(f) be the third derivative of -f**5/270 - 7*f**4/108 - 51*f**2 + 2. Factor w(r).
-2*r*(r + 7)/9
Suppose j = 5*j - 56. Let o be 4/6 - (-4)/12*j. Factor 2/3*b**3 - 8/3 - 10/3*b**2 + o*b.
2*(b - 2)**2*(b - 1)/3
Let x(t) be the second derivative of t**6/285 + 51*t**5/95 + 2701*t**4/114 + 1700*t**3/19 + 2500*t**2/19 - 229*t - 1. Factor x(u).
2*(u + 1)**2*(u + 50)**2/19
Let l(z) be the first derivative of -3*z**4/2 + 272*z**3/3 - 1495*z**2 - 2116*z - 186. Factor l(b).
-2*(b - 23)**2*(3*b + 2)
Let s(z) be the second derivative of -z**6/30 - 3*z**5/20 + 2*z**3/3 - 12*z + 3. Solve s(k) = 0.
-2, 0, 1
Let g(x) = 8*x - 74. Let j(y) = 2. Let p(t) = -g(t) + 4*j(t). Let h be p(10). Factor h*v**3 - 8*v + 4/3*v**2 - 16/3.
2*(v - 2)*(v + 2)*(3*v + 2)/3
Let h be (42/(-35))/((-3)/(-10)). Let m be 1/3*(13 + h). Find k such that 4*k**2 + 6*k - 3 - m*k**2 - 4*k**2 = 0.
1
Let z(v) be the third derivative of v**5/36 - 5*v**4/8 + 20*v**3/9 - 49*v**2. Factor z(m).
5*(m - 8)*(m - 1)/3
Suppose -135*x + 108 + 297 = 0. Solve 0 - 3/2*h**x + 0*h + 0*h**2 - 9/4*h**4 - 3/4*h**5 = 0.
-2, -1, 0
Suppose 11*x = 29 + 15. Let q(d) be the third derivative of 2/45*d**5 + 5/36*d**x + 0*d + 0 + 1/180*d**6 + d**2 + 2/9*d**3. What is g in q(g) = 0?
-2, -1
Let y(i) be the first derivative of i**5/15 - 5*i**4/6 + 16*i**3/9 - 210. Factor y(j).
j**2*(j - 8)*(j - 2)/3
Let 6 + 13/2*x + 1/2*x**2 = 0. Calculate x.
-12, -1
Suppose 2*m = 4*f - 4, 1 = m - 81*f + 80*f. Let q(a) be the first derivative of -a**2 + 0*a + m - 3/2*a**4 + 8/3*a**3. Factor q(b).
-2*b*(b - 1)*(3*b - 1)
Suppose 4*m + k + 4*k = 107, -9 = -3*k. Determine t, given that -2