5*i**4.
5*i**3*(i + 1)*(6*i + 1)
Let q(k) be the first derivative of k**5/5 + 3*k**4/4 - k**3/3 - 3*k**2/2 - 78. Find b, given that q(b) = 0.
-3, -1, 0, 1
Let u(d) be the second derivative of -19*d + 2/15*d**6 - 2/5*d**5 + 4/3*d**3 + 0*d**2 + 0 - 1/3*d**4. Factor u(p).
4*p*(p - 2)*(p - 1)*(p + 1)
Solve 44*s**2 + 0*s**3 - 5*s**3 - 59*s**2 - 10*s = 0.
-2, -1, 0
Let x be (15 - 16)*(-1 + (2 - 3)). Suppose -x*o + 0*j + j = 0, o - 5*j = 0. Solve 9/4*z**3 + 0*z - 3/4*z**4 + o - 3/2*z**2 = 0 for z.
0, 1, 2
Let c = 12 + -117/10. Let j(w) be the second derivative of -1/15*w**3 - 1/60*w**4 + c*w**2 + 0 + 4*w. Factor j(v).
-(v - 1)*(v + 3)/5
Let u(m) be the first derivative of m**4/6 + 14*m**3/9 - 56*m**2/3 + 32*m + 230. Factor u(h).
2*(h - 4)*(h - 1)*(h + 12)/3
Solve 28*z**4 - 16*z**2 + 24*z + 52*z**3 - 168*z**5 - 76*z**2 + 156*z**5 = 0 for z.
-2, 0, 1/3, 1, 3
Factor -5*j**3 - 141822 - 20535*j - 75150 - 54239 - 63830 + 81776 - 555*j**2.
-5*(j + 37)**3
Let j be (0 + 0)*(3 + -1)/2. Let o(x) be the second derivative of 4*x + j - 1/24*x**4 + 1/24*x**3 - 1/80*x**5 + 1/4*x**2. Let o(z) = 0. What is z?
-2, -1, 1
Suppose -4 = 5*c - 14. Suppose 0*p = -p + c. Let 12 - 4*z**2 + 8*z + 3*z**p + 4*z + 4*z**2 = 0. Calculate z.
-2
Let u(a) be the first derivative of a**4 - 28*a**3/3 + 22*a**2 - 20*a + 55. Factor u(g).
4*(g - 5)*(g - 1)**2
Let q(k) be the second derivative of -k**4/6 - 20*k**3/39 + 12*k**2/13 - 33*k + 1. Factor q(a).
-2*(a + 2)*(13*a - 6)/13
Let u(y) = -5*y**3 - 39*y**2 + 69*y - 37. Let n(z) = z**3 + z**2 - z + 1. Let f(g) = -30*n(g) - 5*u(g). Solve f(o) = 0 for o.
1, 31
Let v(i) be the second derivative of i**6/4 + 69*i**5/20 + 9*i**4/8 - 453*i. What is f in v(f) = 0?
-9, -1/5, 0
Let i(v) = v**2 + v - 1. Let x be ((-24)/(-48))/((-2)/24*-3). Let u be i(x). Suppose 0*j + 0 + 1/8*j**2 + 3/8*j**3 + 3/8*j**4 + 1/8*j**u = 0. What is j?
-1, 0
Let y = 421672/9 - 46668. Let h = -184 + y. Factor h - 2/9*i - 2/9*i**2.
-2*(i - 1)*(i + 2)/9
Let p = -77721/5 - -15546. Factor 0*l**2 + 0 - 3/5*l**4 - p*l**3 + 12/5*l.
-3*l*(l - 1)*(l + 2)**2/5
Factor 4*k**2 + 20 + 2*k**3 + 6*k**3 - 4*k**3 + 26*k - 6*k**3.
-2*(k - 5)*(k + 1)*(k + 2)
Let m(w) = 12*w**4 - 3*w**3 - 27*w**2 + 21*w + 33. Let g be 10/6 + 20/(-30). Let o(q) = q**4 - q**2 + q + 1. Let i(k) = g*m(k) - 9*o(k). Factor i(j).
3*(j - 2)**2*(j + 1)*(j + 2)
Let g = 2464/1035 - -4/207. Let x = 1/432 - -2587/2160. Factor x*d**2 - 14/5*d - g.
2*(d - 3)*(3*d + 2)/5
Factor -w**5 - 16*w**2 + 6*w**5 - 19*w**2 + 35*w**4 - 30*w + 25*w**3.
5*w*(w - 1)*(w + 1)**2*(w + 6)
Let j = 15065/63 + -2149/9. Let a = j + 2/21. Find n such that -2/9*n**2 - a + 2/3*n = 0.
1, 2
Let j(i) = i**3 + 4*i**2 + 2*i - 2. Let p be j(-2). Let c be (3/(-12)*p)/((-8)/64). Suppose -1/4*m**c + 0*m + 0*m**2 - 1/4*m**3 + 0 = 0. What is m?
-1, 0
Let j(o) = 3*o**2 - 9. Let f(q) = -3*q**2 - 2*q + 9. Let z(g) = 3*f(g) + 4*j(g). Factor z(b).
3*(b - 3)*(b + 1)
Let s(f) be the first derivative of 5*f**4/4 - 160*f**3/3 + 145*f**2/2 + 310*f - 5. Solve s(b) = 0.
-1, 2, 31
Let t(j) = -j**2 - j - 1. Let p(h) = h**3 - 11*h**2 - 12*h - 4. Let u(x) = p(x) - 4*t(x). Factor u(q).
q*(q - 8)*(q + 1)
Let n(h) = h + 1. Let b = -30 + 22. Let y(g) = 2*g**3 + 4*g**2 - 8*g - 8. Let d(i) = b*n(i) - y(i). Factor d(m).
-2*m**2*(m + 2)
Let h(r) be the third derivative of r**6/780 + 2*r**5/39 + 3*r**4/4 + 54*r**3/13 + 92*r**2. Factor h(i).
2*(i + 2)*(i + 9)**2/13
Let s(y) be the first derivative of -10*y + 9 - 15/2*y**2 - 5/3*y**3. Determine q so that s(q) = 0.
-2, -1
Let w be ((-14)/8)/(1/4). Let v = 7 + w. Factor v*d**2 + 1/2 + 1/4*d**3 - 3/4*d.
(d - 1)**2*(d + 2)/4
Suppose -9*w + w = -32. Factor 16*a**3 - 8*a**2 - 8 + 18*a**5 + 8*a + 2*a**w - 28*a - 14*a**5 + 14*a**4.
4*(a - 1)*(a + 1)**3*(a + 2)
Let m(x) be the first derivative of x**4/16 + 8*x**3/3 - 328. Determine r so that m(r) = 0.
-32, 0
Let z be (-21)/(-6) - (-4)/8. Factor 8*v - 40*v**4 + 64*v**3 - 44*v**2 + 0*v**4 + 12*v**z.
-4*v*(v - 1)**2*(7*v - 2)
Factor -2*o**5 + 57*o + 2*o**4 + 7*o**3 + 22*o**2 + 11*o**3 - 49*o.
-2*o*(o - 4)*(o + 1)**3
Factor 6/11*j + 4/11 - 4/11*j**2.
-2*(j - 2)*(2*j + 1)/11
Let g(v) be the first derivative of -2*v + 46 - 13/10*v**2 - 2/15*v**3 + 1/20*v**4. Factor g(l).
(l - 5)*(l + 1)*(l + 2)/5
Let v(a) be the second derivative of -a**4/48 + 7*a**3/24 + 9*a**2/4 - 227*a. Factor v(f).
-(f - 9)*(f + 2)/4
Let v(d) be the second derivative of 0 - 50*d + 11/6*d**3 - 6*d**2 + 1/12*d**4. Factor v(y).
(y - 1)*(y + 12)
Suppose -26 = 12*r - 74. Determine v, given that 32 - 4*v**3 + 0*v**3 - 16*v**4 + 12*v**2 + 44*v**2 + 80*v - r*v**5 = 0.
-2, -1, 2
Let l(j) = j**3 + 3*j**2 - 2. Let y(p) = -4*p**3 - 13*p**2 - 2*p + 7. Let o(s) = -9*l(s) - 2*y(s). Find c such that o(c) = 0.
-2, -1, 2
Let k(o) = o**3 + 26*o**2 - 27*o + 2. Let u be k(-27). Factor 11*c**2 - 28*c**2 + u*c**3 + 9*c**2.
2*c**2*(c - 4)
Let j(b) be the second derivative of 0 + 1/3*b**4 + 8/3*b**3 + 8*b**2 + 4*b. Factor j(n).
4*(n + 2)**2
Let h be (3 + -2)/(1/2). Let c(u) = 5*u**2 - 5. Let j(a) = -5*a**2 + 5. Let o(w) = h*j(w) + 3*c(w). Determine d, given that o(d) = 0.
-1, 1
Let a(y) be the second derivative of y**4/3 - 40*y**3/3 + 200*y**2 - 42*y. Factor a(s).
4*(s - 10)**2
Let f be (1*(5 + -8) - -3)/(-4). Let s(v) be the first derivative of -1/3*v**3 + f*v - 1 + 1/2*v**2. Factor s(p).
-p*(p - 1)
Let o(y) be the second derivative of -y**5/80 - y**4/4 - 2*y**3 - 8*y**2 - 51*y. Factor o(f).
-(f + 4)**3/4
Let v(o) be the first derivative of -2/5*o**3 - 3/20*o**4 + 0*o**2 + 0*o + 3/25*o**5 - 27. Factor v(a).
3*a**2*(a - 2)*(a + 1)/5
Find r such that -8/7*r + 10/7 - 2/7*r**2 = 0.
-5, 1
Suppose -25 = -5*y, -5*y = -2*z - 2*z + 295. Let g be z/832 - (-2)/13. Determine p so that 0*p + g - 1/4*p**2 = 0.
-1, 1
Determine o, given that -44/7 - 16/7*o**2 + 62/7*o - 2/7*o**3 = 0.
-11, 1, 2
Let l(w) be the second derivative of w**6/96 - 5*w**4/96 - 16*w**2 + 6*w + 1. Let c(q) be the first derivative of l(q). Factor c(o).
5*o*(o - 1)*(o + 1)/4
Let c(t) be the first derivative of -t**7/56 - 11*t**6/72 - t**5/3 + 5*t**4/6 - 17*t**3/3 + 4. Let l(y) be the third derivative of c(y). Solve l(u) = 0.
-2, 1/3
Let l(o) = -6*o**4 - 36*o**3 + 105*o**2 + 390*o - 288. Let i(y) = -5*y**4 - 35*y**3 + 106*y**2 + 392*y - 288. Let f(g) = 3*i(g) - 4*l(g). Factor f(u).
3*(u - 3)*(u + 4)**2*(3*u - 2)
Determine n so that -2*n + 0 - 2/9*n**5 - 16/9*n**4 - 44/9*n**3 - 16/3*n**2 = 0.
-3, -1, 0
Suppose -4*c + 0*x - x + 6 = 0, -12 = -5*c + x. Factor c*v**2 - 6 - 5*v**2 - v - 10*v.
-(v + 3)*(3*v + 2)
Let y(d) be the second derivative of d**6/15 - 41*d**5/30 + 41*d**4/9 + 416*d**3/9 + 128*d**2/3 - 84*d - 1. Determine m so that y(m) = 0.
-2, -1/3, 8
Let t(a) be the first derivative of a**5/5 - 2*a**3/3 - 19*a + 4. Let y(b) be the first derivative of t(b). Factor y(h).
4*h*(h - 1)*(h + 1)
Factor -1/2*a**2 - 1/8*a**3 + 0 + 5/8*a.
-a*(a - 1)*(a + 5)/8
Let i = -26 - -12. Let h = 12 + i. Let m(s) = s**2 + s + 1. Let l(o) = -7*o**2 - 17*o + 18. Let y(x) = h*m(x) - l(x). Solve y(q) = 0.
-4, 1
Let f(b) be the third derivative of 0*b**3 + 26*b**2 + 0*b + 0 + 7/36*b**5 - 25/72*b**4 + 1/630*b**7 - 11/360*b**6. Factor f(v).
v*(v - 5)**2*(v - 1)/3
Let p(l) be the third derivative of -l**7/210 + 19*l**6/480 - 19*l**5/240 - l**4/16 - 5*l**2. Suppose p(c) = 0. What is c?
-1/4, 0, 2, 3
Factor -3*s + s + 28 + 3*s - 33*s + 4*s**2.
4*(s - 7)*(s - 1)
Let c be 226/6 + ((-5)/((-10)/(-18)) - -14). Solve 32/3*b + c + 2/3*b**2 = 0.
-8
Let w(p) be the second derivative of p**4/18 + 11*p**3/9 + 10*p**2/3 + 2*p - 4. Let w(j) = 0. What is j?
-10, -1
Find d such that 139*d**2 - 2767*d + 6*d**2 + 2872*d + 25 + 75*d**3 + 10*d**4 = 0.
-5, -1, -1/2
Let a(l) = l**2 - 40*l - 74. Let n(m) = -440*m - 970 + 5*m**2 + 155 + 5*m**2. Let s be -63 + 3/((-2)/4 + -1). Let q(k) = s*a(k) + 6*n(k). Factor q(w).
-5*(w + 4)**2
Factor -4/3*k**2 - 1 - 13/3*k.
-(k + 3)*(4*k + 1)/3
Solve 1758 + 8*l + 2*l**4 - 1758 - 2*l**3 - 8*l**2 = 0 for l.
-2, 0, 1, 2
Suppose -3*b + 182 = -0*h - 2*h, 0 = -3*b + 5*h + 185. Let j = -57 + b. Determine q, given that 11/3*q**3 + j*q + 2/3 + 5*q**2 + q**4 = 0.
-1, -2/3
Let g(w) be the second derivative of -w**5/270 - w**4/27 - w**3/9 + 4*w**2 + 16*w. Let a(m) be the first derivative of g(m). Factor a(s).
-2*(s + 1)*(s + 3)