- 300*j.
-5*j*(j - 20)*(8*j - 3)
Let i(s) = 10*s**2 - 34*s + 40. Let t(x) = -6*x**2 + 23*x - 27. Let b(m) = 5*i(m) + 8*t(m). Determine v, given that b(v) = 0.
-8, 1
Let a = 4144 + -4140. Let 18/5*b**2 + 9/5 + 24/5*b + 0*b**3 - 3/5*b**a = 0. Calculate b.
-1, 3
Let v(l) be the third derivative of 1/270*l**6 + 1/252*l**8 + 0 + 0*l - 27*l**2 - 2/27*l**4 + 13/945*l**7 - 1/27*l**3 - 2/45*l**5. Find y such that v(y) = 0.
-1, -1/6, 1
Let g(b) be the first derivative of -b**3/4 - 15*b**2/8 - 3*b - 25. Factor g(r).
-3*(r + 1)*(r + 4)/4
Let p(g) be the second derivative of -1/28*g**4 + 11*g + 0*g**3 + 3/14*g**2 + 0. Solve p(k) = 0 for k.
-1, 1
Solve -7 - 384*b**2 + 385*b**2 - 4*b - 2*b = 0.
-1, 7
Let h(g) be the first derivative of -12/5*g**2 - 5/4*g**4 - 4/5*g - 5 - 3*g**3. Factor h(r).
-(r + 1)*(5*r + 2)**2/5
Factor 3/5*g**3 + 12/5*g**2 - 12/5*g + 0 - 3/5*g**4.
-3*g*(g - 2)*(g - 1)*(g + 2)/5
Let x(h) = 7*h**3 + 164*h**2 + 159*h. Let v(c) = 2*c**3 + c**2. Let b(k) = -2*v(k) + x(k). Factor b(g).
3*g*(g + 1)*(g + 53)
Let h be (30/6 + -7)/((3 - -2)*-1). Let q = 266 + -1326/5. What is t in 0 - h*t**2 + q*t = 0?
0, 2
Suppose 3*g - 16 = a, -g - 3*a - 28 = -5*g. Find v such that v**4 + 0*v**5 - 3*v**5 - 5*v**3 - v**3 + 8*v**g = 0.
0, 1, 2
Let k(m) be the second derivative of -m**5 - 65*m**4/12 - 5*m**3/2 - 62*m. Let k(j) = 0. What is j?
-3, -1/4, 0
Suppose 5*v = 7*v + 3*v. Let m(z) be the third derivative of 0*z + 1/6*z**4 + 1/15*z**5 + v + 3*z**2 + 0*z**3. Solve m(k) = 0.
-1, 0
Let f(i) be the second derivative of -i**7/14 + i**6/10 + 9*i**5/4 + 23*i**4/4 + 5*i**3 - 663*i. Let f(x) = 0. What is x?
-2, -1, 0, 5
Let l(n) = n**3 + 11*n**2 - 2*n - 14. Let k be l(-11). Find w such that -w**3 - 3*w**3 + 16*w - k*w**2 - 16 + 12*w**2 = 0.
-2, 1, 2
Suppose -25*z + 28*z - 3 = 0. Factor -2*f**2 + 9*f - 5 - 8*f - z + 7*f.
-2*(f - 3)*(f - 1)
Suppose -15*c - 340 = -185*c. Suppose 0*o**c + 0*o + o**3 - 1/2*o**4 + 0 - 1/2*o**5 = 0. What is o?
-2, 0, 1
Let 19*m - 20 + 21*m - 20*m - 20*m**3 + 5*m**4 + 15*m**2 = 0. Calculate m.
-1, 1, 2
Factor -2/17*r**2 - 1250/17 - 100/17*r.
-2*(r + 25)**2/17
Let m = 207 - 207. Let i(a) be the third derivative of 2/15*a**3 - 5*a**2 - 1/12*a**4 + 0 + 1/300*a**6 + 1/50*a**5 + m*a - 1/525*a**7. Factor i(r).
-2*(r - 1)**3*(r + 2)/5
Let l = -67 + 8717/130. Let m = l - -1/10. Find y, given that m*y - 2/13*y**3 + 2/13*y**2 - 2/13 = 0.
-1, 1
Let i(w) be the first derivative of -5*w**3 + 55*w**2/2 - 95*w + 9. Let n(r) = -23*r**2 + 82*r - 143. Let g(q) = -8*i(q) + 5*n(q). Find m such that g(m) = 0.
3
Let f(d) = 4*d + 30. Let m(g) = -g - 10. Let i(a) = 2*f(a) + 7*m(a). Let x be i(13). Factor l**3 + 1 + 2*l**4 - 2*l + 3 + 0*l**2 + l**x - 6*l**2.
2*(l - 1)**2*(l + 1)*(l + 2)
Factor -200*q + 214*q**2 + 230*q**2 - 449*q**2 - 195.
-5*(q + 1)*(q + 39)
Suppose 5*h = 5*y + 2185, -3*h - 871 = 2*y - 4*h. Let x = y - -5646/13. Suppose 0 - 6/13*w**2 + 2/13*w**3 + x*w = 0. What is w?
0, 1, 2
Let l(j) be the first derivative of 2*j**3/27 - 13*j**2/9 - 3. Determine d, given that l(d) = 0.
0, 13
Let u(b) be the first derivative of -b**4/20 - 6*b**3/5 + 19*b**2/10 + 34. What is n in u(n) = 0?
-19, 0, 1
Let p(g) be the third derivative of g**6/60 + g**5/6 - 73*g**4/12 - 77*g**3/3 + 18*g**2 - 4*g. Let p(k) = 0. Calculate k.
-11, -1, 7
Let g(y) = -y**3 - 2*y**2 - y. Let s(l) = 10*l**3 + 27*l**2 + 9*l. Let n(q) = -36*g(q) - 4*s(q). Factor n(p).
-4*p**2*(p + 9)
Let z(f) be the first derivative of -5*f**6/6 + f**5 + 75*f**4/2 - 90*f**3 - 945*f**2/2 + 2025*f - 51. Factor z(r).
-5*(r - 3)**3*(r + 3)*(r + 5)
Factor 40/3*z - 44/3*z**2 + 4/3*z**3 + 0.
4*z*(z - 10)*(z - 1)/3
Let q(n) be the third derivative of n**6/30 - n**5/5 - n**4 + 16*n**3/3 - 172*n**2. Find t such that q(t) = 0.
-2, 1, 4
Let y(o) be the first derivative of -o**5/140 + o**4/28 - o**3/21 - o - 4. Let j(f) be the first derivative of y(f). Find p such that j(p) = 0.
0, 1, 2
Let w(y) be the second derivative of y**5/10 - 37*y**4/12 + 3*y**3 + 2*y + 22. Let i be w(18). Factor 2/3*b**4 + 0*b + i + 2/3*b**3 + 0*b**2.
2*b**3*(b + 1)/3
Let n(o) = 25*o**5 + 9*o**4 - 33*o**3 + 17*o**2 - 17*o. Let i(q) = 3*q**5 + q**4 - 4*q**3 + 2*q**2 - 2*q. Let m(r) = 51*i(r) - 6*n(r). Factor m(b).
3*b**3*(b - 2)*(b + 1)
Let z(p) be the second derivative of 2*p**4/3 - 2*p**3 + 2*p**2 + 143*p. Suppose z(x) = 0. What is x?
1/2, 1
Factor -37 - 4*a**2 - 13*a + 31*a + 26*a + 105*a.
-(a - 37)*(4*a - 1)
Let v be 3*(-4)/(-48) - (-45)/12. Let j(p) be the second derivative of 0*p**3 + 0*p**2 + 1/36*p**v + 0 - 6*p + 2/45*p**6 - 1/15*p**5. Let j(z) = 0. Calculate z.
0, 1/2
Let a(o) = o + 23. Let n be a(-18). Factor 0 + 4 + n + 4*t - 3*t**3 - t - 9*t**2.
-3*(t - 1)*(t + 1)*(t + 3)
Let p be 3800/456 + 1/6. Factor -p*a**2 - 3*a + 0 - 5/2*a**3.
-a*(a + 3)*(5*a + 2)/2
Factor -675/4*p**3 - 48*p - 3 - 855/4*p**2.
-3*(p + 1)*(15*p + 2)**2/4
Let a(m) be the first derivative of 15 - 2/21*m**3 - 8/7*m**2 - 32/7*m. Factor a(z).
-2*(z + 4)**2/7
Factor -1/5*o**3 + o + 3/5 + 1/5*o**2.
-(o - 3)*(o + 1)**2/5
Let x(j) = -7*j**4 - 8*j**3 + j**2 + 12*j. Let b(w) = 15*w**4 + 15*w**3 - 25*w. Let h(a) = -2*b(a) - 5*x(a). Determine l so that h(l) = 0.
-2, -1, 0, 1
Factor -1/2*c + 1/2*c**3 - 1/8*c**4 + 3/8 - 1/4*c**2.
-(c - 3)*(c - 1)**2*(c + 1)/8
Suppose 37*f - 93*f = 0. Let t(h) be the first derivative of -2/27*h**3 + f*h**2 - 2/45*h**5 + 0*h - 1/9*h**4 - 7. Determine p so that t(p) = 0.
-1, 0
Let m be (3/21)/(1/2). Let w = 837/2 + -5851/14. Factor 0 + 0*x**2 - m*x**5 + 0*x**3 + 0*x + w*x**4.
-2*x**4*(x - 2)/7
Let z(b) be the second derivative of b**5 - 4*b**4/3 - 10*b**3/3 + 8*b**2 + 501*b. Factor z(t).
4*(t - 1)*(t + 1)*(5*t - 4)
Suppose -4/3*d**2 - 6*d - 6 = 0. Calculate d.
-3, -3/2
Let v = -30/13 - -177/26. Let d(q) be the first derivative of 1/6*q**3 + 3/2*q**2 + 1 + v*q. Factor d(y).
(y + 3)**2/2
Let g = 324699/14 + -46385/2. Solve 2/7*i**2 - 1/7*i**3 - g + 1/7*i = 0.
-1, 1, 2
Let o = -18658/5 - -3740. Factor o*c + 3/5*c**2 + 147/5.
3*(c + 7)**2/5
Factor -15/4*p**3 + 21/4*p**2 - 13/4*p + 3/4 + p**4.
(p - 1)**3*(4*p - 3)/4
Let z(j) be the first derivative of j**6/10 - 9*j**5/10 + 13*j**4/4 - 6*j**3 + 6*j**2 - 18*j + 33. Let a(y) be the first derivative of z(y). Factor a(q).
3*(q - 2)**2*(q - 1)**2
Let k(z) = 15*z**3 + 21*z**2 + 18*z. Let d(o) = -o**4 - 16*o**3 - 25*o**2 - 18*o. Let v(t) = 3*d(t) + 2*k(t). Factor v(q).
-3*q*(q + 1)*(q + 2)*(q + 3)
Let n(u) = u**2 + u + 1. Let v(y) = -2*y**2 + 5*y - 10. Suppose 6*p + 3 = -3. Let a(o) = p*n(o) - v(o). Determine c, given that a(c) = 0.
3
Let h(r) be the second derivative of -5*r**7/42 - r**6/6 + 3*r**5/4 + 25*r**4/12 + 5*r**3/3 - 3*r - 16. Factor h(b).
-5*b*(b - 2)*(b + 1)**3
Suppose 2*i - 2 = -v + 4, -2*i + 8 = 2*v. Let s(h) be the second derivative of i*h**2 + 0 + 9/2*h**4 - 5*h - 23/10*h**5 - 13/3*h**3 + 7/15*h**6. Factor s(y).
2*(y - 1)**3*(7*y - 2)
Suppose 3*h = 2*c - 2, -c - 1 = -3*h - 2. Factor -1 + j**2 + j**4 + j**5 + c - j**3 - 2*j**4.
j**2*(j - 1)**2*(j + 1)
Let p be (-40)/(-32) + -3*3/(-12). Factor 8*z**4 - 50 - 75*z**p - 115*z - 2*z**3 - 3*z**3 - 3*z**4.
5*(z - 5)*(z + 1)**2*(z + 2)
Let m(j) be the third derivative of j**5/30 - 5*j**4/12 + 2*j**3 + 6*j**2 - 17*j. Suppose m(x) = 0. What is x?
2, 3
Let b = 4/16463 - -1037153/65852. Find c such that 0 + 29/4*c**4 - 25/2*c - 45/4*c**2 + b*c**3 + 3/4*c**5 = 0.
-5, -2/3, 0, 1
Let x(o) = -23*o**4 - 83*o**3 - 80*o**2 - 10*o - 2. Let c(j) = -45*j**4 - 165*j**3 - 160*j**2 - 15*j - 5. Let w(d) = -2*c(d) + 5*x(d). Factor w(k).
-5*k*(k + 1)*(k + 2)*(5*k + 2)
Suppose 4*y - 949 = -5. Suppose 5*b**2 + y*b + 5*b**4 - 236*b - 14*b**3 + 4*b**3 = 0. What is b?
0, 1
Let t = -46/29 - -3021/58. Let w = -481/10 + t. Factor -6/5*u - 3*u**2 + 0 - 3/5*u**4 - w*u**3.
-3*u*(u + 1)**2*(u + 2)/5
Let r(m) be the second derivative of -1/3*m**3 + 0 + 1/10*m**5 + 0*m**2 + 0*m**4 + 11*m. Factor r(s).
2*s*(s - 1)*(s + 1)
Suppose -24*t + 23 = -12 + 35. Determine i, given that t - 4/3*i - 4/3*i**2 - 1/3*i**3 = 0.
-2, 0
Let d = -3131/7 + 3135/7. Factor d*h**4 + 8/7*h**3 - 12/7*h**2 - 32/7*h - 16/7.
4*(h - 2)*(h + 1)**2*(h + 2)/7
Let a = 152 - 76. Suppose -a = 4*s - 248. Find x, given that s + 8*x + 12*x**3 - 28*x**2 + 28*x**4 - 9*x**5 - 43 - 11*x**5 = 0.
-1, 0, 2/5, 1
Let k(r) = r**3 + 18*r**2