*b**4 - 3*b**2 + 17*b**3 - 17*b**3. Let k(v) = -6*r(v) + 5*u(v). Factor k(f).
-3*f*(f - 1)*(f + 1)*(f + 6)
Suppose -2*c = -4*f + 4, 72*f + 16 = 5*c + 75*f. Let k(l) be the second derivative of 0 + 6*l + 1/16*l**4 + 3/8*l**3 + 3/4*l**c. Let k(q) = 0. What is q?
-2, -1
Suppose -4/7*j**2 + 192/7 - 88/7*j = 0. What is j?
-24, 2
Let b(y) be the second derivative of y**5/190 - y**4/114 - 4*y**3/57 + 4*y**2/19 + 178*y + 2. Factor b(u).
2*(u - 2)*(u - 1)*(u + 2)/19
Factor -2/3*s + 0 + 2/3*s**2.
2*s*(s - 1)/3
Let w(y) = 5*y**3 - 14*y**2 + 9*y - 4. Let i(s) = 25*s**3 - 71*s**2 + 45*s - 21. Let c(v) = 2*i(v) - 11*w(v). Factor c(x).
-(x - 1)**2*(5*x - 2)
Solve 1/8*g**4 + 0 + 0*g - 1/2*g**3 - 1/2*g**2 + 1/8*g**5 = 0.
-2, -1, 0, 2
Let y(k) = 16*k**3 - 11*k. Let c(w) = -145*w**3 + 100*w. Let t(p) = 6*c(p) + 55*y(p). Let s(l) = 11*l**3 - l**2 - 6*l. Let r(a) = -5*s(a) + 6*t(a). Factor r(x).
5*x**2*(x + 1)
Let -1/3*n**2 - 16/3*n + 0 = 0. Calculate n.
-16, 0
Let q(b) be the second derivative of -b**5/50 + b**4/15 + 11*b**3/15 - 12*b**2/5 - 416*b. Factor q(g).
-2*(g - 4)*(g - 1)*(g + 3)/5
Let k = 49 - 44. Factor 2*w**3 + 7*w**3 - 5*w**k - w**3 - 3*w**3.
-5*w**3*(w - 1)*(w + 1)
Let q(i) = 8*i**2 - 2*i - 10. Let j(l) = -7*l**2 + 2*l + 9. Suppose -2 = -w - 7. Let s be w/(2 + 6/(-2)). Let n(z) = s*q(z) + 6*j(z). What is m in n(m) = 0?
-1, 2
Let p be ((-152)/6)/((-1)/(-3)). Let f be p/(2*(-1 - 0)). Let -35*c**3 + 9*c + 1 + f*c**3 + 2 + 9*c**2 = 0. What is c?
-1
Determine b, given that -402040/11*b - 220340/11*b**2 - 13250/11*b**3 - 280/11*b**4 - 194672/11 - 2/11*b**5 = 0.
-46, -1
Suppose 5*m + 15 = 0, 5*m - 10 = -3*i - 7. Factor 18 + g**2 - 2*g + 3*g**2 - i*g**2 - 6.
-2*(g - 2)*(g + 3)
Let l be -2 + 3 - 2/(-2). Let f be (45/(-10) + 4)*((-11 - -16) + -6). Factor f*p + 1/8*p**l + 1/2.
(p + 2)**2/8
Let s be (-39 - -40) + 0 + (-1 - 0). Let t be (51/(-15) - -1) + (s - -3). Factor 6/5*i**2 + t*i**5 - 3/5 - 6/5*i**3 + 3/5*i - 3/5*i**4.
3*(i - 1)**3*(i + 1)**2/5
Suppose 174*i - 54 = 156*i. Let r(h) be the first derivative of -1/2*h**2 - 2/15*h**5 + 1/9*h**i + 1/3*h + 1/4*h**4 + 6. Solve r(q) = 0 for q.
-1, 1/2, 1
Let j(a) be the second derivative of a**4/48 - 5*a**3/12 + 2*a + 18. Factor j(h).
h*(h - 10)/4
Suppose 2*v - 6*v = 76. Let p = 22 + v. Factor -p - 45*s**2 - 5 - 24*s**4 - 56*s**3 - 19*s**2 - 4*s**5 - 36*s.
-4*(s + 1)**4*(s + 2)
Factor 164/3*h**3 + 54*h**2 - 110*h + 4/3.
2*(h - 1)*(h + 2)*(82*h - 1)/3
Let k be 20/18*22*12/1320. Let 2/9*c**3 - 2/9*c**2 - k*c + 2/9 = 0. Calculate c.
-1, 1
Let r(s) be the third derivative of s**8/8400 + s**7/4200 - s**6/1800 - s**5/600 + 7*s**3/3 + 6*s**2. Let t(y) be the first derivative of r(y). Factor t(z).
z*(z - 1)*(z + 1)**2/5
Let q(f) be the second derivative of -f**6/2 + 7*f**5/4 - 25*f**4/12 + 5*f**3/6 - 2*f - 24. Let q(n) = 0. Calculate n.
0, 1/3, 1
Let y(p) = p**3 + 20*p**2 + 3*p + 64. Let c be y(-20). Factor 0 - 2/9*b**c - 8/9*b + 2/9*b**3 + 8/9*b**2.
-2*b*(b - 2)*(b - 1)*(b + 2)/9
Suppose 3*j - 2*j - 3 = 0. Let b be (-14)/(-35) - (j/(-30) - 0). Factor 0*v**4 + 0 + v**2 - 3/2*v**3 + b*v**5 + 0*v.
v**2*(v - 1)**2*(v + 2)/2
Let l(o) be the second derivative of -1/54*o**4 + 3*o - 1/90*o**5 + 1/9*o**2 + 1/27*o**3 + 0. Solve l(x) = 0.
-1, 1
Let n(l) be the first derivative of l**6/900 - l**4/60 + 2*l**3 + 5. Let z(p) be the third derivative of n(p). Factor z(b).
2*(b - 1)*(b + 1)/5
Let g = 35 - 32. Suppose -g*q - 4 = -4*q. Factor 0 + 0*m - 1/3*m**q + 0*m**2 + 1/3*m**3.
-m**3*(m - 1)/3
Suppose 2*r**2 - 8/3*r**3 + 8/3*r + 2/3*r**4 - 8/3 = 0. What is r?
-1, 1, 2
Let i(v) be the third derivative of v**7/5040 - v**6/480 + v**5/120 + 3*v**4/8 - 5*v**2. Let q(u) be the second derivative of i(u). Factor q(f).
(f - 2)*(f - 1)/2
Let s(u) be the second derivative of -1/18*u**4 + 7*u + 0 + 0*u**2 - 1/18*u**3 - 1/60*u**5. Factor s(b).
-b*(b + 1)**2/3
Let o(h) be the third derivative of h**8/84 + 8*h**7/105 - 4*h**6/15 - 14*h**5/15 + 7*h**4/6 + 20*h**3/3 - 43*h**2 - h. Find i such that o(i) = 0.
-5, -1, 1, 2
Let x(z) be the second derivative of z**4/66 + 98*z**3/33 + 2401*z**2/11 - 206*z. Suppose x(d) = 0. What is d?
-49
Let h(b) be the third derivative of -147*b**6/340 + 203*b**5/170 - 46*b**4/51 + 16*b**3/51 + 2*b**2 + 63*b. Suppose h(w) = 0. What is w?
4/21, 1
Let g(p) be the second derivative of 1/10*p**6 - 23*p + 3*p**2 - 1/2*p**3 + 0 + 3/20*p**5 - 3/4*p**4. Factor g(n).
3*(n - 1)**2*(n + 1)*(n + 2)
Let m(o) be the first derivative of o**4/6 - 4*o**3/9 + o**2/3 - 18. Solve m(a) = 0.
0, 1
Let q(k) = -6*k - 4. Let g be q(-1). Solve -3*i**g - 39*i**4 - i**2 + 2 + 41*i**4 = 0.
-1, 1
Suppose -3*k = 5*x + 9, 3*k - 3*x - 12 = 3. Solve -8*w**2 - 14*w**2 + 19*w**2 + 3*w**4 - k*w + 3*w**3 - w = 0 for w.
-1, 0, 1
Let c(l) be the third derivative of -l**7/420 - l**6/12 - 5*l**5/4 - 125*l**4/12 + 7*l**3/3 - 9*l**2. Let s(v) be the first derivative of c(v). Factor s(z).
-2*(z + 5)**3
Let v(i) be the third derivative of 14*i**2 + 0*i + 0*i**4 + 1/15*i**5 - 2/3*i**3 + 0. Factor v(c).
4*(c - 1)*(c + 1)
Factor -6*r**4 - 8*r - 196*r**2 + 2*r**4 + 8*r**3 + 200*r**2.
-4*r*(r - 2)*(r - 1)*(r + 1)
Let q(y) = 5*y**3 + 3*y**2 - 14. Let o(g) = -45*g**3 - 25*g**2 + 125. Let m(p) = 6*o(p) + 55*q(p). Suppose m(a) = 0. What is a?
-2, 1
Let c(m) be the third derivative of m**5/3 + 25*m**4/24 + 5*m**3/6 - m**2 - 4. Suppose c(l) = 0. What is l?
-1, -1/4
Let j = -72 + 107. Let k = 38 - j. Factor -2/3*n**k + 0*n + 0 - 1/3*n**2.
-n**2*(2*n + 1)/3
Let s be ((-5)/18)/((-120)/72). Let u(r) be the first derivative of 2/35*r**5 - s*r**6 + 0*r**2 - 2 + 1/4*r**4 + 0*r - 2/21*r**3. Let u(p) = 0. Calculate p.
-1, 0, 2/7, 1
Let -260*o**3 - o**4 + 135*o**3 - 4*o**2 + 127*o**3 + 3*o**2 = 0. What is o?
0, 1
Suppose -2*o + 4 = 2*o + s, 0 = -4*o - 4*s + 16. Let n(q) = 2*q. Let y be n(2). Determine z so that -2/3*z**3 + 2/3*z**5 + 0 + o*z + 0*z**2 + 0*z**y = 0.
-1, 0, 1
Suppose -245 = -25*i - 10*i. Let h(w) be the first derivative of -4/3*w + i + 7/18*w**6 + 53/12*w**4 + 31/9*w**3 + 11/5*w**5 + 0*w**2. Let h(q) = 0. What is q?
-2, -1, 2/7
Suppose 0 = -5*s - 15, 0*h - h - 4*s = 8. Let b(o) be the third derivative of 0 + 0*o - 9*o**2 + 0*o**3 + 1/30*o**5 + 1/6*o**h. Determine j so that b(j) = 0.
-2, 0
Let n(u) be the second derivative of -9*u**5/20 + u**4/2 + u**3/2 + 37*u. Determine a so that n(a) = 0.
-1/3, 0, 1
Let o(x) be the third derivative of 0*x**5 - 1/420*x**7 + 0 + 45*x**2 + 1/240*x**6 + 0*x**4 + 0*x + 0*x**3. Factor o(v).
-v**3*(v - 1)/2
Let q(o) be the third derivative of 0*o**4 + 0*o**3 + 0 - 1/150*o**6 + 0*o**5 + 0*o + o**2 - 2/525*o**7. Factor q(j).
-4*j**3*(j + 1)/5
Suppose 51*g = 46*g + 45. Let h be g/14 + (-5)/35. Determine c so that 0 - 3*c**3 - 1/2*c - h*c**5 + 2*c**4 + 2*c**2 = 0.
0, 1
Let i(r) be the third derivative of 0*r**3 + 9/64*r**4 + 0*r + 0 + 28*r**2 - 1/320*r**6 - 1/20*r**5. Factor i(y).
-3*y*(y - 1)*(y + 9)/8
Suppose 2/3 - 65/3*l**3 + 7*l**2 + 17/3*l + 25/3*l**4 = 0. Calculate l.
-1/5, 1, 2
Let l(z) = z**5 - 5*z**4 - z**3 + 5*z**2 + 4*z. Let y = -16 + 11. Let h(o) = -o**4 + o**3 + o**2 - o - 1. Let d(f) = y*l(f) + 20*h(f). Factor d(w).
-5*(w - 2)**2*(w + 1)**3
Let m(c) be the third derivative of -2*c**7/105 + c**6/15 + c**5/5 + 275*c**2. Factor m(z).
-4*z**2*(z - 3)*(z + 1)
Let j(c) be the first derivative of -4*c - 1/4*c**4 - 4 - 2*c**3 - 6*c**2. Let a(v) be the first derivative of j(v). Suppose a(b) = 0. What is b?
-2
Let l = 919/896 - -15/128. Suppose -l - 10/7*b**2 + 16/7*b + 2/7*b**3 = 0. Calculate b.
1, 2
Factor 0 - 7/5*a**2 - 2*a - 1/5*a**3.
-a*(a + 2)*(a + 5)/5
Let s(b) be the first derivative of b**4/14 + 32*b**3/7 + 768*b**2/7 + 8192*b/7 + 52. Factor s(l).
2*(l + 16)**3/7
Suppose 4*h = 5*g + 37 - 272, -5*h - 5*g - 305 = 0. Let r be (18/h)/(((-36)/(-16))/(-3)). Factor -r*c**2 - 4/5*c - 2/5.
-2*(c + 1)**2/5
Suppose -156*l + 146*l = 0. Let f(g) be the first derivative of 1/14*g**4 + 7 + l*g + 0*g**3 - 1/7*g**2. Factor f(s).
2*s*(s - 1)*(s + 1)/7
Let p = -33293/5 - -6661. Determine m, given that 0 - 6/5*m**5 + 27/5*m**3 - 12/5*m - p*m**2 + 3/5*m**4 = 0.
-2, -1/2, 0, 1, 2
Let v be (8/36)/((-18)/(-81)). Determine c so that -7/2*c + 1/2*c**4 - 5/2*c**3 + 9/2*c**2 + v = 0.
1, 2
Let k be 3520/10164 - (-4)/(-66). Factor 0 + k*d**3 + 2/7*d**4 + 0*d**2 + 0*