a) = 0.
-1, 2/7, 1, 3
Factor -28 - 26*r - 4248*r**2 + 2128*r**2 + 2122*r**2.
2*(r - 14)*(r + 1)
Let a(m) = -2*m**2 + 125*m + 1877. Let d be a(75). Factor -3/8 + 1/2*p - 1/8*p**d.
-(p - 3)*(p - 1)/8
Suppose 4*p - 50 = -3*r, 2*r + 4 + 0 = 0. Let s be 10/(-4)*p/(-7). Determine f so that -6*f + 4*f**3 - 3*f**5 + 2 + 0*f**5 - 6*f**4 + s*f**5 + 4*f**2 = 0.
-1, 1
Let i(b) be the third derivative of 0*b**3 + 0*b**4 + 6*b**2 + 2/45*b**6 + 0*b - 1/45*b**5 + 0. Factor i(s).
4*s**2*(4*s - 1)/3
Let u(h) be the first derivative of 8/3*h**6 - 4/5*h**5 - 4*h**4 - 1 + 0*h**2 + 0*h + 4/3*h**3. Determine n so that u(n) = 0.
-1, 0, 1/4, 1
Factor -1964 - 3036 - 1493*q**3 - 967*q**3 - 29258*q**2 + 24600*q - 50*q**4.
-2*(q + 25)**2*(5*q - 2)**2
Factor 4*i**2 + 9*i + 0*i - 24 + 18*i - 7*i.
4*(i - 1)*(i + 6)
Solve 0 - 120/7*t**2 + 15/7*t**4 + 69/7*t**3 + 36/7*t = 0.
-6, 0, 2/5, 1
Let i(u) be the second derivative of -u**6/135 - u**5/90 + 5*u**4/18 - 23*u**3/27 + 10*u**2/9 - 2*u + 5. Suppose i(v) = 0. Calculate v.
-5, 1, 2
Suppose -1 + 11 = 2*d. Suppose 0 = -2*h + 13 - 7. Factor -9*k + 4*k**2 - d - 13*k**2 - 3*k**h + 2.
-3*(k + 1)**3
Let l(t) be the second derivative of 0 - 1/40*t**5 - 5/24*t**4 + 0*t**3 + 0*t**2 - 11*t. Solve l(j) = 0.
-5, 0
Let j(f) be the second derivative of -f**5/4 + 25*f**4/4 - 10*f**3 - 70*f**2 + 762*f. Factor j(r).
-5*(r - 14)*(r - 2)*(r + 1)
Let g be (168/144)/((-5)/((-45)/7)). Factor -3*m - g*m**2 + 9/2.
-3*(m - 1)*(m + 3)/2
Let r(h) be the first derivative of h**7/2940 - h**6/105 + 3*h**5/35 - 8*h**4/21 + h**3 - 29. Let x(a) be the third derivative of r(a). Factor x(y).
2*(y - 8)*(y - 2)**2/7
Let s(f) be the first derivative of -2*f**5/65 + 2*f**4/13 + 18*f**3/13 + 38*f**2/13 + 32*f/13 - 619. What is d in s(d) = 0?
-2, -1, 8
Let k(w) be the third derivative of -w**7/42 - w**6/4 - w**5 - 25*w**4/12 - 5*w**3/2 + 7*w**2 + 1. Factor k(v).
-5*(v + 1)**3*(v + 3)
Let t(w) be the second derivative of w**6/10 + 21*w**5/20 - 3*w**4/4 - 19*w**3/2 + 21*w**2 + 259*w. Factor t(i).
3*(i - 1)**2*(i + 2)*(i + 7)
Let t(w) = -w**2 - 12*w - 9. Let l be t(-11). Let c(n) be the first derivative of -n**l + 3/2*n**4 + 4 + 0*n - 4/3*n**3. Factor c(r).
2*r*(r - 1)*(3*r + 1)
Let x be ((-115)/345)/((-1)/3). Factor -q**2 - 5/2*q + 1/2*q**5 + 2*q**4 + 2*q**3 - x.
(q - 1)*(q + 1)**3*(q + 2)/2
Let x(m) be the first derivative of m**4/2 - 14*m**3/3 + 15*m**2 - 18*m + 21. Suppose x(d) = 0. What is d?
1, 3
Let m(o) be the first derivative of -2*o**3/21 + o**2/7 + 24*o/7 - 94. Factor m(y).
-2*(y - 4)*(y + 3)/7
Let p(x) = 2*x - 6. Let i be p(4). Let z be ((-6)/4)/(3 + 33/(-4)). Find c such that -z*c**i - 2/7 - 4/7*c = 0.
-1
Let l(s) be the second derivative of s**5/80 + s**4/12 + s**3/8 + s - 142. What is x in l(x) = 0?
-3, -1, 0
Let q(r) be the third derivative of r**8/10080 + r**7/10080 - r**5/60 + 27*r**2. Let j(k) be the third derivative of q(k). Determine g, given that j(g) = 0.
-1/4, 0
Let h(y) = 4*y**2 - 6*y + 4. Let b(n) = -5*n**2 + 7*n - 4. Let a(l) = 3*b(l) + 4*h(l). Let q be a(4). Solve -2*p + 3*p - 4*p**2 - 13*p - q = 0 for p.
-2, -1
What is o in 0 + 0*o**2 + 6*o**3 + 0*o - 20/3*o**4 + 2/3*o**5 = 0?
0, 1, 9
Let g be (25/12 - 4) + (-16 - -19). Let l(h) be the first derivative of -3/2*h**2 - g*h**3 - 3/8*h**4 - 1/20*h**5 - h - 4. Solve l(c) = 0.
-2, -1
Let o(n) = -7*n**4 - 31*n**3 - n**2 + 33*n + 4. Let j(b) = 17*b**4 + 61*b**3 + 3*b**2 - 66*b - 10. Let i(z) = -6*j(z) - 15*o(z). Solve i(w) = 0.
-33, -1, 0, 1
Let t(d) = d**2 - 4*d + 4. Let a(c) = c**2 - 9*c - 20. Let w be a(11). Let k be t(w). Let j**2 + k*j**3 - 1/2*j**4 - 1/2 + 0*j = 0. What is j?
-1, 1
Let v(f) be the first derivative of -2/21*f**3 - 2/7*f**2 + 3 + 0*f. Factor v(m).
-2*m*(m + 2)/7
Factor 8*t**3 - 8*t**2 - 2*t**3 - 16*t - 4*t**3 + 6*t.
2*t*(t - 5)*(t + 1)
Let k(g) be the second derivative of g**7/70 - g**6/90 - g**5/15 - 7*g**3/6 + 11*g. Let b(u) be the second derivative of k(u). Factor b(n).
4*n*(n - 1)*(3*n + 2)
What is t in -32/3 - 2/9*t**2 - 38/9*t = 0?
-16, -3
Factor 8*y**3 + 0 + 12*y + 58/3*y**2 + 2/3*y**4.
2*y*(y + 1)*(y + 2)*(y + 9)/3
Let s(x) be the first derivative of -14*x**5/25 + 47*x**4/10 + 14*x**3/5 - 47*x**2/5 - 28*x/5 - 3. Determine r so that s(r) = 0.
-1, -2/7, 1, 7
Factor -1/6*x**2 + 2/3*x - 2/3.
-(x - 2)**2/6
Suppose 0 = 8*o + 471 + 105. Let l be o/(-33) + 6/(-33). Factor -6/5 + 3/5*u**l - 3/5*u.
3*(u - 2)*(u + 1)/5
Let g(v) be the second derivative of v**5/15 - v**4 + 10*v**3/3 - 14*v**2/3 - 152*v + 1. Factor g(b).
4*(b - 7)*(b - 1)**2/3
Let f = 198 - 198. Let h(g) be the second derivative of f + g**3 + 5*g - 9/2*g**2 - 1/12*g**4. Let h(l) = 0. What is l?
3
Let o(t) be the second derivative of -5*t**4/12 - 9*t**3/2 - 14*t**2 - 258*t. Factor o(n).
-(n + 4)*(5*n + 7)
What is l in 0*l + 0 + 19/3*l**2 - 1/3*l**3 = 0?
0, 19
Let f(w) = w**3 + 2*w**2 - 5*w - 2. Let v be f(-3). Let p be v/(-18) - (-5)/(180/8). Factor 2/7*l**3 + 0*l + p - 2/7*l**2.
2*l**2*(l - 1)/7
Let f be 4/10 - 34008/(-130). Suppose o = -t - 2*o + f, 0 = -3*t + 2*o + 764. Suppose 40*h**3 + 5*h**4 + 160*h**2 + 320*h + t + 1/4*h**5 = 0. What is h?
-4
Let i(b) be the first derivative of b**4/20 + 2*b**3/3 + 33*b**2/10 + 36*b/5 - 134. Factor i(m).
(m + 3)**2*(m + 4)/5
Let r(u) = u**2 - u. Let x(f) = f**2 - 181*f + 180. Let q(h) = 6*r(h) - x(h). Factor q(c).
5*(c - 1)*(c + 36)
Let o(f) be the first derivative of -1/240*f**5 + 0*f**4 - f**2 - 1 + 0*f + 0*f**3. Let b(k) be the second derivative of o(k). Factor b(c).
-c**2/4
Let a(g) be the third derivative of -g**6/360 + 19*g**5/60 - 37*g**4/24 + 55*g**3/18 - 55*g**2 + 2*g. Let a(u) = 0. What is u?
1, 55
Let l(d) = 23*d - 2. Let y be l(1). Let h be (-2)/(-3) - y/(-9). Factor 9*q**3 - h*q**5 - 19*q**3 + 5*q**3 + 8*q**3.
-3*q**3*(q - 1)*(q + 1)
Let i(v) be the second derivative of v**5/210 - 5*v**4/84 + 19*v**2 - 15*v + 2. Let z(w) be the first derivative of i(w). Factor z(x).
2*x*(x - 5)/7
Find l such that -20/7*l + 0 + 8*l**3 + 10/7*l**4 + 26/7*l**2 = 0.
-5, -1, 0, 2/5
Factor 4/9 + 0*z**2 - 2/9*z**3 + 2/3*z.
-2*(z - 2)*(z + 1)**2/9
Let a(n) be the third derivative of -n**6/240 - n**5/15 + 3*n**4/16 - 636*n**2. Find c such that a(c) = 0.
-9, 0, 1
Factor -1/3*s**3 + 2*s**2 + 8/3 + 5*s.
-(s - 8)*(s + 1)**2/3
Factor -146/15*k - 74/15 - 14/3*k**2 + 2/15*k**3.
2*(k - 37)*(k + 1)**2/15
Let b(y) be the second derivative of -y**6/240 + y**5/120 + y**4/48 - y**3 + 6*y. Let l(a) be the second derivative of b(a). Find x, given that l(x) = 0.
-1/3, 1
Let s(n) = -n**2 + 49. Let q be s(0). Factor -q*y**2 - 3 - 42*y - 4 - 2.
-(7*y + 3)**2
Suppose -n = q + 34, -3*q + 158 = -4*n + 29. Let d = 36 + n. Factor 0*f**d + 0*f**2 + 0*f + 2/13*f**5 + 0 + 0*f**4.
2*f**5/13
Factor -24*b - 6*b**4 - 43 + 2*b**5 - 39 - 2*b**3 + 90 + 22*b**2.
2*(b - 2)*(b - 1)**3*(b + 2)
Find p such that -70*p**3 - 2003*p + 1015*p - 55 - 5*p**4 + 818*p - 180*p**2 = 0.
-11, -1
Let k(j) = -j**5 - j**4 - 2*j**3. Let l(p) = -9*p**4 + 21*p**3 - 28*p**2 + 12*p. Let w(u) = -4*k(u) + 4*l(u). Factor w(x).
4*x*(x - 3)*(x - 2)**2*(x - 1)
Solve -1/2*g**3 + 3429500 + 285*g**2 - 54150*g = 0 for g.
190
Let f(d) be the second derivative of 5*d**7/84 + 25*d**6/12 + 125*d**5/4 + 3125*d**4/12 + 15625*d**3/12 + 15625*d**2/4 - d + 32. Determine g so that f(g) = 0.
-5
Let g be (-6 + 247/52)*(4 - 6). Determine a, given that 1 - 1/2*a**3 + 2*a**2 - g*a = 0.
1, 2
Solve -34*t**4 + 3*t**4 + 768*t + 16*t**4 + 36*t**4 + 207*t**3 + 666*t**2 + 288 = 0 for t.
-4, -1, -6/7
Find c such that -16*c + 2*c**4 + 281*c**3 + 2*c**4 - 269*c**3 = 0.
-2, 0, 1
Factor 21/2*g - 45/4 + 3/4*g**2.
3*(g - 1)*(g + 15)/4
Factor -16/13*m**3 + 0 + 2/13*m**4 + 40/13*m**2 - 32/13*m.
2*m*(m - 4)*(m - 2)**2/13
Let b be (-290)/(-22) - 6/33. Let s = b - 8. Let s*g**2 + 27 + 3*g**2 - 5*g**2 - 18*g = 0. Calculate g.
3
What is t in -2/3*t**3 + 1/6*t**2 + 0 + t + 1/6*t**4 = 0?
-1, 0, 2, 3
Let q(o) be the second derivative of o**4/12 + o**3 + 4*o**2 + 71*o. Factor q(u).
(u + 2)*(u + 4)
Let t = 5321/3 - 1773. Solve 0 - t*p - 2/3*p**2 = 0 for p.
-1, 0
Suppose -10*z + 39 + 11 = 0. Let p be (1/6)/((-18)/(-486)) - 2. Find m, given that 15/2*m + p*m**2 + z = 0.
-2, -1
Let t(p) = -84*p + 1856. Let a be t(22). Factor 10/3*j**3 + 4/3 + a*j**2 + 6*j.
2*(j + 1)**2*(5*j + 2)/3
Let r = 56 - 55. S