*a. Factor g(b).
-3*(b - 1)**2*(4*b - 1)
Find g, given that 6*g**3 - 22*g - g**3 - 7*g**3 + g**3 - 3*g**2 + 40 + 40*g = 0.
-5, -2, 4
Let g = -28 + 34. Suppose 3*j**2 + g*j**3 - 6*j + 170 - 170 - 3*j**4 = 0. Calculate j.
-1, 0, 1, 2
Let h(a) be the third derivative of -3/200*a**6 - 1/150*a**7 + 0*a**3 + 1/30*a**4 + 1/25*a**5 + 0 + 0*a - a**2. Determine f, given that h(f) = 0.
-2, -2/7, 0, 1
Let i(r) = 4*r**2 + 12*r - 36. Let o(w) = 4*w**2 + 11*w - 35. Let h be 1*(-1 + -2)/(-3)*3. Let j(t) = h*i(t) - 4*o(t). Factor j(u).
-4*(u - 2)*(u + 4)
Let a = 1529 + -1524. Let w(j) be the first derivative of 0*j**3 + 1/5*j**a - j - 13 + 1/2*j**4 - j**2. Factor w(u).
(u - 1)*(u + 1)**3
Let y(f) = 4*f - 86. Let x be 420/18 + 4/(-3). Let l be y(x). Factor 0*r - 1/7*r**l + 0 - 4/7*r**3.
-r**2*(4*r + 1)/7
Let y(p) be the second derivative of 5/12*p**4 + 10*p**2 + 0 - 21*p - 10/3*p**3. Let y(a) = 0. What is a?
2
Let w(c) be the second derivative of -c**5/20 - c**4/2 - 2*c**3 - 3*c**2 + 6*c. Let i(d) be the first derivative of w(d). What is u in i(u) = 0?
-2
Factor 41*x**3 + 13*x**2 - 9*x**3 - 29*x**3 - 8 + 2*x.
(x + 1)*(x + 4)*(3*x - 2)
Let o(z) = -61*z**2 + 31*z + 6. Let f(g) = g**3 - g**2 - 3. Let w(u) = 6*f(u) + 3*o(u). Factor w(n).
3*n*(n - 31)*(2*n - 1)
Let l(x) = x**2 + 9*x - 1. Let d be l(-9). Let i = 3 - d. Solve -2*k**5 + 15*k**4 - 15*k**i = 0 for k.
0
Let 147/2 - 1/4*r**3 - 2*r**2 + 35/4*r = 0. What is r?
-7, 6
Let x(c) be the first derivative of -1/2*c**3 - 2*c - 3/4*c**4 + 3/20*c**5 - 5 + 1/10*c**6 + 3*c**2. Let d(u) be the first derivative of x(u). Factor d(s).
3*(s - 1)**2*(s + 1)*(s + 2)
Let y(z) be the third derivative of -z**7/1680 + 11*z**6/960 - 11*z**5/160 + 37*z**4/192 - 7*z**3/24 - 6*z**2 - 17. Determine j so that y(j) = 0.
1, 2, 7
Suppose 2*d - 5*s = -0*d + 17336, -4*d + 34672 = -s. Factor d - 8668 + b**3 - 2*b + b**2.
b*(b - 1)*(b + 2)
Let j(x) be the second derivative of 8/33*x**3 - 3/11*x**2 + 0 + 1/22*x**4 + 16*x. Factor j(r).
2*(r + 3)*(3*r - 1)/11
Let b(l) be the third derivative of -l**6/24 + 5*l**5/6 - 115*l**4/24 + 35*l**3/3 - 51*l**2 - l. Factor b(u).
-5*(u - 7)*(u - 2)*(u - 1)
Let j(f) be the second derivative of -2/19*f**2 + 2*f + 0 - 1/114*f**4 - 1/19*f**3. Factor j(x).
-2*(x + 1)*(x + 2)/19
Let p(c) = c**4 + 2*c**3 - c. Let r(i) = 2*i**4 - 3*i**3 + 3*i**2 + 8*i. Let g(h) = 3*p(h) - 3*r(h). Find z such that g(z) = 0.
-1, 0, 3
Suppose 12*c = 20*c + 8. Let n be ((-4)/6)/(c - (-8)/32). Let 4/3*u**2 + 0 + n*u**5 - 16/9*u**3 + 8/9*u - 4/3*u**4 = 0. Calculate u.
-1, -1/2, 0, 1, 2
Let h = 712 - 709. Let g(p) be the first derivative of h + 49/27*p**3 - 7/9*p**2 + 1/9*p. Find m such that g(m) = 0.
1/7
Let b(l) = 12*l**3 + 5*l**2 - 16*l - 13. Let v(r) = 24*r**3 + 9*r**2 - 33*r - 27. Let j(s) = -9*b(s) + 4*v(s). Factor j(n).
-3*(n - 1)*(n + 1)*(4*n + 3)
Let j(c) be the third derivative of c**6/90 + 34*c**5/45 - 35*c**4/18 + 117*c**2. What is g in j(g) = 0?
-35, 0, 1
Let a(q) be the third derivative of 0 - 5/3*q**4 - 6*q**2 - 1/15*q**5 + 0*q - 50/3*q**3. Suppose a(t) = 0. Calculate t.
-5
Let s(k) be the second derivative of 1/20*k**5 + 1/4*k**4 + 1/42*k**7 - 1/3*k**3 + 0*k**2 - 1/10*k**6 + 0 + 10*k. Solve s(z) = 0 for z.
-1, 0, 1, 2
Suppose -9*p + 204 = 59*p. Let h(j) be the first derivative of 9/2*j**2 + j**p - 2 + 6*j. Find x such that h(x) = 0.
-2, -1
Let f = -241/4 - -61. Let c be -5 - (-24)/(6 - 3). Factor 0 - c*j**2 + 3*j + f*j**3.
3*j*(j - 2)**2/4
Let o(q) be the second derivative of q**4/102 - 172*q**3/51 + 7396*q**2/17 - 22*q - 6. Factor o(u).
2*(u - 86)**2/17
Let d = 166 + -164. Let o(z) be the third derivative of -2/3*z**3 - 1/20*z**5 + 1/240*z**6 + 6*z**d + 0 + 1/4*z**4 + 0*z. Factor o(s).
(s - 2)**3/2
Let w(u) be the first derivative of -u**6/3 + 64*u**5/25 + 103*u**4/10 - 692*u**3/15 + 56*u**2 - 128*u/5 + 828. Let w(t) = 0. What is t?
-4, 2/5, 1, 8
Let n = 1975 - 5768/3. Let u = n + -51. Let 38/3*l + u + 56/3*l**4 + 142/3*l**3 + 40*l**2 = 0. What is l?
-1, -2/7, -1/4
Suppose -6*b + 8 = -28. Suppose 2*w + 0*w - 20 = 3*x, -4*w + 5*x + 36 = 0. Solve -b*s + 2*s**w - 4 + 4*s**3 + 2*s**2 + 5*s**3 + 2*s**3 - 5*s**3 = 0.
-2, -1, 1
Let s(w) = -2*w - 8. Let x be s(-5). Let r(k) = 3*k**3 + 12*k**2 - 33*k - 9. Let b(m) = m**3 + 3*m**2 - 8*m - 2. Let a(v) = x*r(v) - 9*b(v). Factor a(o).
-3*o*(o - 1)*(o + 2)
Let a(d) be the third derivative of d**8/40320 - d**7/10080 - d**6/720 - d**5/15 + 25*d**2. Let j(n) be the third derivative of a(n). What is v in j(v) = 0?
-1, 2
Factor -17*p - 7*p + 0*p**2 - p**2 + 4*p**2.
3*p*(p - 8)
Let o(l) be the first derivative of 13/12*l**4 + 2/3*l**3 - 2*l**2 + 1/4*l**5 - 3 - 3*l. Let q(u) be the first derivative of o(u). Factor q(c).
(c + 1)*(c + 2)*(5*c - 2)
Let t(c) be the first derivative of -c**2/2 + 14*c + 11. Let s be t(12). Factor -2/11 - 2/11*y**s - 4/11*y.
-2*(y + 1)**2/11
Let b(t) be the second derivative of t**7/42 - 71*t**6/30 + 468*t**5/5 - 1782*t**4 + 13608*t**3 + 52488*t**2 - 74*t. Factor b(a).
(a - 18)**4*(a + 1)
Factor -2 + 31*d + 18 + 16*d**3 - 3*d**2 + 17*d - 57*d**2.
4*(d - 2)**2*(4*d + 1)
Let s = -289/15 - -61/3. Factor 2/15*g**3 + 8/15 + s*g + 2/3*g**2.
2*(g + 1)*(g + 2)**2/15
Let p be 7/((-49)/21) + 30. Let f be -3*(-4 + 96/p). Let 4/3 + 1/3*b**2 + f*b = 0. Calculate b.
-2
Let n(h) be the third derivative of -h**4/24 - 7*h**3/6 + 6*h**2. Let m be n(-9). Factor -4*c**3 - 2 + m*c**4 + 2 + 4*c**5 - 2*c**5.
2*c**3*(c - 1)*(c + 2)
Suppose 16*n + 0 - 44*n**3 - 142/3*n**4 + 88/3*n**2 - 10*n**5 = 0. Calculate n.
-3, -2, -2/5, 0, 2/3
Let s(f) = f**2 - 6*f + 2. Let m be s(7). Let v be ((-6)/(-54))/(3/m). Solve -1/3*l**3 - v*l + 0 - l**4 + 2/3*l**5 + l**2 = 0.
-1, 0, 1/2, 1
Suppose -3*z + 4*z = 0. Let n = 11337 - 11333. Determine d so that 0*d**2 + 0 + z*d + 1/8*d**3 + 1/8*d**n = 0.
-1, 0
Let p(f) be the first derivative of f**4/4 + 9*f**3 + 84*f**2 - 196*f - 420. Solve p(u) = 0.
-14, 1
Let o(n) = 2*n**2 - 3*n - 2. Let v(m) = m - m**2 - 2*m**2 + 4*m - 20 + 23. Let l(j) = -5*o(j) - 3*v(j). Factor l(w).
-(w - 1)*(w + 1)
Let l(g) be the second derivative of -g**5/25 - 3*g**4/4 - 107*g**3/30 - 12*g**2/5 - 965*g. Suppose l(a) = 0. Calculate a.
-8, -3, -1/4
Suppose -y = -3 + 6. Let k be (4/y)/(28/(-42)). Suppose 0 + 1/4*c + c**3 + 5/4*c**k = 0. What is c?
-1, -1/4, 0
Let k be 2/(-2)*2 + 7. What is h in -k*h**4 + 5*h**2 + 38*h**3 - 68*h**2 - 3*h**2 + 18*h - h**4 = 0?
0, 1/3, 3
Let l(q) be the third derivative of -q**7/7560 - q**6/540 - q**5/120 - 17*q**4/24 - 13*q**2. Let f(s) be the second derivative of l(s). Factor f(d).
-(d + 1)*(d + 3)/3
Let c(g) = -g**2 + 8*g - 5. Let x be c(7). Suppose -16 = x*n - 24. What is d in 0*d**2 + d + 0*d**2 + 0*d**4 + 3*d**2 + d**n + 3*d**3 = 0?
-1, 0
Suppose -j + 3 + 8 = 0. Factor -j*b**2 + 11*b + 12*b**3 - 2 + 2*b**5 - 9*b**2 - 10*b**4 + 8*b**3 - b.
2*(b - 1)**5
Let d(i) be the third derivative of 0*i + 4/9*i**3 + 1/90*i**5 + 0 - 12*i**2 - 5/36*i**4. Factor d(p).
2*(p - 4)*(p - 1)/3
Solve 2/11*y**3 + 0 - 40/11*y + 38/11*y**2 = 0.
-20, 0, 1
Let 35*a**3 - 120*a**2 + 0 - 5/3*a**4 + 340/3*a = 0. Calculate a.
0, 2, 17
Let y(r) be the first derivative of 4*r**5/45 + 5*r**4/3 + 28*r**3/3 + 18*r**2 + 192. Find l such that y(l) = 0.
-9, -3, 0
Suppose 0 = -33*d + 49*d - 96. Let c(n) be the third derivative of -2/15*n**5 + 1/60*n**d - 13*n**2 + 0*n + 0*n**3 + 0 + 0*n**4. Find w, given that c(w) = 0.
0, 4
Let o be ((-47)/3055)/(2/4). Let v = o + 199/130. Find u, given that -9/2*u**3 - 3/2*u**2 - v*u**4 + 9/2*u + 3 = 0.
-2, -1, 1
Solve -3/7*p**3 + 3/7 - 3/7*p**2 + 3/7*p = 0 for p.
-1, 1
Let a(h) be the first derivative of 0*h + 1/9*h**3 + 1/3*h**2 - 7 - 1/12*h**4. Suppose a(p) = 0. What is p?
-1, 0, 2
Suppose 38 - 6 = -2*f. Let s = -13 - f. Let -n**2 - 3 - 10*n**2 + 13*n**3 + 2*n - 4*n**4 + s = 0. Calculate n.
0, 1/4, 1, 2
Factor -5*f**3 + 4*f**4 - 5*f**4 + f**5 + 5*f**2 - 4*f**4 + 4*f**5.
5*f**2*(f - 1)**2*(f + 1)
Let u(i) be the first derivative of -i**7/14 - i**6/5 - 3*i**5/20 - 4*i + 16. Let m(q) be the first derivative of u(q). Let m(f) = 0. Calculate f.
-1, 0
Factor -5*k**2 + 4*k**2 + 6*k - 4*k**2 + 5*k**2 - 2*k**2.
-2*k*(k - 3)
Let t(f) = 3*f**3 + 4*f**2 + 22*f + 2. Let z be t(0). Determine u so that -1/4*u**z + 5/2*u - 25/4 = 0.
5
Let h(m) = 13*m**3 - 41*m + 53. Let c(