(a) - 9*i(a). Factor d(b).
-3*b**3*(b - 1)*(b + 1)
Let q(p) be the first derivative of -2*p**5/45 - p**4/3 - 26*p**3/27 - 4*p**2/3 - 8*p/9 - 3. Find f, given that q(f) = 0.
-2, -1
Let m(w) be the second derivative of 2*w**7/21 + 11*w**6/90 - w**5/6 - 11*w**4/36 - w**3/9 + 12*w. Find d such that m(d) = 0.
-1, -2/3, -1/4, 0, 1
Suppose -3*o - 4*w + 6 = 0, o + 0*w - 2 = w. Let a be 3/o - 2/(-4). Factor -2*h + 0*h**a - 3*h + 3*h - 2*h**2.
-2*h*(h + 1)
Let c(q) = -9*q**2 + 106*q - 609. Let d(l) = 100*l**2 - 1165*l + 6700. Let x(o) = -45*c(o) - 4*d(o). Suppose x(z) = 0. What is z?
11
Let p(w) = -w. Let j(d) = 14*d**2 + 3*d. Let i = -5 + 4. Let r(c) = i*p(c) + j(c). Factor r(s).
2*s*(7*s + 2)
Suppose 2*c = -h - 4 - 0, -2*h - 24 = -4*c. Let b be h/(-21) - (-14)/49. Factor -2/3*p**4 + 0*p + 0*p**3 - b + 4/3*p**2.
-2*(p - 1)**2*(p + 1)**2/3
Let n be -3 - -5 - (0 - 0). Let w(y) be the first derivative of 0*y**3 + 0*y - n + 0*y**2 - 1/10*y**5 + 1/8*y**4. Factor w(t).
-t**3*(t - 1)/2
Suppose 4*k = 6*k + 66. Let h(g) = -48*g**2 - 15*g + 33. Let b(v) = 3*v**2 + v - 2. Let u(t) = k*b(t) - 2*h(t). Let u(z) = 0. Calculate z.
-1, 0
Let w(u) be the first derivative of -u**6/2 + 12*u**5/5 - 9*u**4/2 + 4*u**3 - 3*u**2/2 + 20. Suppose w(i) = 0. What is i?
0, 1
Factor -2*n**4 - 3*n**3 + 4*n**4 + 2*n**2 - 4*n**4 + 4*n**3 - n**5.
-n**2*(n - 1)*(n + 1)*(n + 2)
Let f be 8/44 - 160/154. Let m = f + 25/21. Factor 0 - 1/3*y**4 - 1/3*y + m*y**2 + 1/3*y**3.
-y*(y - 1)**2*(y + 1)/3
Let z(h) = -22*h**2 - 22*h - 7. Let a(i) = -15*i**2 - 15*i - 5. Let n(m) = 7*a(m) - 5*z(m). Factor n(f).
5*f*(f + 1)
Let u(t) be the second derivative of 3*t**5/20 + t**4/4 - 5*t. Factor u(f).
3*f**2*(f + 1)
Let i(y) = y**2 + 4*y - 3. Let k(f) = -9*f**2 - 33*f + 25. Let g(u) = 51*i(u) + 6*k(u). Factor g(d).
-3*(d - 1)**2
Let f(t) be the second derivative of t**8/144 + 8*t**7/315 + 11*t**6/360 + t**5/90 - 3*t**2 + 3*t. Let g(l) be the first derivative of f(l). Factor g(c).
c**2*(c + 1)**2*(7*c + 2)/3
Let o(j) be the first derivative of 0*j**4 - 1/30*j**5 + 0*j**3 + 2*j + 0*j**2 - 2 + 1/45*j**6. Let m(z) be the first derivative of o(z). Factor m(w).
2*w**3*(w - 1)/3
Let u(z) be the first derivative of -z**3/7 + 15*z**2/14 - 16. Suppose u(f) = 0. Calculate f.
0, 5
Let j(l) be the third derivative of l**5/30 - l**3/3 + 13*l**2. Factor j(h).
2*(h - 1)*(h + 1)
Let c(d) be the second derivative of -d**6/90 - d**5/60 + d**4/12 + 5*d**3/18 + d**2/3 - d. Factor c(l).
-(l - 2)*(l + 1)**3/3
Let j be 123/15 - (-5 + 13). Find m such that 1/5*m**2 + j*m**3 + 0 - 2/5*m = 0.
-2, 0, 1
Let w(k) = 10*k**2 + 15*k + 15. Let z(o) = 11*o**2 + 14*o + 14. Let n(q) = 6*w(q) - 5*z(q). Suppose n(l) = 0. What is l?
-2
Let h(q) = -q**3 + 4*q**2 - q - 2. Let m be h(4). Let n(l) = 2*l**2 - 6*l + 12. Let t(z) = 2*z**2 - 5*z + 11. Let o(c) = m*t(c) + 7*n(c). Factor o(s).
2*(s - 3)**2
Factor -z**5 + 11 - 27 + 16 + z**3.
-z**3*(z - 1)*(z + 1)
Let p be 67 + -8 + (1 - 3). Let r = p + -227/4. Factor 0*i + 1/4*i**4 - 1/2*i**2 + r*i**3 + 0.
i**2*(i - 1)*(i + 2)/4
Let n = 89/3 + -27. Let v(w) be the first derivative of -n*w**3 + 4 - w**2 + 0*w. Factor v(l).
-2*l*(4*l + 1)
Let p(f) = 2*f - 4. Let c be (-3)/2 + 45/10. Let r be p(c). Find o such that 6*o**2 - 2*o**5 - 6*o**4 - o**5 - o**2 + 3*o**3 + o**r = 0.
-2, -1, 0, 1
Let o(t) be the third derivative of -t**7/70 + t**6/20 - t**4/4 + t**3/2 + 2*t**2. Factor o(h).
-3*(h - 1)**3*(h + 1)
Suppose -2 = 3*s - 2*z, -s + 3*z + 0*z - 3 = 0. Suppose 2/11*i**2 - 2/11*i + s = 0. Calculate i.
0, 1
Let b(m) be the second derivative of m**7/70 - m**5/10 + m**3/2 - 3*m**2/2 + 2*m. Let u(c) be the first derivative of b(c). Factor u(h).
3*(h - 1)**2*(h + 1)**2
Factor -3*l**3 - 5 + 4 + 2*l**4 + l**2 + 1.
l**2*(l - 1)*(2*l - 1)
Let f(k) = k + 1. Let h be 18/(-12) + (-15)/(-6). Let j(r) = -2*r**2 + 10. Let u(l) = h*j(l) - 4*f(l). Factor u(o).
-2*(o - 1)*(o + 3)
Let w be ((-2)/(-3))/((-1)/(-3)). Let p be ((-9)/6)/((-1)/2). Find f such that 2/3*f**p + 0 + 4/3*f**w + 2/3*f = 0.
-1, 0
Factor -3/4*i**3 - 7/4*i**2 + 0*i + 1.
-(i + 1)*(i + 2)*(3*i - 2)/4
Let l(f) = -f + 2. Let k be (3/(-1) - -3)/2. Let w be l(k). Let -1/4*h**4 + 0 + 1/4*h**3 + 1/4*h**w - 1/4*h = 0. Calculate h.
-1, 0, 1
Suppose 3*z - 12 = -42. Let f(d) = -3*d**3 - 10*d**2 + 4*d - 1. Let s(q) = q**3 + q**2. Let r(t) = z*s(t) - 2*f(t). Determine o, given that r(o) = 0.
1/2, 1
Let z be (-2)/(3 + 66/(-18)). Factor 0*t + 1/3*t**2 + 2/3*t**z + 1/3*t**4 + 0.
t**2*(t + 1)**2/3
Suppose -4*l = z - 8, -6 + 0 = -3*l + 3*z. Let k(o) be the second derivative of 0*o**l + o + 0*o**4 - 1/18*o**3 + 1/60*o**5 + 0. Suppose k(a) = 0. Calculate a.
-1, 0, 1
Let d = -7 + 10. What is z in -6*z**2 + 8*z**4 - 2*z**2 + 3*z**3 - 4*z**5 + z**d = 0?
-1, 0, 1, 2
Let g(u) be the second derivative of u**4/48 - u**3/8 + 5*u. Factor g(d).
d*(d - 3)/4
Let y(o) = -4*o**2 + 10. Let p(d) = 13*d**2 - d - 29. Suppose 19 = x - 2*i, 5*x = x - 5*i + 63. Let h(m) = x*y(m) + 6*p(m). Factor h(v).
2*(v - 1)*(5*v + 2)
Let u = -9310538/122969 + 4/17567. Let m = u - -76. Determine j, given that 2/7*j**3 - 2/7*j - 2/7*j**2 + m = 0.
-1, 1
Let s = 96 - 381/4. Let -3/4*x - 1/4*x**3 - s*x**2 - 1/4 = 0. What is x?
-1
Let k(r) = -11*r**4 - 16*r**3 + 15*r**2 + 40*r + 14. Let v(c) = 100*c**4 + 145*c**3 - 135*c**2 - 360*c - 125. Let l(i) = -55*k(i) - 6*v(i). Factor l(w).
5*(w - 2)*(w + 1)**2*(w + 2)
Factor 4*c**3 + 9*c + 17*c - 26*c - 4*c**2.
4*c**2*(c - 1)
Let k(n) = -n**3 + 3*n**2 + 2*n - 6. Let f be k(4). Let i be 5*(-1 - f/10). Factor 0 + 1/5*u**i + 2/5*u.
u*(u + 2)/5
Suppose 9 = 3*a, 5*c + 3*a - a - 31 = 0. Let 0*h + 1/3*h**3 + h**c + 0 - 5/3*h**4 + 1/3*h**2 = 0. What is h?
-1/3, 0, 1
Determine w, given that -6 - 45*w - 189/2*w**2 - 147/4*w**3 = 0.
-2, -2/7
Factor -10*i**3 - 21 + 11 - 36*i**2 + 16*i + 10.
-2*i*(i + 4)*(5*i - 2)
Let p(o) be the third derivative of -o**7/420 + o**5/60 - o**3/12 - 6*o**2. Let p(g) = 0. What is g?
-1, 1
Suppose 5*w + 8 = -2, -9 = -b + 3*w. Let f = 6 - b. Factor -7*m**3 + m + 2*m**2 + 2*m**3 + 2*m**f.
-m*(m - 1)*(3*m + 1)
Let u(y) be the third derivative of y**8/224 - y**7/140 - y**6/80 + y**5/40 + 13*y**2. Factor u(f).
3*f**2*(f - 1)**2*(f + 1)/2
Suppose -g + 2*g = 5. Suppose g*l - 4*l - 4 = 0. Determine z, given that z - 11*z + 40*z**2 + 6*z**l - 28*z**3 - 6*z = 0.
0, 2/3, 2
Let f = 16 + -10. Let a = 7 - 5. Factor -f*g**4 + 2*g**5 + 2*g**3 + 0*g**5 + a*g**4.
2*g**3*(g - 1)**2
Let l(c) be the second derivative of -c**4/12 + 2*c**3/9 - c**2/6 + 2*c. Solve l(v) = 0.
1/3, 1
Let f be (-7)/(42/36*-3). Let -4/5*j**3 + 2/5 - 14/5*j**4 - 6/5*j**5 + f*j + 12/5*j**2 = 0. What is j?
-1, -1/3, 1
Let p(z) = -z**2 + 3*z + 4. Let x be p(3). Solve -2*j - x*j**3 + 2*j + 5*j**2 - 2*j + j**4 + 0*j**3 = 0 for j.
0, 1, 2
Let t(o) = -6*o**3 + 12*o**2 - 20*o + 20. Let a(c) = -5*c**3 + 12*c**2 - 21*c + 19. Let v = -2 - -5. Let f(p) = v*t(p) - 4*a(p). Factor f(w).
2*(w - 2)**3
Let s(u) be the second derivative of 0 + 3*u + 5/3*u**3 + 1/3*u**4 - 3*u**2. Solve s(w) = 0.
-3, 1/2
Let b(t) be the third derivative of -1/40*t**5 - 1/80*t**6 + 1/4*t**3 + 0*t + 0 - 3*t**2 + 1/16*t**4. Factor b(i).
-3*(i - 1)*(i + 1)**2/2
Let j = 2667/3340 + 1/668. Let 6/5*v**5 + 0*v + 0 + j*v**3 + 14/5*v**4 + 0*v**2 = 0. Calculate v.
-2, -1/3, 0
Let t = 3634/7 - 518. Determine o, given that -t + 8/7*o + 10*o**2 = 0.
-2/5, 2/7
Let q(k) = k**3 - 4*k**2 - 6*k - 5. Let t be q(5). Let f = 12 + t. Determine u so that f*u + 2/3*u**3 - 2/3 - 2*u**2 = 0.
1
Let f be 6/(-48)*54 + 7. Factor 1/4*v - 1/4*v**2 - f*v**3 + 1/4.
-(v - 1)*(v + 1)**2/4
Let l(o) = -o**3 + 5*o**2 + 3. Let h be l(5). Suppose z - h*z = -6. Determine j so that 1 + z*j + 2*j**3 + 3*j**4 - 4*j**2 + 0*j**4 - 5*j = 0.
-1, 1/3, 1
Let w(x) be the third derivative of -x**9/2520 + 11*x**8/10080 - x**7/1890 + x**4/8 + 4*x**2. Let i(q) be the second derivative of w(q). Factor i(y).
-2*y**2*(y - 1)*(9*y - 2)/3
Factor -7/4*p**4 + 5/2*p**3 + 5/4 + 1/4*p**5 - 11/4*p + 1/2*p**2.
(p - 5)*(p - 1)**3*(p + 1)/4
Let l(u) = 4*u - 2. Suppose -12 = -4*d + 4*s - 0*s, 0 = -2*d - 4*s - 6. Let k be l(d). Solve 0 - 1/2*a + 1/4*a**k = 0.
0, 2
Let o(j) be the first derivative of -15*j**4/28 + 3*j**3/7 + 48*j**2/7 + 36*j/7 + 8. Factor o(x).
-3*(x - 3)*(x + 2)*(5*x + 2)/7
Let z(q) be the first der