*4 - 6*s**3 + 25*s**2 + 30*s + 19. Let u(q) = 7*a(q) - 4*n(q). Factor u(p).
3*(p - 2)*(p + 1)**3
Suppose -z + 10 = z. Factor 0*t**3 - 2*t**z + 3*t**3 - t**3.
-2*t**3*(t - 1)*(t + 1)
Let y(s) = -s**5 - 6*s**4 + 7*s**3 + 6*s**2. Let k(n) = 2*n**5 + 13*n**4 - 15*n**3 - 13*n**2. Let l(z) = 6*k(z) + 13*y(z). Let l(g) = 0. What is g?
-1, 0, 1
Let u = 395/2 + -16589/84. Let q(l) be the third derivative of 2*l**2 + 0*l + u*l**4 + 0 - 1/210*l**5 + 0*l**3. Factor q(s).
-2*s*(s - 1)/7
Factor -12*c - 3 + 33*c - 11*c**3 - 33*c**2 + 26*c**3.
3*(c - 1)**2*(5*c - 1)
Factor 4/9*i + 0 - 4/9*i**4 + 4/9*i**2 - 4/9*i**3.
-4*i*(i - 1)*(i + 1)**2/9
Let q(x) = 328*x**3 - 140*x**2 + 20*x + 4. Let z(k) = k**3 + k**2 + k + 1. Let o(y) = q(y) - 4*z(y). Factor o(p).
4*p*(9*p - 2)**2
Suppose 2*t + 2*q = 6*q - 30, -5*t = -q + 75. Let i = t + 16. Factor -1/2*u**2 + i - 1/2*u.
-(u - 1)*(u + 2)/2
Suppose 3*f**3 - 15*f + 7 - f**2 - 2*f**2 - 16 = 0. What is f?
-1, 3
Let v(i) = -i + 1. Let r(u) = 2*u**2 - 2. Let z(f) = r(f) + 2*v(f). Determine y so that z(y) = 0.
0, 1
Let t(a) = a**5 - a**4 - a**3 + a**2 - 1. Let p(d) = 45*d**5 - 21*d**4 - 66*d**3 + 18*d**2 + 21*d + 6. Let w(n) = p(n) + 3*t(n). Solve w(q) = 0 for q.
-1, -1/4, 1
Suppose 25 = -5*c - 25. Let m = c - -11. Factor -j + 1/4*j**2 + m.
(j - 2)**2/4
Let g(k) = 6*k**2 + 6*k - 22. Let i(w) = -2*w**2 - 2*w + 7. Let l(q) = -q**2 + 9*q + 3. Let v be l(9). Let y(s) = v*g(s) + 10*i(s). Factor y(r).
-2*(r - 1)*(r + 2)
Let p(a) = a**2 + a - 1. Let l(u) = -7*u**5 + 16*u**4 - 11*u**3 + 6*u**2 + 4*u - 4. Let b(h) = -l(h) + 4*p(h). Factor b(y).
y**2*(y - 1)**2*(7*y - 2)
Let i(l) be the third derivative of l**8/3024 + l**7/378 + l**6/360 - l**5/60 + 21*l**2. Factor i(m).
m**2*(m - 1)*(m + 3)**2/9
Let k = 1 + 3. Let i(s) be the second derivative of 0 - 1/2*s**k - 1/10*s**5 - s**3 - s**2 - s. Suppose i(h) = 0. Calculate h.
-1
Find c such that -54/7*c**3 + 6/7*c**5 + 51/7*c**2 + 60/7*c - 3/7*c**4 - 36/7 = 0.
-3, -1, 1/2, 2
Let c be 21/9 + (1 - 7)/18. What is d in 0*d**c - 2/7*d + 0 + 2/7*d**3 = 0?
-1, 0, 1
Suppose -2*c - m + 2 = -5*m, m = 2*c - 8. Let u be 52/30 + (-2)/c. Determine j, given that u - 2/3*j**2 + 2/3*j = 0.
-1, 2
Let c(b) = -8*b**4 + 7*b**3 + 13*b**2 - 5*b - 5. Let m(s) = 39*s**4 - 36*s**3 - 64*s**2 + 25*s + 25. Let r(u) = -11*c(u) - 2*m(u). Let r(f) = 0. Calculate f.
-1, -1/2, 1
Suppose 3*f**3 - 218*f - 36*f**2 - 6*f**4 + 42*f**4 - 15*f**5 + 230*f = 0. Calculate f.
-1, 0, 2/5, 1, 2
Let y be (-1 - -2 - -3) + -5 + 5. Factor 0*v**3 - 2/5*v**y + 0*v + 2/5*v**2 + 0.
-2*v**2*(v - 1)*(v + 1)/5
Let n(q) = 17*q**3 - 2*q**2 - q. Let g be n(-1). Let x = -11 - g. Factor -x - 2*f**2 + 7.
-2*f**2
Let k = 44 + -32. Let l = -57/5 + k. What is z in -l*z**2 - 3/5*z + 3/5*z**3 + 3/5 = 0?
-1, 1
Let h(l) be the third derivative of 0*l**3 + 4*l**2 + 1/40*l**6 + 0*l**5 + 0 + 0*l + 1/112*l**8 + 0*l**4 - 1/35*l**7. Solve h(u) = 0 for u.
0, 1
Let h(l) = -11*l**4 + 10*l**3 + 19*l**2 - 14*l. Let p(i) = -100*i**4 + 90*i**3 + 170*i**2 - 125*i. Let n(u) = -35*h(u) + 4*p(u). Factor n(m).
-5*m*(m - 1)*(m + 1)*(3*m - 2)
Suppose -4*o + 2 + 10 = 0. Suppose z = -2*x - x + 11, 6 = o*x. Factor -p**5 - 19*p + 17*p - 4*p**2 + 4*p**4 + 3*p**z.
2*p*(p - 1)*(p + 1)**3
Let d = -9 - -9. Suppose 5*p - 2*p = 0. Factor -1/3*q**2 + p*q + 1/3*q**4 + 0 + d*q**3.
q**2*(q - 1)*(q + 1)/3
Factor -4/5 - 4/5*i**5 - 4/5*i**4 - 4/5*i + 8/5*i**2 + 8/5*i**3.
-4*(i - 1)**2*(i + 1)**3/5
Let q(u) be the third derivative of u**6/1440 + u**5/120 + u**4/24 - 5*u**3/6 + 2*u**2. Let m(b) be the first derivative of q(b). Factor m(t).
(t + 2)**2/4
Suppose 0*x + 4*j - 6 = -x, 3*j = -2*x + 7. Let d(f) be the second derivative of 1/5*f**2 - x*f + 0*f**3 + 0 - 1/30*f**4. Determine q, given that d(q) = 0.
-1, 1
Let r(z) be the first derivative of -z**4 + 16*z**3/3 + 6*z**2 + 3*z + 1. Let g(j) be the first derivative of r(j). Determine q so that g(q) = 0.
-1/3, 3
Solve 1/4*u**2 + 5/4 + 3/2*u = 0.
-5, -1
Let v(u) be the first derivative of -u**6/480 + u**5/240 + u**2 + 1. Let z(o) be the second derivative of v(o). Suppose z(f) = 0. Calculate f.
0, 1
Let l(h) = -h**2 + h. Let t(c) = c**2 - c + 1. Let n(o) = 4*o**2 - 5*o + 1. Let m(k) = -n(k) + t(k). Let s(a) = 4*l(a) - 2*m(a). Factor s(u).
2*u*(u - 2)
Let k be (-6)/(-14) + (-96)/(-560). Solve 0 - k*z**2 - 3/5*z = 0.
-1, 0
Let d(t) be the third derivative of t**7/105 - t**6/15 + t**5/10 + 9*t**2. Factor d(k).
2*k**2*(k - 3)*(k - 1)
Let h(k) be the first derivative of 4*k**5/15 - k**4 + 4*k**3/3 - 2*k**2/3 + 1. Factor h(l).
4*l*(l - 1)**3/3
Suppose 3*a = -3*o - o + 6, -2*o = a. Let x be (1/(-4))/((-3)/a). What is t in -3/4*t + 1/4 + x*t**2 = 0?
1/2, 1
Suppose -3*g - 4*v = -2*v + 326, g - 3*v + 116 = 0. Let b = -768/7 - g. Solve 2/7*z**3 - 2/7 - b*z + 2/7*z**2 = 0.
-1, 1
Determine q so that 0 + 0*q - 1/5*q**2 = 0.
0
Let d(c) = -c**2 + 6*c + 3. Let h be d(3). Suppose m + 7 = 3*b, -2*b + 3*m + h = 6*m. Factor 4*o**2 + b*o**2 - 3*o - o**3 + 1 - 4*o**2.
-(o - 1)**3
Let z(l) be the third derivative of l**8/616 + 4*l**7/385 + 3*l**6/110 + 2*l**5/55 + l**4/44 - 6*l**2. Suppose z(o) = 0. What is o?
-1, 0
Let j(m) be the second derivative of m**6/1800 - m**5/600 - m**4/60 - m**3/2 - 2*m. Let d(k) be the second derivative of j(k). Suppose d(n) = 0. Calculate n.
-1, 2
Let r(c) be the third derivative of -c**5/300 + c**3/30 + 3*c**2. Find p such that r(p) = 0.
-1, 1
Let j(l) = 25*l**3 + 75*l**2 + 35*l - 15. Let s(a) = 37*a**3 + 112*a**2 + 53*a - 22. Let r(c) = -8*j(c) + 5*s(c). Factor r(f).
-5*(f + 1)*(f + 2)*(3*f - 1)
What is t in 2*t**3 + 17*t - 10*t - 4*t - 5*t**3 = 0?
-1, 0, 1
Let i = 20 - 15. Suppose -w = -5*o + 16, 20 = 6*o - o - i*w. Factor -3/2*c + 3/2*c**2 + 1/2 - 1/2*c**o.
-(c - 1)**3/2
Suppose 5*f = -5*c + 40, f + 19 = 3*f + 3*c. Let u be (4/f)/(14/5). Let 0*v**2 + 2/7*v - u*v**3 + 0 = 0. What is v?
-1, 0, 1
Let n(l) be the second derivative of -l**4/6 - 2*l**3/3 - l**2 + 7*l. Let n(q) = 0. What is q?
-1
Let c(r) be the third derivative of -1/144*r**4 + 0*r + 1/1260*r**7 - 2*r**2 + 0 + 0*r**3 - 1/240*r**6 + 1/120*r**5. Suppose c(z) = 0. Calculate z.
0, 1
Let u = 596 - 7159/12. Let k = u - -11/12. Factor -1/3*o + 1/3*o**2 + 1/3*o**3 + 0 - k*o**4.
-o*(o - 1)**2*(o + 1)/3
Let h(f) = 5*f - 18. Let m be h(4). Determine d, given that 2/7*d**m + 32/7 + 16/7*d = 0.
-4
Let p = -15 + 18. Suppose 5*b**2 - 3*b - 9 + p + 4*b**2 = 0. Calculate b.
-2/3, 1
Let 0 - 6/7*x + 2/7*x**2 = 0. Calculate x.
0, 3
Factor 17/6*u - 1/6*u**4 + 5/2*u**2 + 1 + 1/2*u**3.
-(u - 6)*(u + 1)**3/6
Let a = -18/5 + 133/30. What is i in i + 1/6 + a*i**2 = 0?
-1, -1/5
Suppose 4*t = -2*d + 54, -3*d + 3*t = t - 57. Factor -4*l**3 - 17*l + d*l + 0*l**3.
-4*l*(l - 1)*(l + 1)
Let d(n) be the first derivative of -n**6/180 + 3*n**2/2 - 2. Let g(o) be the second derivative of d(o). Suppose g(j) = 0. What is j?
0
Let a(p) be the second derivative of -p**4/72 + p**3/9 - p**2/3 + 8*p. Solve a(q) = 0 for q.
2
What is c in 0 + 0*c + 0*c**2 - 6/7*c**3 - 2/7*c**4 = 0?
-3, 0
Suppose 0 = -3*w + 4*w. Let h(z) be the first derivative of 0*z**4 + 2/15*z**5 + 0*z**2 - 1 + 1/9*z**6 + w*z + 0*z**3. Factor h(v).
2*v**4*(v + 1)/3
Let o(x) = -x**2 - x + 7. Let q be o(3). Let v be 4/10 - 13/q. Factor 0*i**2 + 0*i - 1/5*i**5 + 1/5*i**v + 0*i**4 + 0.
-i**3*(i - 1)*(i + 1)/5
Let s(v) be the first derivative of -v**4/36 - v**3/27 + v**2/18 + v/9 - 42. Let s(f) = 0. Calculate f.
-1, 1
Let g(y) = -71*y**2 - 16*y - 6. Let t(m) = 995*m**2 + 225*m + 85. Let s(l) = 85*g(l) + 6*t(l). Find o such that s(o) = 0.
-2/13, 0
Let k(f) = -f**3 - 3*f**2 + 3*f - 1. Let v(s) = s**2 + 1. Let t(g) = -k(g) - 3*v(g). Find l such that t(l) = 0.
-1, 2
Factor -1/6*s**4 - 1/2*s**2 + 2/3 + 2/3*s - 2/3*s**3.
-(s - 1)*(s + 1)*(s + 2)**2/6
Let g(w) be the third derivative of w**6/216 - w**5/180 - w**4/108 - 6*w**2. Solve g(r) = 0.
-2/5, 0, 1
Let m(c) be the second derivative of -c**5/20 + 19*c**4/12 - 33*c**3/2 + 81*c**2/2 + 19*c. Solve m(h) = 0 for h.
1, 9
Let x be (-4)/((-640)/104) + (-1)/4. Determine h so that -x*h - 6/5*h**3 + 8/5*h**2 + 0 = 0.
0, 1/3, 1
Let z(t) be the third derivative of t**8/560 - t**7/840 - t**6/120 + t**5/120 - t**3/6 - 2*t**2. Let r(f) be the first derivative of z(f). Factor r(q).
q*(q - 1)*(q + 1)*(3*q - 1)
Let l(j) be the fi