69*n**2 - 9*n - 45. Let i(v) = -m(v) + 6*z(v). Factor i(r).
-3*(r - 1)*(r + 1)*(r + 23)
Suppose 3*a - 23 = -5*l, 12 = a - 3*l - 5. Factor -4*h - 4*h**3 - h**3 + 5*h**2 + a*h + 3*h.
-5*h*(h - 2)*(h + 1)
Determine v so that 13*v - 80 - 3*v**2 + 0*v**2 + 17*v + 8*v**2 = 0.
-8, 2
Suppose -g + 0 = 3*n - 5, 0 = -5*g + 3*n + 7. Factor 60*f**4 - 3*f**g + 5*f**2 - 62*f**4.
-2*f**2*(f - 1)*(f + 1)
Let m(g) be the first derivative of g**3/6 + g**2 + 3*g/2 + 11. Find z such that m(z) = 0.
-3, -1
Let r(m) be the second derivative of m**4/4 + 7*m**3/2 + 9*m**2 + 16*m. Factor r(q).
3*(q + 1)*(q + 6)
Solve -143*c**4 + 641*c - 127*c**4 - 129*c + 32*c**3 - 4*c**5 - 256 - 304*c**2 + 290*c**4 = 0 for c.
-4, 1, 2, 4
Let y(q) = 2*q**2 + 11*q + 7. Let n be y(-5). Factor -2*o**2 + 3*o**2 - o**2 - 5*o**n - 20*o**3.
-5*o**2*(4*o + 1)
Let r = 114 + -1252/11. Let s(u) be the first derivative of 6 - 4/33*u**3 - r*u - 3/11*u**2. Solve s(x) = 0 for x.
-1, -1/2
Let a(t) = 3*t**2 + 3*t - 8. Let l be a(-10). Suppose -78 = 4*b - l. Factor 6*d**2 - 46 + b + 2*d**3.
2*d**2*(d + 3)
Let b = 597 - 594. Let x(l) be the first derivative of -4/11*l - 3 + 2/33*l**b - 1/11*l**2. Factor x(a).
2*(a - 2)*(a + 1)/11
Let d(r) be the first derivative of 2*r**3/33 - 474*r**2/11 + 112338*r/11 + 294. Determine g so that d(g) = 0.
237
Let u(t) be the first derivative of -t**4/12 + 53*t**3/3 - 2133*t**2/2 + 6241*t/3 + 45. Find v such that u(v) = 0.
1, 79
Let p be 4/(-300)*(16/(-4))/4. Let g(h) be the second derivative of 0*h**4 + 0*h**5 + 0*h**2 + p*h**6 + 0*h**3 - 1/105*h**7 + 0 + 5*h. Let g(b) = 0. What is b?
0, 1
Let f(g) = -33*g + 827. Let p be f(25). What is w in 12/7*w**3 - 8/7 + 4/7*w**p + 4/7*w**4 - 12/7*w = 0?
-2, -1, 1
Let j(z) be the first derivative of -z**6/3600 + z**5/600 - 5*z**3 + 2. Let i(u) be the third derivative of j(u). Determine v, given that i(v) = 0.
0, 2
Suppose -u = 4*s - 21, 5*u = -17 + 2. Suppose 0 = b - s*b + 2*x + 2, -b - 4*x - 4 = 0. Factor 0 + 8/3*l**4 + 2/3*l**2 - 7/3*l**3 + b*l - l**5.
-l**2*(l - 1)**2*(3*l - 2)/3
Suppose 89*x - 15 = 84*x. Suppose 0 = -5*l - 4*a + 5, -2*l - x*l - 5*a = 0. Factor 4/3*m**l + 0*m - 4/3*m**4 + 4/3*m**2 + 0 - 4/3*m**3.
4*m**2*(m - 1)**2*(m + 1)/3
Suppose 7*m = 12*m + 360. Let q be (-1 - 0/3)*m. Find t, given that 26*t**2 - q*t**4 - 27*t - 21*t**3 + 22*t**2 + 3 - 15*t**2 + 48*t**5 + 36*t**2 = 0.
-1, 1/4, 1
Factor d - d - 10248*d**3 + 28*d**2 + 10246*d**3.
-2*d**2*(d - 14)
Let r(g) = g**2 + 16*g - 23. Let b(s) = -2*s**2 - 2*s - 1. Let d(x) = 3*b(x) + 3*r(x). Factor d(o).
-3*(o - 12)*(o - 2)
Let d(t) be the second derivative of -1 - 1/4*t**5 + 5/4*t**4 - 9*t + 15/2*t**3 + 25/2*t**2. Factor d(b).
-5*(b - 5)*(b + 1)**2
Let l(q) be the first derivative of 0*q + 0*q**3 - 1/84*q**4 + 2*q**2 - 5 + 1/210*q**5. Let h(s) be the second derivative of l(s). Factor h(t).
2*t*(t - 1)/7
Suppose -b - b + 6 = 0. Let s(q) be the first derivative of 3/4*q**4 + 1/2*q**2 + q**3 + 1/5*q**5 + 0*q + b. Find l such that s(l) = 0.
-1, 0
Let o(d) be the first derivative of -d**4/18 - 4*d**3/9 + 64*d/9 + 537. Solve o(c) = 0 for c.
-4, 2
Let j = 550 + -544. Let m(z) be the second derivative of 3/110*z**5 - 1/33*z**j + z + 0*z**2 + 0*z**3 + 0 + 1/33*z**4. Factor m(v).
-2*v**2*(v - 1)*(5*v + 2)/11
Let v(c) be the third derivative of 3*c**3 + 0 - 32*c**2 - 1/30*c**5 + 0*c + 0*c**4. Solve v(k) = 0.
-3, 3
Let t(r) be the first derivative of -r**6/75 - r**5/25 + r**4/30 + 2*r**3/15 + 13*r - 10. Let n(l) be the first derivative of t(l). Let n(j) = 0. Calculate j.
-2, -1, 0, 1
Let j(r) = -r - 2. Suppose -5*n - 18 = 2. Let y be j(n). Solve -64*a**2 + 28*a**y + 2 - 3 + 12*a = 0 for a.
1/6
Determine l, given that 52*l - 29*l**3 + 27 + 50*l**2 + 2*l**4 - 23*l**3 - 62 - 15 - 2*l**2 = 0.
-1, 1, 25
Let r = 1703 - 5108/3. Let -1/3 + 2/3*t**3 + 0*t**2 - 2/3*t + r*t**4 = 0. Calculate t.
-1, 1
Factor -9*j**3 - 8*j**5 + j + 3*j**2 - 15*j**4 + j + 2*j**5 + j.
-3*j*(j + 1)**3*(2*j - 1)
Let m be (-3000)/(-3750)*(-1 - (-1 - 2)). Find j, given that 2/5*j**4 + 0 + 0*j**2 + m*j - 6/5*j**3 = 0.
-1, 0, 2
Let m be (-3)/3*(-1 - 2) - 0. Let k(c) be the first derivative of 3/32*c**4 + 0*c + 10 + 0*c**2 + 1/8*c**m. Factor k(g).
3*g**2*(g + 1)/8
Let f(x) be the first derivative of x**9/6048 - x**8/1680 + x**7/1680 - 19*x**3/3 - 16. Let v(m) be the third derivative of f(m). Factor v(s).
s**3*(s - 1)**2/2
Let x = -953/35 + 139/5. Let d(o) = 2*o**3 - 72*o**2 + o - 34. Let n be d(36). Solve -48/7*c - x*c**4 - 52/7*c**n - 24/7*c**3 - 16/7 = 0.
-2, -1
Let a = 77 + -73. Factor -3*o + o**3 - o**2 + 2*o + 79*o**a - 78*o**4.
o*(o - 1)*(o + 1)**2
Let p(c) be the first derivative of 1/32*c**4 - 1/240*c**5 + 0*c + 0*c**3 - 4*c**2 + 1. Let o(q) be the second derivative of p(q). Factor o(b).
-b*(b - 3)/4
Let x(r) = r**5 + 49*r**4 + 58*r**3 + 5*r**2 + 7*r. Let b(m) = m**5 - m**4 + m**2 - m. Let l(a) = -7*b(a) - x(a). What is g in l(g) = 0?
-3, -2, -1/4, 0
Let m(a) be the third derivative of 0 - 22*a**2 + 0*a - 1/15*a**5 + 1/2*a**4 - 4/3*a**3. Determine z so that m(z) = 0.
1, 2
Suppose z + a - 7 = 0, -3*a + 4 = -2. Factor -3/8*x**z + 0*x + 9/8*x**3 + 3/4*x**2 + 0*x**4 + 0.
-3*x**2*(x - 2)*(x + 1)**2/8
Let r(u) be the third derivative of -u**7/840 + u**6/40 - 9*u**5/40 + 9*u**4/8 - 27*u**3/8 - 521*u**2. Factor r(s).
-(s - 3)**4/4
Factor 10*n**3 - 16/3*n**4 + 0 - 2/3*n - 4*n**2.
-2*n*(n - 1)**2*(8*n + 1)/3
Let -72*y**3 - 240*y**3 + 56*y**5 - 2*y**4 + 294*y**4 - 67*y + 323*y - 244*y**2 - 48 = 0. Calculate y.
-6, -1, 2/7, 1/2, 1
Factor -127 + 86 + 89 - 4*k**3 + 40*k**2 + 92*k.
-4*(k - 12)*(k + 1)**2
Let -20/7*l - 24/7 + 4/7*l**2 = 0. Calculate l.
-1, 6
Let n(w) = -2*w**2 - 5*w + 12. Let i(f) = -f. Suppose -8 = 5*c + 7. Let l(d) = c*i(d) + n(d). Find k such that l(k) = 0.
-3, 2
Let q = 716 - 487. Let h = q - 158. Factor h*l**3 + 3*l**5 - 10*l**4 - 69*l**3 + 5*l**5.
2*l**3*(l - 1)*(4*l - 1)
Factor 1/2*r**2 + 0*r - 1/2*r**3 + 0.
-r**2*(r - 1)/2
Let c be 11/14 + 15/30. Factor c*l**2 + 3/7*l + 0 - 12/7*l**3.
-3*l*(l - 1)*(4*l + 1)/7
Let o(d) = -2*d**2 + d + 1. Let n(i) = -3*i**4 - 21*i**3 - 35*i**2 - 32*i - 5. Let m(k) = -n(k) - 5*o(k). Suppose m(w) = 0. What is w?
-3, -1, 0
Let r(i) be the third derivative of i**7/280 + i**6/20 + 3*i**5/16 - i**4/4 - 2*i**3 - 3*i**2 - 216*i. Determine y so that r(y) = 0.
-4, -1, 1
Let f(m) be the first derivative of -1/3*m**3 - 1/5*m**5 + 2*m - 3/2*m**2 + 3/4*m**4 - 12. Factor f(l).
-(l - 2)*(l - 1)**2*(l + 1)
Factor 2/13*u**2 - 32/13 + 30/13*u.
2*(u - 1)*(u + 16)/13
Let q = -1/170 - -91/1020. Let z(p) be the second derivative of 1/2*p**2 + 0 - q*p**4 - 4*p + 0*p**3. Factor z(s).
-(s - 1)*(s + 1)
Let w(x) be the first derivative of 2*x**6/3 + 32*x**5/5 + 22*x**4 + 112*x**3/3 + 34*x**2 + 16*x - 135. Solve w(f) = 0 for f.
-4, -1
Let z(f) = 9*f - 8*f + 18*f - 3*f - 9*f**2 + 18. Let i(q) = -8*q**2 + 16*q + 18. Let g(j) = 7*i(j) - 6*z(j). Factor g(p).
-2*(p - 9)*(p + 1)
Let h be (-11 - -8) + (2534/120)/7. Let o(c) be the third derivative of 4/3*c**3 - 1/10*c**5 + h*c**6 + 0*c - 2*c**2 + 0*c**4 + 0. Factor o(b).
2*(b - 2)**2*(b + 1)
Let d(s) be the second derivative of -s**8/13440 + s**7/5040 + 13*s**4/12 + 21*s. Let t(n) be the third derivative of d(n). Suppose t(q) = 0. Calculate q.
0, 1
Let i be (10 + 189/(-20))*4. Suppose 0 = -0*u - 5*u. Factor -2/5*n + u + i*n**2.
n*(11*n - 2)/5
Let t(n) = -5*n - 2. Let v be t(-1). Suppose 16 - 20*y**2 - 2*y**5 + 305*y**v - 325*y**3 + 6*y**5 + 16*y + 4*y**4 = 0. What is y?
-2, -1, 1, 2
Suppose 160/11*n + 2/11*n**4 + 48/11*n**3 + 0 + 168/11*n**2 = 0. What is n?
-20, -2, 0
Let p(c) be the first derivative of -5/3*c**3 + 0*c - 37 + 5/2*c**2. Find v, given that p(v) = 0.
0, 1
Let j(i) be the third derivative of 3*i**7/14 + 23*i**6/8 - 26*i**5/3 + 15*i**4/2 - 11*i**2 + 2*i. Factor j(q).
5*q*(q + 9)*(3*q - 2)**2
Let w(t) = -t**2 + 10*t. Let k be w(7). Let x be (-4)/2*k/(-7). Factor 8*z**2 + 5*z - z + x*z + 0*z + 2.
2*(z + 1)*(4*z + 1)
Suppose 2*a + 4 = c, 0*c + 2*c - 15 = -3*a. Suppose -8*z = -7*z - 2. Factor -4 + c*k - 4*k + 10*k - 5*k**z.
-(k - 2)*(5*k - 2)
Let y(v) be the first derivative of 4/15*v**3 + 196/5*v + 28/5*v**2 + 39. Factor y(s).
4*(s + 7)**2/5
Let j(l) be the first derivative of -l**4/18 - 62*l**3/9 - 961*l**2/3 - 59582*l/9 + 177. Factor j(v).
-2