- 7. Factor a(z).
-3*z**2*(z - 1)**2*(z + 1)/4
Let l(a) be the third derivative of a**7/28 + 13*a**6/80 + a**5/10 - a**4/4 + 50*a**2. Determine h, given that l(h) = 0.
-2, -1, 0, 2/5
Let w(j) be the first derivative of j**4/24 + j**3/2 + 9*j**2/4 + 7*j - 3. Let i(t) be the first derivative of w(t). Factor i(o).
(o + 3)**2/2
Suppose -47 + 97 = 10*y. Factor 0*p**2 + 2/7*p**y + 0*p - 2/7*p**4 + 0*p**3 + 0.
2*p**4*(p - 1)/7
Let b = -8733987/634 - -13776. Let z = b - -8565/1268. Factor -z*x**4 + 0*x**3 + 2*x + 1/4 + 9/2*x**2.
-(x - 1)*(3*x + 1)**3/4
Let f = -145 + 1306/9. Let u(j) be the second derivative of 0 + 1/15*j**5 - 1/63*j**7 + j - f*j**3 + 0*j**4 + 0*j**6 + 0*j**2. Solve u(o) = 0.
-1, 0, 1
Let u(x) be the first derivative of 0*x**2 + 3/40*x**5 + 0*x**3 + 3 + x + 1/8*x**4. Let k(a) be the first derivative of u(a). What is w in k(w) = 0?
-1, 0
Let a(w) be the first derivative of 8*w**3/15 + 3*w**2/5 - 2*w/5 - 4. Let a(l) = 0. Calculate l.
-1, 1/4
Let d(j) = -2*j - 6. Let k be d(-4). Let t(q) be the second derivative of 0 + 0*q**4 + 0*q**3 - 1/105*q**6 - k*q - 1/147*q**7 + 0*q**5 + 0*q**2. Factor t(b).
-2*b**4*(b + 1)/7
Let d be (8/(-12))/((-5)/10). Let b(h) be the second derivative of d*h**2 - 4/9*h**3 + 0 - h + 1/18*h**4. Determine m, given that b(m) = 0.
2
Find a such that 2/3 - 2/3*a**2 + 0*a = 0.
-1, 1
Find q such that 2*q**2 + 5*q - 3*q + 6 - q + 7*q = 0.
-3, -1
Let q(p) = 105*p**3 - 295*p**2 + 120*p + 50. Let j(f) = 35*f**3 - 98*f**2 + 40*f + 17. Let w(k) = 10*j(k) - 3*q(k). Determine o so that w(o) = 0.
-2/7, 1, 2
Let t(a) be the second derivative of a**5/5 + a**4/2 + a**3/3 + 18*a. Determine z so that t(z) = 0.
-1, -1/2, 0
Let i = -52 - -417/8. Let t(f) be the first derivative of -1/4*f**2 - 1/3*f**3 + 1 + 0*f - i*f**4. Suppose t(a) = 0. Calculate a.
-1, 0
Let i be -3 - (-12)/((-4)/(-2)). Solve 2*t**2 + 5*t**3 - 6*t**3 - i*t**2 = 0.
-1, 0
Suppose 6*x - x - 30 = 0. Let q be 26/8 + 2/(-8). Factor x*t**q - 2*t**4 - 4*t - 2*t + 12*t**4 - 14*t**2 + 4.
2*(t - 1)*(t + 1)**2*(5*t - 2)
Let r(c) = -c**3 + 10*c**2 - 10*c + 12. Let m be r(9). Determine q so that -2*q**2 - 2 + 4*q + m*q**2 - 3*q**2 = 0.
1
Let r(p) = 5*p**4 + 9*p**3 + 8*p**2 - 13. Let h(w) = w**4 + 2*w**3 + 2*w**2 - 3. Let k = -13 - -17. Let v(n) = k*r(n) - 18*h(n). Factor v(f).
2*(f - 1)**2*(f + 1)**2
Factor -2 + 0*p**2 - p + 7*p - 2 - 2*p**2.
-2*(p - 2)*(p - 1)
Let b(d) be the first derivative of d**4 - 20*d**3/3 + 14*d**2 - 12*d + 30. Let b(j) = 0. Calculate j.
1, 3
Solve 0 - 16/7*p - 20/7*p**2 + 4/7*p**5 + 12/7*p**3 + 20/7*p**4 = 0.
-4, -1, 0, 1
Suppose -42 = -7*a - 7*a. Factor 16/7*b - 8/7 - 2/7*b**2 - 6/7*b**a.
-2*(b - 1)*(b + 2)*(3*b - 2)/7
Let f be 2*-1 - ((-702)/24)/13. Let y(h) be the first derivative of 1/5*h**5 - 1/4*h**4 + 1/2*h**2 - 1/4*h**3 - f*h + 2. Factor y(b).
(b - 1)*(b + 1)*(2*b - 1)**2/4
Factor -4/3*h**2 - 10/3*h**3 + 0 - h**4 + 8/3*h.
-h*(h + 2)**2*(3*h - 2)/3
Let i = 11 + -8. Determine k so that 20 + 7*k - 3*k**2 - 3*k**4 - 18 + k**4 - k**i + 9*k**2 = 0.
-1, -1/2, 2
Let q(z) = -6*z**2 - z - 15. Let x = -23 - -12. Let k(l) = -3*l**2 - l - 8. Let p(c) = x*k(c) + 6*q(c). Suppose p(u) = 0. What is u?
2/3, 1
Suppose b + k = 6, 3*b = 2*b - 2*k + 10. Suppose -2*i = 3*i - 110. Solve -50*z**4 + 10*z**3 - 57*z**3 - 13*z**3 - 8 + i*z**b + 24*z = 0 for z.
-1, 2/5
Let z be 28/196 - (0 + -1). Find x, given that 0*x - 8/7*x**3 + 0 - z*x**4 - 2/7*x**2 = 0.
-1/2, 0
Factor -16*y**2 - 21*y**4 + 19*y**3 + 5*y**5 + 5*y**3 + 5*y**4 + 4*y - y**5.
4*y*(y - 1)**4
Factor -6 + 90*v + v**2 + v**2 - 94*v.
2*(v - 3)*(v + 1)
Let i = 6 + -1. Factor -4 + i*p - p**4 - 3*p + 3*p**2 - 2*p**3 + 2*p + 0*p.
-(p - 1)**2*(p + 2)**2
Let b(w) = w**2 - 17*w + 18. Let i be b(1). Factor -2/7*k**i + 4/7*k + 6/7.
-2*(k - 3)*(k + 1)/7
Let b be (-7)/(-3) - (-5)/(-15). Factor 0*h**b + 3*h**3 + 2*h - 2*h**2 - 4*h**2 + h**3.
2*h*(h - 1)*(2*h - 1)
Let m be ((-12)/(-2))/((-15)/10). Let n = m - -7. Factor 2*q**3 + 4*q**3 - 2*q + q**5 + n*q - 4*q**2 + 0*q - 4*q**4.
q*(q - 1)**4
Suppose -2*i - 5*u - 11 = 0, 0*u - 5*u = 4*i + 7. Find l, given that -3/2*l**3 + 0 + l**i + 1/2*l**4 + 0*l = 0.
0, 1, 2
Let s(m) be the second derivative of -m**8/120 - 3*m**7/140 - m**6/90 + m**3/6 - 2*m. Let x(h) be the second derivative of s(h). Solve x(d) = 0.
-1, -2/7, 0
Let w(m) be the second derivative of m**7/6300 - m**5/300 - m**4/6 + 5*m. Let v(p) be the third derivative of w(p). Factor v(f).
2*(f - 1)*(f + 1)/5
Suppose -4*h + 12 + 3 = 5*o, -2*o = 2. Let i(w) be the second derivative of w + 1/30*w**h + 1/6*w**4 + 1/3*w**3 + 1/3*w**2 + 0. Factor i(z).
2*(z + 1)**3/3
Let g = 32/7 + -185/42. Let n(x) be the second derivative of 0 - 2*x**2 + 3*x - 1/3*x**3 + g*x**4. Suppose n(t) = 0. What is t?
-1, 2
Suppose 5 = -4*p + 1. Let x = p + 5. Find t such that t**3 + 0*t**x - t - t**2 + 0*t**4 + t**4 = 0.
-1, 0, 1
Suppose f + r = 6*r, 0 = r + 1. Let b = f - -9. Solve -6*j**3 + 0*j**2 - 6*j**b - 3*j**5 + j**5 - 2*j**2 = 0 for j.
-1, 0
Let l(p) = 19*p + 440. Let i be l(-23). Find v such that 3/2*v**i + 0*v - 1/2*v**2 + 0 - 3/2*v**4 + 1/2*v**5 = 0.
0, 1
Suppose 2*k - 16*q - 13 = -13*q, 5*k = 5*q + 25. Factor 0 + 0*u + 2/13*u**3 + 0*u**k + 2/13*u**5 + 4/13*u**4.
2*u**3*(u + 1)**2/13
Let q = -1/297 - -601/2079. Factor 1/7*s**2 + q*s + 0.
s*(s + 2)/7
Let l(t) be the first derivative of -t**8/8400 + t**6/1800 - t**3 + 4. Let d(s) be the third derivative of l(s). Solve d(a) = 0.
-1, 0, 1
Let j(t) be the third derivative of -t**5/60 + t**4/24 + t**3/3 - 2*t**2 - 15*t. What is k in j(k) = 0?
-1, 2
Let m be -6*(-3)/(-1 - -4). Let g be (2 - m) + (-68)/(-16). Factor 0*r**2 - 1/4*r + g*r**3 + 0.
r*(r - 1)*(r + 1)/4
Let z(s) = 33*s - 3. Let w be z(3). Let i be 4 + 9/((-243)/w). Let 0 + 2/9*y**4 - i*y**3 + 2/9*y**2 + 0*y = 0. Calculate y.
0, 1
Let q(x) be the second derivative of x**5/130 - 3*x**4/26 + 9*x**3/13 - 27*x**2/13 - 2*x. Solve q(d) = 0 for d.
3
Let t(k) be the third derivative of -1/120*k**6 - 1/6*k**3 + 0 - 1/20*k**5 + 0*k - k**2 - 1/8*k**4. Factor t(d).
-(d + 1)**3
Let j be (36/(-8) + 4)*-12. Suppose 0 = -3*y + j. Let -3/4*s**y + 3/4*s + 3/4 - 3/4*s**3 = 0. Calculate s.
-1, 1
Suppose 0 = 2*n + 9 - 13. Let b be (-5)/(-10)*n/2. Find d such that b*d**2 + 9/2 - 3*d = 0.
3
Let r = 467 + -467. Find i such that i**2 + r + 3/2*i**3 + 1/2*i**4 + 0*i = 0.
-2, -1, 0
Suppose -2*m**2 - 22*m + 13*m + 11*m = 0. What is m?
0, 1
Let i(k) be the first derivative of 2/5*k**5 + 162*k + 36*k**3 - 5 - 108*k**2 - 6*k**4. Let i(b) = 0. What is b?
3
Let v = -369 - -1477/4. Factor 1/4*g**2 - v*g**3 + 1/2*g + 0.
-g*(g - 2)*(g + 1)/4
Find u, given that 1/10*u - 1/10*u**2 + 0 = 0.
0, 1
Suppose 18*j + 3/2*j**2 + 54 = 0. Calculate j.
-6
Let t(l) be the first derivative of -l**6/6 - 3*l**5/5 + l**4/4 + 7*l**3/3 - 4*l - 17. Factor t(x).
-(x - 1)**2*(x + 1)*(x + 2)**2
Let a(v) be the second derivative of -5*v**4/36 + 10*v**3/9 + 25*v**2/6 + 2*v. Factor a(d).
-5*(d - 5)*(d + 1)/3
Let f(v) be the first derivative of 2*v**3/9 - v**2 + 4*v/3 - 2. Solve f(z) = 0.
1, 2
Let l(f) = 3*f**4 + 11*f**3 - 11*f**2 + 9*f - 4. Let p(g) = 7*g**4 + 23*g**3 - 21*g**2 + 18*g - 9. Let k(a) = 9*l(a) - 4*p(a). Factor k(r).
-r*(r - 3)**2*(r - 1)
Let h(i) be the first derivative of -i**5/90 + i**4/27 + i**3/27 - 2*i**2/9 - 3*i - 1. Let d(v) be the first derivative of h(v). Factor d(j).
-2*(j - 2)*(j - 1)*(j + 1)/9
Let s(u) = -u**3 - 17*u**2 + 18*u - 2. Let p be s(-18). Let v be 0 - p - (-84)/(-49). Factor 4/7*c + 2/7 + v*c**2.
2*(c + 1)**2/7
Let n be ((-3)/10)/((-24)/20). Let a(u) be the second derivative of 3/10*u**5 + 1/6*u**6 + 0 + n*u**4 + 1/12*u**3 + 0*u**2 + 2*u + 1/28*u**7. Factor a(q).
q*(q + 1)**3*(3*q + 1)/2
Suppose -6 = -3*z, -3*r + 22 + 14 = 3*z. Let x be (-4)/r + (-2988)/(-120). What is c in -21/2*c**2 - 2 - 12*c + x*c**3 = 0?
-2/7, 1
Suppose -5*u + 25 = 0, -6*m + 17 = -2*m + u. Let v = 119 - 119. Factor -1/6*c**m + v*c**2 - 1/3 + 1/2*c.
-(c - 1)**2*(c + 2)/6
Let r = 2 + 3. Suppose -r*v = -3*a + 5, a = -4*a + 25. Suppose 0*u**2 + 2 - v*u**2 + 0 = 0. What is u?
-1, 1
Let c = 6 - 7. Let v be (-5)/c + (-4)/2. Find n such that n - 5*n**4 - n**v + 5*n**4 + 0*n**4 - n**4 + n**2 = 0.
-1, 0, 1
Let h(n) = -2*n**2 + 5*n. Let c = 8 + -7. Let l be (2 - c)/2*-10. Let i(o) = -3*o**2 + 8*o. Let k(a