*a. Let w(g) = g**4 + g**3 - g**2 + g. Let t(y) = -l(y) - 11*w(y). Let t(x) = 0. What is x?
-3/55, 0, 1/4, 5
Let q(i) = 17*i - 253. Let j be q(15). Factor -1198*z + 2*z**2 + 4*z**j + 1122*z - 2*z**2.
4*z*(z - 19)
Let f(b) = -b**2 + 8*b + 22. Let o be f(10). Let z(j) be the second derivative of -10/9*j**3 + 0 + 25/3*j**o - 13*j + 1/18*j**4. Find h such that z(h) = 0.
5
Let m(f) be the first derivative of -14/9*f**3 + 1/6*f**4 + 36 + 0*f + 0*f**2. What is o in m(o) = 0?
0, 7
Let -2075*y**2 + 27*y**3 + 702*y**2 + 569*y**2 - 180*y = 0. What is y?
-2/9, 0, 30
Let m(k) be the second derivative of 0*k**2 + k + 2 - 1/90*k**5 + 0*k**3 + 7/54*k**4. Determine l so that m(l) = 0.
0, 7
Determine g so that 0 - 2/11*g**2 + 108/11*g = 0.
0, 54
Let y be -16*-9*16/1728. Factor -4/3 - 4/3*p + 1/3*p**4 + y*p**3 + p**2.
(p - 1)*(p + 1)*(p + 2)**2/3
Let y = 20 + -20. Suppose -j + 3*j = 4*a + 32, a + 4 = y. Factor -13*q - j + 2*q + 5 - 7*q**2 - 1.
-(q + 1)*(7*q + 4)
Suppose -5*s + 3*z = -59, -4*z - 32 = 40*s - 42*s. Let i(v) be the third derivative of 0*v + s*v**2 + 1/2*v**3 - 1/80*v**5 - 3/32*v**4 + 0. Factor i(y).
-3*(y - 1)*(y + 4)/4
Let f(i) be the first derivative of -128*i**3/3 + 74*i**2 - 20*i + 2552. Factor f(z).
-4*(z - 1)*(32*z - 5)
Suppose 2*x - 11*d = -6*d + 83, -4*x + 121 = -d. Solve -58*b + 47*b + x*b + 3*b**2 + 48*b = 0.
-22, 0
Let l(m) be the first derivative of 4/9*m**3 + 27*m - 1 + 7/6*m**2 + 1/36*m**4. Let i(k) be the first derivative of l(k). Factor i(u).
(u + 1)*(u + 7)/3
Find y, given that 1131/4*y**2 - 9/4*y**4 - 105 - 213*y - 141/2*y**3 = 0.
-35, -1/3, 2
Factor -1/3*d**4 + 0 - 46/3*d**3 - 160*d**2 + 384*d.
-d*(d - 2)*(d + 24)**2/3
Let t(o) be the first derivative of -3*o**5/14 - o**4/84 + 23*o**3/42 - 3*o**2/7 - 90*o + 183. Let x(v) be the first derivative of t(v). Solve x(m) = 0.
-1, 3/10, 2/3
Let r(f) be the first derivative of 103 + 0*f + 1/2*f**4 + 0*f**3 - 4/5*f**5 + 0*f**2 + 1/3*f**6. Factor r(y).
2*y**3*(y - 1)**2
Suppose 3154*h - 9*h**3 + 55*h**3 + 2920 + 0*h**4 + h**4 + 717*h**2 + 412 + 850*h = 0. Calculate h.
-17, -14, -1
Let v(w) be the first derivative of w**4/32 - 15*w**3/4 + 2193*w**2/16 - 1849*w/2 - 760. Factor v(o).
(o - 43)**2*(o - 4)/8
Let v(a) = 31057*a + 372686. Let m be v(-12). Factor 2/11*d**m + 2/11 - 4/11*d.
2*(d - 1)**2/11
Let k(s) be the third derivative of s**9/10080 + s**8/4480 - s**7/280 - 41*s**4/6 - 58*s**2 + s. Let x(a) be the second derivative of k(a). Factor x(h).
3*h**2*(h - 2)*(h + 3)/2
Let a(i) = -i**4 - i**3 - i**2 + 3. Let x = 48 - -1. Let l = 46 - x. Let n(u) = 2*u**4 + 4*u**3 + 2*u**2 - 8. Let d(b) = l*n(b) - 8*a(b). Factor d(s).
2*s**2*(s - 1)**2
Suppose -6 = -39*g + 37*g. Let m(d) = -d**2 + 88*d - 1031. Let w be m(14). Find b, given that -3/2*b**w + b**2 + 0 + 0*b - b**4 + 3/2*b**g = 0.
-1, -2/3, 0, 1
Let a = 25669 - 25345. Let o = 127/18 - 50/9. Find u such that a - o*u**3 + 27*u**2 - 162*u = 0.
6
Determine c so that -21/2*c**3 + 1/2*c**5 + 54*c + 0 + 99/2*c**2 - 11/2*c**4 = 0.
-3, -1, 0, 3, 12
Suppose -3*r - 3*b = -12, 174*r = 175*r - 4*b + 1. Factor -162*u + 18*u**2 - 2/3*u**r + 486.
-2*(u - 9)**3/3
Factor -9216*g**2 - 442368 + 128/3*g**4 - 119808*g + 4/3*g**5 + 128*g**3.
4*(g - 16)*(g + 12)**4/3
Let i(l) be the first derivative of l**5/10 - l**4/6 - 16*l**3/3 - 20*l**2 - 14*l - 19. Let v(q) be the first derivative of i(q). Suppose v(p) = 0. What is p?
-2, 5
Suppose 3911 = 25*g - 24*g. Solve -7825*k + 3910*k - 8*k**2 + g*k = 0.
-1/2, 0
Let c(l) = -9*l**2 + 66*l - 252. Let z(d) = -17*d**2 + 131*d - 504. Let f(n) = 11*c(n) - 6*z(n). Suppose f(j) = 0. Calculate j.
6, 14
Let s be 3 - (-53 + (-8)/(-4)). Let d be 18/4*24/s. Find x such that -3*x - 956*x**2 + 960*x**d - x + 3*x**3 = 0.
-2, 0, 2/3
Let b be (-1*(-12)/(-8))/((-2)/12) - -4. Let t(l) be the third derivative of 0*l - b*l**2 + 0 + 0*l**4 + 0*l**3 + 1/24*l**6 + 1/3*l**5. Factor t(w).
5*w**2*(w + 4)
Let c be ((-520)/39)/(25/(-90)). Let -c*m + 2*m**3 - 5*m**3 - 39*m**2 + 15*m**2 = 0. What is m?
-4, 0
Let b(k) be the first derivative of -k**6/11 - 1982*k**5/55 - 321*k**4/22 + 1986*k**3/11 + 2972*k**2/11 + 120*k - 7604. Find j such that b(j) = 0.
-330, -1, -1/3, 2
Suppose j - m = 3*j - 4, -2*j + 3*m + 4 = 0. Find r such that 178 + 122 + j*r**2 - 52*r + 38 = 0.
13
Let a(y) = 10*y**2 + 68*y + 644. Let k = -137 - -133. Let g(v) = 8*v**2 + 69*v + 645. Let z(n) = k*g(n) + 3*a(n). Factor z(i).
-2*(i + 18)**2
Let 14400 - 4557*m**2 + m**5 - 6239*m**2 + 323*m + 157*m + 2188*m**3 + 117*m**4 + 1052*m**3 = 0. Calculate m.
-60, -1, 2
Let 0 - 25541*x**2 + 3*x**4 + 0 - 528*x**3 + 25010*x**2 = 0. Calculate x.
-1, 0, 177
Let b(o) = -o**2 + 9*o + 20. Let w be b(12). Let y be 4/(-14) - w/7. Factor 75*z**y + 12 + 3*z**4 - 30*z**3 - 21 + 9.
3*z**2*(z - 5)**2
Let f = -308 + 311. Suppose -s + 9 = f*a, -6*a - 4*s + 4 = -2*a. Factor -6/5 - 27/5*w**2 - 3*w**3 - 21/5*w - 3/5*w**a.
-3*(w + 1)**3*(w + 2)/5
Suppose -11*d + 63 = 2*o - 8, 5*d + 15 = 5*o. Solve -d + 1/3*s**2 + 2/3*s = 0 for s.
-5, 3
Let h be ((-3)/9 - 0)/((4 + -6)/8). Suppose 2*k + 3*u = 4, -8*k - u = -3*k - 10. Factor -16/9*p - 2/9*p**4 - h*p**3 + 0 - 8/3*p**k.
-2*p*(p + 2)**3/9
Let l = 209849/100 + -2098. Let m(u) be the second derivative of -26*u + 0 + 7/15*u**4 - 2/15*u**3 + 0*u**2 - l*u**5. Solve m(v) = 0 for v.
0, 2/7
Solve -37*z**3 - 441*z**4 - 57*z**2 + 445*z**4 - 18*z**3 - 45*z**3 - 159*z**2 = 0 for z.
-2, 0, 27
Let q = -801 - -584. Let k = 219 + q. Factor 1/3*o**k + 8/3*o + 7/3.
(o + 1)*(o + 7)/3
Suppose -z = 4*o - 14, -4*o - 24 = 4*z - 44. Let -90*i + 47*i + 30 + 56*i - i**z = 0. What is i?
-2, 15
Let s(h) be the third derivative of 0*h + 1/30*h**6 + 0*h**3 + 0 - 1/15*h**5 - 1/3*h**4 - 119*h**2. Factor s(w).
4*w*(w - 2)*(w + 1)
Let c(n) = 35*n**2 + 54*n - 43. Suppose 35 - 46 = -k. Let b(v) = 12*v**2 + 18*v - 14. Let y(o) = k*b(o) - 4*c(o). Factor y(a).
-2*(a + 3)*(4*a - 3)
Let y(j) = 153 + 3*j - 162 + 2*j + 7*j**2 + 3*j. Let x(m) = 2 + 0 + 4 - 5 + m**2. Let l(p) = -3*x(p) + y(p). Solve l(z) = 0.
-3, 1
Let o(z) be the second derivative of -1/3*z**4 - 1/5*z**5 + 0 - 1/21*z**7 + 247*z - z**2 + 1/5*z**6 + z**3. Factor o(x).
-2*(x - 1)**4*(x + 1)
Determine k, given that 642*k - 55 + 3*k**2 + 139 - 37 - 47 = 0.
-214, 0
Let p be (44/5)/(16/120). Let r = -64 + p. What is t in -5 - 10*t + 4*t**2 - 6*t**2 - 3*t**r = 0?
-1
Suppose 2*j + 2*v = 136, 0 = -2*v - 4 + 2. Let x = -64 + j. Factor -2*m**3 - 5*m + x*m + 20*m**4 - 23*m**3 + 10*m**2 - 5*m**5.
-5*m**2*(m - 2)*(m - 1)**2
Let o = 146813 + -734064/5. Solve -o*k**2 - 729/5 + 54/5*k = 0 for k.
27
Let w = 2214/301 - 304/43. Suppose w*i**2 + 2/7 + 4/7*i = 0. What is i?
-1
Find p, given that 0 - 116/7*p**3 + 1/7*p**4 + 0*p + 0*p**2 = 0.
0, 116
Factor 39/2*a**3 + 1/2*a**4 + 89*a**2 + 138*a + 68.
(a + 1)*(a + 2)**2*(a + 34)/2
Let q(l) = l**4 - l**3 + l**2 - 2*l - 2. Let o(d) = -9*d**4 + 39*d**3 + 30*d**2 + 24*d + 24. Let b(z) = o(z) + 12*q(z). Factor b(x).
3*x**2*(x + 2)*(x + 7)
Let y(k) be the first derivative of -2*k**3/39 + 87*k**2/13 - 6930. Factor y(f).
-2*f*(f - 87)/13
Let q be ((90 - -67) + -160)*((-1)/(-1))/(-1). Factor -q*m - 3/2*m**2 + 0.
-3*m*(m + 2)/2
Let s(a) be the second derivative of 3*a + 5/4*a**3 + 3/4*a**2 + 3/40*a**5 - 7 + 17/32*a**4. Find j such that s(j) = 0.
-2, -1/4
Let s(d) be the third derivative of d**7/70 - 162*d**6/5 + 157464*d**5/5 - 17006112*d**4 + 5509980288*d**3 + 12*d**2 - 22*d. Factor s(l).
3*(l - 324)**4
Let z(l) = -8*l**4 + 68*l**3 + 234*l**2 + 288*l - 6. Let j(m) = -14*m**4 + 134*m**3 + 469*m**2 + 576*m - 11. Let w(t) = 6*j(t) - 11*z(t). What is a in w(a) = 0?
-6, -2, 0
Let z = 2 - -140. Factor -277*f + z*f - f**3 + 4*f**2 + 147*f.
-f*(f - 6)*(f + 2)
Factor 64/9 + 10/9*a**3 + 56/9*a**2 - 184/9*a.
2*(a - 2)*(a + 8)*(5*a - 2)/9
Let s be (-2)/(-12)*(0 + 1). Let q = 176526 + -176524. Solve -1/6*b**3 + 0*b + 1/6*b**4 + 1/6*b**5 + 0 - s*b**q = 0 for b.
-1, 0, 1
Suppose -270*u**2 + 8891*u**4 + 88*u - 8893*u**4 - 574*u - 42*u**3 = 0. Calculate u.
-9, -3, 0
Let t(v) be the third derivative of -8 - v**2 + 5/3*v**4 + 1/15*v**5 + 0*v - 22/3*v**3. Find m, given that t(m) = 0.
-11, 1
Factor -1/2*l**3 - 5/2*l**2 + 5/2 + 1/2*l.
-(l - 1)*(l + 1)*(l + 5)/2
Factor -75/4*u**2 - 77/4*u - 13/2 + 1/4*u**4 - 23/4*u**3.
(u - 26)*(u + 1)**3/4
Let g(c) be