7. Let g(d) = -20*d**3 - 112*d**2 + 42*d - 6. Let h(u) = i*f(u) + 7*g(u). Factor h(w).
-4*w*(w + 6)*(5*w - 2)
Let z(o) = -2*o + 6. Let d = -78 + 80. Let a be z(d). Factor 2*w**2 + 10*w - 3*w + 1 + 1 + w**a.
(w + 2)*(3*w + 1)
Suppose 8*r + 158 = 1502. Suppose -5*c + r = 2*c. Factor -13 + 3*x - 11 - 3*x**2 + c*x + 0*x.
-3*(x - 8)*(x - 1)
Let d(q) be the second derivative of 80/39*q**4 + 6/65*q**5 - 28/39*q**6 - 7/39*q**7 + 0*q**2 - 64/39*q**3 - 104*q + 2. Determine c, given that d(c) = 0.
-2, 0, 4/7
Let m = 3688/345 - 1191/115. Factor 14/3*u + 0 - m*u**2.
-u*(u - 14)/3
Let u(y) be the first derivative of 135/2*y**2 + 5/4*y**4 + 15*y**3 + 33 + 135*y. Factor u(t).
5*(t + 3)**3
Suppose -5*a + 110 = -113*o + 109*o, 23 = a - o. Factor -1/3*p**2 - 25/3*p + a.
-(p - 2)*(p + 27)/3
Solve 214/17*n**3 + 3920/17 + 2/17*n**4 + 4744/17*n + 1812/17*n**2 = 0.
-98, -5, -2
Suppose -239*k + 1534 = 547 - 447. Determine d, given that k*d**2 + 3*d**4 + 0 - 1/2*d**5 - 2*d - 13/2*d**3 = 0.
0, 1, 2
Determine d so that 1210/3 + 2/3*d**2 - 404*d = 0.
1, 605
Let k(b) be the first derivative of -b**6/12 - 9*b**5/2 - 100*b**4 - 3520*b**3/3 - 7680*b**2 - 26624*b + 1425. Determine l, given that k(l) = 0.
-13, -8
Let f be (-1 + 4)/((-2745)/366) + 54/10. Let j(a) = -a**2 + 19*a + 70. Let l be j(22). Factor -8/7*p**l + 12/7*p**3 + 0 - 8/7*p**2 + 2/7*p + 2/7*p**f.
2*p*(p - 1)**4/7
Let q(j) be the second derivative of j**4/12 - 7*j**3 - 144*j**2 - 2038*j. Solve q(d) = 0 for d.
-6, 48
Let x(y) be the first derivative of 1/16*y**4 - 11/36*y**3 - 1/6*y**2 - 46 + 0*y. Determine k so that x(k) = 0.
-1/3, 0, 4
Suppose -78*v - 35*v - 124*v + 42*v = -390. Factor -13/3*j + v + 8/3*j**2 - 1/3*j**3.
-(j - 6)*(j - 1)**2/3
Let u(z) be the third derivative of -z**6/24 - 92*z**5/3 - 3665*z**4/24 - 305*z**3 - 3925*z**2. Factor u(l).
-5*(l + 1)**2*(l + 366)
Let s(t) be the third derivative of t**8/30240 + t**7/756 - t**5/15 - t**4/24 + 145*t**2. Let a(r) be the third derivative of s(r). Factor a(q).
2*q*(q + 10)/3
Let x(c) be the third derivative of 1/150*c**6 - 8/15*c**4 + 2*c**2 - 4/75*c**5 + 128/15*c**3 + 6*c + 0. Find r such that x(r) = 0.
-4, 4
Let z(d) be the third derivative of d**7/630 - d**6/120 - d**5/180 + d**4/24 - 1292*d**2. Factor z(k).
k*(k - 3)*(k - 1)*(k + 1)/3
Let w be -7 + 4 + 2 + (-6 - -3) + 4. Let p(a) be the first derivative of 32 + w*a - 1/3*a**3 - 3/2*a**2. Solve p(r) = 0 for r.
-3, 0
Let v be (((-10)/(-3))/((-472)/2832))/(-1*11). Factor 0 - v*l + 4/11*l**3 + 38/11*l**2.
2*l*(l + 10)*(2*l - 1)/11
Let y(w) be the first derivative of w**3/6 - w**2/4 - 66*w - 799. Suppose y(l) = 0. Calculate l.
-11, 12
Find i such that -490*i**3 - 340*i + 1668*i**2 - i**5 - 980*i - 58*i + 70*i**4 + 154*i - 23*i**4 = 0.
0, 1, 6, 34
Let s(p) be the third derivative of -p**7/735 + 51*p**6/140 - 76*p**5/105 - 17*p**2 - 4*p. Solve s(x) = 0.
0, 1, 152
Factor -405/4*n - 3/4*n**3 - 207/2*n**2 + 411/2.
-3*(n - 1)*(n + 2)*(n + 137)/4
Let h(c) be the third derivative of c**8/84 + c**7/21 - 5*c**6/12 + c**5/6 + 23*c**4/12 - 10*c**3/3 + 7*c**2 - 22. Suppose h(t) = 0. What is t?
-5, -1, 1/2, 1, 2
Let b(o) = -3226*o + 145173. Let m be b(45). What is i in 2/9*i**4 + 8*i**2 + 8/3*i**m + 0 + 64/9*i = 0?
-8, -2, 0
Let b(p) be the third derivative of -p**8/2184 - 43*p**7/1365 - 53*p**6/260 - 3*p**5/10 - p**2 - 512. Suppose b(o) = 0. What is o?
-39, -3, -1, 0
Factor 76/11*m + 82/11*m**2 + 2/11*m**3 - 160/11.
2*(m - 1)*(m + 2)*(m + 40)/11
Let i = 76534 + -76531. Factor -1587/4*m + 0 - 3/4*m**i + 69/2*m**2.
-3*m*(m - 23)**2/4
Let o(z) be the second derivative of -z**4/42 + 407*z**3/21 - 58*z**2 + 1745*z. Let o(p) = 0. What is p?
1, 406
Solve -2/5*f**3 + 0 + 6/5*f**2 + 836/5*f = 0 for f.
-19, 0, 22
Let f(p) be the third derivative of -p**2 - 972*p**3 - 279/2*p**4 + 0*p + 53/30*p**6 + 2/105*p**7 + 673/15*p**5 + 164. Determine u, given that f(u) = 0.
-27, -1, 2
Let c be (-5)/(-45)*(10 - 0)*3. Let w(y) be the first derivative of -4*y**2 + 3/2*y**4 - c*y**3 + 8*y + 5. Solve w(a) = 0 for a.
-1, 2/3, 2
Let x(o) be the third derivative of o**10/3360 + o**9/5040 - o**4/24 + o**3/6 + 6*o**2. Let v(g) be the second derivative of x(g). Factor v(j).
3*j**4*(3*j + 1)
Let w(f) be the third derivative of f**4/12 - 16*f**3/3 - 9*f**2. Let h be w(18). Suppose -6*i - h*i + 0*i + 6*i + 2*i**2 = 0. Calculate i.
0, 2
Let q = 734 - 423. Let g = q + -309. Determine v so that 0*v + 18/7 - 2/7*v**g = 0.
-3, 3
Factor 130 - 5*b + 114*b**2 + 130*b**2 - 384*b**2 + 110*b**2.
-5*(b - 2)*(6*b + 13)
Let q(y) = y**2 - 17*y + 68. Let d be q(6). Factor 308*u**2 - 3*u + u - 322*u**d.
-2*u*(7*u + 1)
Suppose -c + 151 = -4*x - 4*c, -75 = 2*x + c. Let d = x + 40. Factor 2*v - 7*v**4 + 3*v**4 - 8*v**d + 2*v**5 + 4*v**2 + 7*v - 3*v.
2*v*(v - 3)*(v - 1)*(v + 1)**2
Let f be 74/185 + 3173/10*2. Suppose 32*p**5 + 42*p**5 - 81*p**5 + 288 - f*p**3 + 2042*p**2 - 464*p - 1072*p - 152*p**4 = 0. Calculate p.
-12, 2/7, 1
Let m = 8957 - 8952. Let w(f) be the first derivative of 3 + 3/2*f**2 + 3/5*f**m + 9/4*f**4 + 0*f + 3*f**3. Factor w(l).
3*l*(l + 1)**3
Let b(m) be the first derivative of m**5/35 - 9*m**4/28 - 190*m**3/21 + 474. Find d, given that b(d) = 0.
-10, 0, 19
Let n(t) be the second derivative of t**5/80 - 53*t**4/48 - 55*t**3/12 - 5782*t + 2. Solve n(x) = 0 for x.
-2, 0, 55
Let q = -131 - -144. Suppose -14 = -q*t + 12. Suppose -k**3 - 20/7*k - 8/7 + 26/7*k**t = 0. What is k?
-2/7, 2
Let w(s) = -10*s**2 + 126*s - 131. Let f(x) = -14*x**2 + 124*x - 130. Let n(z) = 3*f(z) - 4*w(z). Factor n(k).
-2*(k - 1)*(k + 67)
Let r be (-16 - (-13161)/820)/((-2)/(-16)). Let j(w) be the second derivative of 0*w**2 + 5/3*w**4 - 4*w**3 + 0 - 2/15*w**6 + r*w**5 - 14*w. Solve j(q) = 0.
-2, 0, 1, 3
Factor -2/5*m - 44 + 2/5*m**2.
2*(m - 11)*(m + 10)/5
Let h(w) be the second derivative of -w**6/30 + 7*w**5/15 - 4*w**4/3 - 32*w**3/3 - 5*w**2 + 45*w. Let x(z) be the first derivative of h(z). Factor x(f).
-4*(f - 4)**2*(f + 1)
Let k(b) = -2*b**3 - 36*b**2 - 62*b - 26. Let s(z) = -z**3 - 36*z**2 - 63*z - 25. Let w = -225 + 228. Let u(d) = w*k(d) - 2*s(d). Factor u(o).
-4*(o + 1)**2*(o + 7)
Let m(k) be the first derivative of -24/11*k**2 + 0*k - 50/33*k**3 - 1/22*k**4 - 125. Let m(w) = 0. Calculate w.
-24, -1, 0
Let z(i) be the first derivative of 361*i + 19*i**2 - 77 + 1/3*i**3. Factor z(n).
(n + 19)**2
Let w(n) = 190*n - 37. Let x be w(17). What is k in -216 - 894*k - 3071 + 5*k**3 + 7734*k - x - 365*k**2 = 0?
1, 36
Suppose -8636*l = -8675*l - 30 - 19 + 166. Determine x, given that 108 + 3/4*x**5 + 126*x + 3/4*x**2 - 75/4*x**l - 3/4*x**4 = 0.
-3, -1, 4
Let j = -577 + 579. Let d = 0 - -4. Factor -12*n**3 - 41*n - 2*n**j - 2*n**2 + 49*n + 4*n**d + 4*n**5.
4*n*(n - 1)**2*(n + 1)*(n + 2)
Let g = -194869 - -976373/5. Factor -17576/5 - 78/5*s**2 - g*s - 1/5*s**3.
-(s + 26)**3/5
Let d(u) be the third derivative of 62/21*u**3 + 0*u - 2 - 1/210*u**5 + 20*u**2 - 29/84*u**4. Let d(t) = 0. What is t?
-31, 2
Let 5997 + 76*m**2 + 5974 + 2*m**3 + 146*m + 5967 - 17866 = 0. Calculate m.
-36, -1
Let r = -38880/7 - -5556. Find w such that 4/7*w**4 + 0*w + r*w**3 + 0 + 8/7*w**2 = 0.
-2, -1, 0
Let b be (-3)/(-6) - 14/(-4). Suppose 0 = 39*f - 358 + 46. Suppose -f*d**4 + 12*d**3 - 2*d**4 + 12*d**4 - 6*d**b = 0. What is d?
0, 3
Let p(z) be the second derivative of -z**7/1890 + 7*z**6/540 - 2*z**5/15 - 29*z**4/3 + 11*z. Let i(m) be the third derivative of p(m). Factor i(s).
-4*(s - 4)*(s - 3)/3
Let p(b) be the first derivative of -b**6/2 - 9*b**5/10 - b**4/4 + 120*b + 268. Let k(o) be the first derivative of p(o). Solve k(h) = 0.
-1, -1/5, 0
Let s(c) = c**3 - 7*c**2 + 8*c + 2. Let w(q) = -3*q**3 + 13*q**2 - 15*q - 5. Suppose 9*t = -2*t + 55. Let k(z) = t*s(z) + 2*w(z). Solve k(g) = 0 for g.
-10, 0, 1
Suppose -45*k**4 - 61*k**3 + 120 + 12*k**5 - 21*k**5 + 14*k**5 + 157*k - 75*k**2 + 13*k - 114*k**3 = 0. What is k?
-2, -1, 1, 12
Let y be (192/(-19) + 10)*912/(-64). Let -y - 1/6*f**2 - f = 0. What is f?
-3
Let z(x) be the first derivative of 0*x + 66 + 7*x**3 - 3/5*x**5 + 9*x**2 + 0*x**4. Factor z(p).
-3*p*(p - 3)*(p + 1)*(p + 2)
Let -3/4*j**2 + 3/8*j**5 + 3 - 21/8*j**3 + 9/2*j + 0*j**4 = 0. Calculate j.
-2, -1, 2
Let q(j) be the second derivative of j**4/72 + 43*j**3/18 + 82*j**2/3 - 1265*j. Factor q(n).
(n +